# Practical deployment of real-time railway traffic management algorithms: impact of process meta-parameters

Federico Naldini, Paola Pellegrini, Joaquín Rodriguez

► To cite this version:

Federico Naldini, Paola Pellegrini, Joaquín Rodriguez. Practical deployment of real-time railway traffic management algorithms: impact of process meta-parameters. ODS 2022, International Conference on Optimization and Decision Science, Prof. Fabio Schoen; GOL - Global Optimization Laboratory "Gerardo Poggiali" - UniFI, University of Florence, Italy; Airo - The Italian Association of Operations Research; DINFO (Dept. of Information Engineering, Università degli Studi di Firenze), Aug 2022, Firenze, Italy. pp.91. hal-04402651

HAL Id: hal-04402651

https://univ-eiffel.hal.science/hal-04402651v1

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<figure><img src="image_1.png" /></figure>

ODS 2022

INTERNATIONAL CONFERENCE ON
OPTIMIZATION AND DECISION SCIENCE

FIRENZE (ITALY) August 30th - September 2nd - 2022
ODS2022 – Book of abstracts

the ODS2022 Organizing committee

August 2022
This book contains all of the abstracts accepted for presentation at the In-
ternational Conference on Optimization and Decision Science, ODS2022, held
in Florence from August 30th to September 2nd, 2022. The conference is orga-
nized within AIRO, the Italian Operations Research Society, with the support of
DINFO (Dept. of Information Engineering, Università degli Studi di Firenze).
The conference theme is open in the fields of operations research, optimization,
problem solving and decision making, and their applications. A special focus is
on the theme "Operations Research: inclusion and equity".

The book of abstracts contains over 230 contributions, 30 of which associ-
ated to papers accepted for publication in the AIRO Springer Series volume de-
voted to the conference. The contributions are organized into 5 parallel streams
and about 35 sessions, 14 of which are invited sessions/streams. Four plenary
sessions enrich the scientific part of the conference; they are given by world-
renowned professors, and they are related to extremely topical and important
issues, namely the use of quantitative analytical methods to promote equality
and equity, in the many facets that these terms may have. Abstracts are listed
day by day, session by session.

The ODS 2022 Organizing Committee
## Acknowledgments

We sincerely thank all those who contributed to the realization of the conference, and in particular, the members in the Program Committee, those in the Organization Committee, and all of the DINFO PhD's and PostDocs, in particular, from GOL, the Global Optimization Lab, who have been invaluable in the organization of such a complex event.

The organization of ODS2022 gratefully acknowledges the Institutional support of DINFO, Dipartimento di Ingegneria dell'Informazione, Università degli Studi di Firenze and of AIRO, the Italian Association for Operations Research:

<figure><img src="image_2.png" /></figure>

UNIVERSITÀ
DEGLI STUDI
FIRENZE

**DINFO**
DIPARTIMENTO DI
INGEGNERIA
DELL'INFORMAZIONE

<figure><img src="image_3.png" /></figure>

We also acknowledge the financial contributions from:

EURO

THE ASSOCIATION OF
EUROPEAN OPERATIONAL
RESEARCH SOCIETIES

<figure><img src="image_4.png" /></figure>

FirLab

OPTIT

optimal solutions

<figure><img src="image_5.png" /></figure>

ACTOR

<figure><img src="image_6.png" /></figure>

SAPIENZA
UNIVERSITÀ DI Roma

<figure><img src="image_7.png" /></figure>

Findomestic

GRUPPO BNP PARIBAS

<figure><img src="image_8.png" /></figure>

verizon✓
connect

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

M.A.I.O.R.

A CLEVER DEVICES COMPANY

<figure><img src="image_11.png" /></figure>

## Special acknowledgment

We tried, in many cases, to rely on the professional help from social cooperatives and not-for-profit organizations. We would like to thank them here and
to inform participants that part of their registration fees went to support the activities of these organizations.

ZENZERO
catering bio equo
www.zenzero cooperativa.it

<figure><img src="image_12.png" /></figure>

Zenzero catering bio equo, for the coffee breaks

<figure><img src="image_13.png" /></figure>

Flo concept, for the ODS2022 bags and backpacks

Istituto
degli
Innocenti

<figure><img src="image_14.png" /></figure>

Istituto degli Innocenti, host for the first plenary and the welcome cocktail

<figure><img src="image_15.png" /></figure>

Viviamo In Positivo VIP Firenze OdV, for the organization of the treasure hunt in Florence

## Invited Sessions

We also acknowledge the precious contributions of the organizers of Invited Sessions:

**AMUO** Advances in Multiobjective Optimization, organized by Marianna De Santis (Sapienza, Univ. di Roma), Pierluigi Mansueto (Univ. di Firenze)

**EQVA** Equilibria, variational models and applications, organized by Mauro Passacantando (Univ. di Pisa)

**GO** Global Optimization, organized by Fabio Schoen (Univ. di Firenze)

**HCM** Health Care Management, organized by Giuliana Carello (Politecnico di Milano), Elena Tanfani (Univ. di Genova)

**KNAP** Knapsack Problems, organized by Adam Letchford (Lancaster University), Laura Galli (Univ. Pisa)

**MLO4EMD** Machine learning-based optimization for extreme metamaterials design, organized by Andrea Bacigalupo (University of Genoa), Francesca Fantoni (University of Brescia), Giorgio Gnecco (IMT Lucca)

**MUOS** Multicriteria Optimization for sustainability, organized by Marianna De Santis, Lavinia Amorosi (Sapienza, Univ. di Roma)

**NODAI** Numerical optimization for data analysis and imaging, organized by Benedetta Morini, Simone Rebegoldi (Univ. di Firenze)
**NOML** Nonlinear Optimization and Machine Learning, organized by Matteo Lapucci (Univ. di Firenze), Marco Sciandrone (Sapienza Univ di Roma)

**OML** Optimization for machine learning, organized by Cesare Molinari, Vas-silis Apidopoulos, Silvia Villa (MaLGa, DIMA, Università degli Studi di Genova)

**OPTSM** Optimization in Public Transport and Shared Mobility, organized by Andrea D'Ariano (Univ Roma Tre), Valentina Cacchiani (Univ. di Bologna)

**OUUTA** Optimization under Uncertainty: Theory and Applications, orga-nized by Francesca Maggioni (Univ. di Bergamo), Patrizia Beraldi (Univ. Calabria)

**PRPI** Path and routing problems in industry, organized by Marco Locatelli (Univ. di Parma)

**RAVIEP** Recent Advances in Variational Inequalities and Equilibrium Prob-lems, organized by Patrizia Daniele, Laura Scriminali (University Catania)

Special thanks to AIROyoung for the organization of the special session devoted to a selected group of PhD thesis presentations.

And a special thanks to Verizon Connect Italy for the support given to two female young researchers through the ODS2022/Verizon Connect prize.
OUUTA, Optimization under Uncertainty: The-
ory and Applications; Invited Session

TU 14:10 PM1 001

Nema Abu Jomaa nema7271@hotmail.com

Bar-Ilan University, Ramat-Gan 52900, Israel and The International Committee of the Red Cross (ICRC), Geneva, Switzerland
Kogan, Konstantin, Bar-Ilan University, Ramat-Gan 52900, Israel

*Optimal ordering under a low-quality substitute in case of shortage and stochastic lead time*

Delivery lead time is becoming a key factor which uncertainty sig-
nificantly affects supply chain performance. Empirical studies in differ-
ent industries show that stock-out-based substitution is a common way
to handle shortages. Notably, during the COVID-19 pandemic, the de-
mand for medical supplies intensely increased, not only because of the fast
spread of the infection but also because the related shortages of genuine
products contributed to an increase in number of substandard medical
products. In this work we consider a finite replenishment cycle in a hu-
manitarian organization where (i) a high-quality material is characterized
by a stochastic lead time, (ii) the demand during the replenishment cycle
is known but it can be affected by last minute requests. Furthermore,
in case of shortage, the high-quality material can be substituted with a
low-quality material, but the substitute impacts the demand. Specifically,
the demand increases due to the fact that the low-quality product wears
out faster than the other product. The formulation involves continuous-
time inventory depletion and associated purchase and inventory holding
costs. The goal is to order the supplies so that to minimize the total
cost of meeting the demand during the replenishment cycle. We formal-
ize the analysis with the aid of a number of scenarios characterizing the
cases when there is no need to substitute the high-quality products with
the low-quality ones; when there exists a time point such that the high-
quality products will be substituted with the low-quality products; and
when the high-quality products will be substituted twice over the time
horizon. All scenarios account for a last-minute demand. With the aid
of these scenarios, we reduce the problem to minimizing a cost function
consisting of two convex functions determined along two adjacent order
quantity intervals thereby implying not-necessarily convex optimization.

OUUTA, Optimization under Uncertainty: Theory and
Applications; Invited Session
TU 14:30 PM1 001

Demetrio Laganà demetrio.lagana@unical.it

Department of Mechanical, Energy and Management Engineering,
University of Calabria

Stoia, Sara, Department of Mechanical Energy and Management
Engineering University of Calabria; Ohlmann, Jeffrey W., Depart-
ment of Business Analytics University of Iowa Iowa City United
State

*Pickup and delivery requests through a multi-company e-commerce platform*

Delivery services have been developed within the grocery and restau-
rant domain such as for non-food items with different platforms but the
demand patterns and consumer behavior differ in the case of food and
non-food products. A single e-platform serving a wide range of local busi-
nesses could provide the volume and smooth the non-stationary demand
pattern typical of restaurant delivery. There is an opportunity for local
brick-and-mortar companies to utilize such an e-platform, particularly if
paired with a high level of customer service (professional shopper consul-
tation, favorable return policy, etc.) to support shop local initiatives and
stave off a retail apocalypse. A primary motivation for local businesses to
join an e-platform is to compete with the distribution power of companies
like Amazon [Mattioli, June 17 2021], even because the global COVID-19
pandemic has altered consumer behavior (perhaps permanently) and local
brick-and-mortar stores may need to serve as showrooms (for in-person
shopping) and/or dark stores (warehouses), with employees serving as
salespeople and/or as order-pickers. Schrotenboer et al. [2021] examine a
similar setting motivated by local delivery via bicycle. In our problem we
assume that a third-party logistics (3PL) company receives the customer
requests stochastically throughout the day and dispatches these requests
to available vehicles, using a fleet of dedicated vehicles and a fleet of
crowdsourced vehicles that arrives stochastically during the day by offer-
ing a known limited time availability. The incorporation of crowdshippers
has implications on sustainability of city logistics by reducing the number
of vehicles dedicated to deliveries. In the treatment of our problem, we
consider two aspects of the logistical design of a delivery system: cost
and service. Our formulation focuses on workforce costs as these repre-
sent a major component of operating costs. Along the service dimension,
we focus on on-time delivery with particular modeling of time-dependent
travel times. To represent the stochastic nature of the arrival of customer
requests and of the availability of crowdshippers, we model the problem
as a Markov decision process (MDP) over finite, discrete-time horizon and
the solution approach is based on an approximate dynamic programming
method.

[1] D. Mattioli. Shops join forces against amazon. The Wall Street

OUUTA, Optimization under Uncertainty: Theory and
Applications; Invited Session
Journal, June 17 2021. [2] A. H. Schrotenboer, M. A. Broek, P. Buijs, and M. W. Ulmer. Fighting the e-commerce giants: Efficient routing and effective consolidation for local delivery platforms. arXiv preprint arXiv:2108.12608, 2021.
TU 14:50 PM1 001

Daniel Faccini daniel.faccini@unibg.it

Department of Management, Information and Production Engineer-
ing University of Bergamo

Guzin, Bayraksan, The Ohio State University; Francesca Maggioni,
University of Bergamo; Ming, Yang, The Ohio State University

*Bounds for Multistage Mixed-Integer Distributionally Robust Optimization*

Multistage mixed-integer distributionally robust optimization (DRO) forms a class of extremely challenging problems since their size grows exponentially with the number of stages. One way to model the uncertainty in multistage DRO is by creating sets of conditional distributions (the so-called conditional ambiguity sets) on a finite scenario tree and requiring that such distributions remain close to nominal conditional distributions according to some measure of similarity/distance (e.g., phi-divergences or Wasserstein distance). In this talk, new bounding criteria for this class of difficult decision problems are provided through scenario grouping using the ambiguity sets associated with various commonly used phi-divergences and the Wasserstein distance. Our approach does not require any special problem structure such as linearity, convexity, stagewise independence, and so forth. Therefore, while we focus on multistage mixed-integer DRO, our bounds can be applied to a wide range of DRO problems including two-stage and multistage, with or without integer variables, convex or nonconvex, and nested or non-nested formulations. Numerical results on a multistage mixed-integer production problem show the efficiency of the proposed approach through different choices of partition strategies, ambiguity sets, and levels of robustness.
TU 15:10 PM1 001

Giovanna Miglionico gmiglionico@dimes.unical.it

Università della Calabria

Beraldi, Patrizia, Università della Calabria; Giallombardo, Giovanni,

Università della Calabria

*A Robust Optimization Approach for Designing Renewable Energy Charging Stations*

We consider strategic and operational planning decisions arising in managing plug-in electric vehicle (PEV) charging stations. At a strategic level, we face the problems of both defining the optimal configuration of the energy system of a PEV charging station and of setting the optimal retail prices for PEV-charging energy. These decisions depend on the unknown values for the productivity of the renewable resources, for the number of PEV clients and for the wholesale prices. Based on the worst possible outcome for these random variables the PEV owner would like to make the best operational decisions regarding the quantity of supplementary energy to be produced. A similar problem has been considered in [1] where a bilevel robust optimization model is first formulated and then transformed into an equivalent single-level problem to be solved by a column-and-constraint-generation algorithm. We test the PEV charging station robust optimization formulation on a series of instances drawn from the literature.

[1] Bo Zeng, Houqi Dong, Ramteen Sioshansi, Fuquiang Xu and Ming Zeng, Bilevel Robust Optimization of Electric Vehicle Charging Stations with Distributed Energy Resources. IEEE Transactions on Industry Applications, 56 (5), pp. 5836-5847 [2] Manlio Gaudioso, Giovanni Giallombardo and Giovanna Miglionico, Minimizing Piecewise-Concave Functions Over Polyhedra. MATHEMATICS OF OPERATIONS RESEARCH, 43 (2), pp. 580597.
TU 15:30 PM1 001

Daniele Manerba daniele.manerba@unibs.it

Università degli Studi di Brescia

Fotio Tiotsop, Lohic, Politecnico di Torino; Fadda, Edoardo, Politecnico di Torino; Bierlaire, Michel, Ecole Polytechnique Fédérale de Lausanne

*Stochastic Programs with extreme behaviors-focused second stages: a Deterministic Equivalent Formulation*

A closed deterministic form of a two-stage Stochastic Programming (SP) problem is obtainable when the expected optimum of the second-stage problem can be analytically calculated. However, in practice, this is almost always impossible given the complexity of the multidimensional integral of such an expected value. In this work, we consider and formally define a large class of two-stage Stochastic Programs whose second-stage expected optimum is Decomposable into a finite number of expectations of Extreme Values (tsSP-DEV). Typical applications of tsSP-DEVs can be found, e.g., in location-allocation problems under allocation costs uncertainty. In a sense, a tsSP-DEV involves characteristics both from the classical SP paradigm and from the Robust Optimization one. In fact, the tsSP-DEV optimization perspective is still focused in making here-and-now decisions by also evaluating the expected value of an uncertain problem over all the possible future situations, but assuming that such a value can be obtained as a function of extreme future behaviors.

We show that a closed-form analytical expression of the expected second-stage optimum of any tsSP-DEV can be derived by exploiting some results coming from the Extreme Value Theory [1], and thus an equivalent deterministic version of the SP problem can be obtained. This can be done under the mild hypothesis that the involved uncertain data follow a Multivariate Extreme Value (MEV) distribution. The MEV family includes many common distributions, and some of them are of practical interest since they enable a modeling of the second-stage problem uncertainty structure through well-known and widely used Discrete Choice Models (e.g., Logit, Nested Logit, Cross-Nested Logit). Finally, a tsSP-DEV special case, named two-stage Stochastic Programs embedding Discrete Choice Problems (tsSP-DCP), is further defined. In a tsSP-DCP, the second stage consists of a sequence of independent Discrete Choice Problems (DCPs), each one triggered or weighted by the value of a specific first-stage variable. In this case, the deterministic equivalent problem results to be linear and thus further properties can be derived. This allows to well-approximate many realistic uncertain MILP problems by solving their deterministic versions [2].

We validate our approach through numerical experiments on common combinatorial optimization SP problems and compare its efficiency and effectiveness with respect to scenario-based paradigms.

**OUUTA, Optimization under Uncertainty: Theory and Applications; Invited Session**
[1] D. McFadden (1978). Modelling the choice of residential location. A Karlquist et al., ed., Spatial interaction theory and residential location, 7596. North-Holland, Amsterdam. [2] E. Fadda, L. Fotio Tiotsop, D. Manerba, R. Tadei (2020). The stochastic multi-path Traveling Salesman Problem with dependent random travel costs. Transportation Science 54 (5), 1372-1387.
HCM, Health Care Management; Invited Session

TU 14:10 PM1 002

Maddalena Nonato maddalena.nonato@unife.it

DE, Università di Ferrara, Italy

Cappanera, Paola, DINFO, Università degli Studi di Firenze Italy;

Gavanelli, Marco, DE, Università degli Studi di Ferrara, Italy;

Roma, Marco, DINFO, Università degli Studi di Firenze, Italy

*The value of exploiting information in Logic-Based Benders Decomposition for chronic outpatients scheduling by Answer Set Programming*

Chronic patients living at home often need to take tests or receive treatments (health services in general) at hospital premises in a periodic way, as prescribed by well-assessed clinical pathways. In addition, due to increased life expectancy, the number of elderly patients having several Non-transmissible Chronic Diseases (NCDs) at the same time (co-morbidities) is steadily growing; these patients must follow several clinical pathways at the same time, thus making health service synchronization of paramount importance to ensure system efficiency and patients satisfaction. A further source of complexity is due to timing conflicts potentially arising between health services: for example, a treatment with a certain drug may invalidate the results of a medical examination if the two health services are done too close in time. Therefore, an appointment schedule should obey several time constraints, such as predetermined service frequencies, beside complying with patient needs. Moreover, resource availability, regarding both personnel and devices at hospital care units, is limited, thus reducing the options for booking. This criticality has been further exacerbated by the current pandemic situation in which, at hospitals, resources have been devoted mostly to patients with high intensity care needs. Inevitably, this has had negative effects on the management of chronic patients: on the one hand, many screening or monitoring activities have been delayed, and in many cases cancelled; on the other hand, many patients have preferred to avoid attending hospitals for fear of becoming infected. For these reasons, it is estimated that the service demand for chronic patients will grow significantly in the near future. This suggests managing the scheduling of the clinical pathways of enrolled patients in a centralized manner. From the patient point of view, synchronizing different services reduces the number of accesses to the hospital or even avoids potential duplications that may arise when the same health service is present in different protocols. In this work, we provide a declarative approach to this challenging problem, encoding it in Answer Set Programming (ASP). Computational results show that when all of the constraints are given in one shot, the resulting monolithic approach soon fails to provide a feasible solution as the dimension of the problem grows. In order to

HCM, Health Care Management; Invited Session
improve the scalability of the monolithic approach, we propose a decomposition of the problem inspired by Logic-Based Benders Decomposition (LBBD), a technique that extends Benders decomposition principles to other formalisms, such as Constraint Programming. According to LBBD, a master problem and a set of independent sub-problems are iteratively solved until all subproblems admit a feasible solution. Master problem and subproblems efficiently communicate and exchange information to reduce the search space. The propagation of information from one subproblem to others is of key importance in the design of an efficient system. The computational experience will thus pursue two targets: first, we will show the impact on efficiency of using decomposition instead of the monolithic approach; second, we will compare several ways of propagating information. The decomposition algorithms as well as the monolithic approach will be tested on realistic instances.

HCM, Health Care Management; Invited Session
TU 14:30 PM1 002

Christine Di Martinelly c.dimartinelly@ieseg.fr

IESEG School of Management, Univ. Lille, CNRS, UMR 9221 -
LEM - Lille Economie Management, F-59000 Lille, France

Duenas, Alejandra, ICN Business School, CEREFIGE, Nancy, France;
Glaize, Annabelle; Fagnot, Isabelle, KEDGE Business School, Tal-
ence, France

*An approach to healthcare services decision-making using fuzzy ELEC-TRE III. An outpatient chemotherapy service application.*

Each day, healthcare institutions face the challenges of maintaining high-quality care and patient satisfaction while dealing with budget restrictions and a constantly increasing patient load. Oncology hospitals share the same struggle. An outpatient chemotherapy service is a complex care system that includes a multi-step process, complex procedures and interdisciplinary caregivers. Bringing changes and improvements need to be carefully considered and accepted by all stakeholders. In such a context, we propose a decision-making approach based on business process improvement (BPI) and multi-criteria decision making to help an oncology department in their reorganization. BPI is used as a tool to structure the decision-aid process, and to identify the stakeholders, the improvement solutions and the criteria to assess them. As there is some ambiguity in the stakeholders consensus on the improvement solutions, a fuzzy-ELECTRE III method is used. An online questionnaire is given to ten stakeholders to identify the relative importance of the improvement solutions over the selected decision criteria. Their preferences are assessed and the concordance, discordance and credibility matrices are built. We have decided to add the weights of stakeholders characteristics to the decision matrix to include the differences of perspectives and experiences. A sensitivity analysis is finally performed to study the impact of a change in the methods parameters. Results provide the priorities and the least preferred options for the outpatient services.

HCM, Health Care Management; Invited Session
TU 14:50 PM1 002

Martina Doneda martina.doneda@polimi.it

Politecnico di Milano / IMATI CNR

Yalçında, Semih, Yeditepe Üniversitesi; Lanzarone, Ettore, Università degli Studi di Bergamo

*A framework for at-home blood collection considering donor preferences*

In all health care systems, Blood Donation Supply Chains (BDSCs) play a fundamental role in several sectors, including hematology, trauma management and surgery. According to recent statistics (2019), the production of blood units for transfusion still falls short of satisfying the ever-increasing demand. This is due to a combination of factors, the main one being that blood can only be produced from human donors. Meeting demand has always been the main objective of the system, and several decision tools have been developed during the years to help reach it. However, during the COVID-19 pandemic, new and unexpected issues emerged. As blood drives were cancelled because of lockdowns and donors feared going to donations centers, shortages of units have increased dramatically. This is due to the lack of a direct channel between donors and blood banks. According to the Italian National Blood Center, in April 2020 the production of red blood cells was 36.4% less than the one of the previous year. At the same time, healthcare services are now moving towards a more decentralized paradigm. Considering these factors, in this work we consider an integrated framework to collect blood directly at the donors homes. To do so, we link the Blood Donation Appointment Scheduling (BDAS) and the Multi-Trip Vehicle Routing Problem with Time Windows (MTVRP-TW) problems in an organic way. Our approach consists of three planning phases: in the first one, we create possible time slots for donor appointments, with the aim of balancing the production of the different blood types, to ensure better manageable stock levels. Then, we turn these slots into real appointments, according to the received booking requests. Here, we compromise between the preferences expressed by calling donors and the requirements of the center, including scheduling and routing constraints. Lastly, a fleet of bloodmobiles is dispatched to perform the collection. The second and third phases are linked in such a way that the outcome of the former serves the purpose of helping the computation of the latter, providing an improved starting point. The proposed integrated framework is then tested and validated against data obtained from the most prominent Italian blood provider. We also prove the cost-effectiveness of the implementation of the proposed solution.

HCM, Health Care Management; Invited Session
TU 15:10 PM1 002

Giuliana Carello giuliana.carello@polimi.it

Politecnico di Milano

Passacantando, Mauro, Università di Pisa; Tanfani, Elena, Università di Genova

*Patient Appointment Scheduling for Chemotherapy treatments*

The number of patients affected by cancer is expected to increase in the next years and, thus, the need for chemotherapy treatments will increase accordingly. We assume that chemotherapy treatments are delivered in an outpatient setting. Further we consider a cancer centre shared by different specialties where patients affected by different pathologies are treated. Managing the activities of shared cancer centres involves different decisions hierarchically linked (Lamè et al. 2016). First, at a strategic level, the capacity planning of the main resources involved must be determined. Then, at a tactical planning level, the available resources (such as beds, seats, nurses, clinicians, rooms for visit) must be allocated to the clinical specialties. At this stage the cyclic timetable determines the days when the different cancer groups are treated, referred to as Master Chemotherapy Planning (Carello et al. 2022). The clinician rostering over a mid-term planning horizon that covers the cyclic schedule must be determined, as well. Finally, at an operational level, the assignment and sequencing of patients needing chemotherapy must be determined for each day of a given planning horizon (Garaix et al., 2020). In this work, we focus on the operational level decision. We assume that the resources have been assigned to the pathologies, and that in each day the assignment of rooms to pathologies and clinicians is given. The set of days of the week in which patients can be treated, depending on their pathology, is therefore known as the solution of by ad hoc optimization models (Carello et al., 2022). The obtained weekly pattern repeats over a month. In this work, we consider the problem of assigning patients to days in the considered planning horizon. Further, we solve the appointment scheduling problem for each day. The problem can be seen as a multi-appointment scheduling problem (Marynissen and Demeulemeester, 2020) where we have to decide the starting time of each activity involved in the day hospital (in particular, oncologist visit and infusion delivery) for each patient. We consider different objectives using a patient centered approach aimed at maximizing the quality of the patient experience. We formulated the problem as a multi-objective optimization model and we tackle the problem by sequentially solving three ILP models, in a lexicographic multi-objective fashion. The models and solution procedure are tested on real data from an Italian hospital.

[1] Marynissen J., Demeulemeester E. (2020). Literature review on multi-appointment scheduling problems in hospital settings. European Journal of Operational Research, 272 (2), 407-419. [2] Carello, G., Landa,

HCM, Health Care Management; Invited Session
P., Tànfani, E., Testi, A. (2022). Master chemotherapy planning and clinicians rostering in a hospital outpatient cancer centre. Central European Journal of Operations Research, 30, 159-187. [3] Lamè G., Jouini O., Stat Le Cardinal J. (2016). Outpatient chemotherapy planning: A literature review with insight from a case study. IIE Transactions on Healthcare System Engineering, 6(3), 127-139. [4] Garaix T., Rostami T., Xie X. (2020). Daily outpatient chemotherapy appointment scheduling with random deferrals. Flexible Services and Manufacturing Journal, 32(1), 129-153.
# Applications of OR; Contributed Session

TU 14:10 PM1 003

Imen Chaabouni imen.chaabouni.1@ulaval.ca

Laval University, Quebec

Lehoux, Nadia, Department of Mechanical Engineering, Université

Laval, Quebec City, Quebec, Canada

*Evaluation of economic impacts for a demand response program within a sawmill*

In this paper, we propose an economic evaluation method for a typical sawmill in Quebec, Canada, which is considering participating in a Demand Response (DR) program such as that provided by Hydro-Quebec, the local electricity utility. In this method, the variation in costs associated with program participation is tracked, including unmet demand, inventory utilization, and electricity bill costs against potential revenues generated from participation in DR events. These are evaluated for different scenarios with a varying number of DR hours that could occur during winter. For this purpose, a suitable mathematical model was selected from the literature. Using real data collected between December 2019 and February 2020 and employing techniques based on demand shedding and demand shifting at the planing stage, the results revealed that participating in Hydro-Quebec's DR program is possible with limited backorder quantities. It was also shown that each additional production hour added to the weekly calendar, load shifting strategy, reduced costs by about 70%, in the case of 80 DR hours per winter season. Furthermore, a 0.44% cost reduction can be achieved for DR events of 16 hours by adding 2.5 hours per week of overtime to the production calendar (about C$ 17,665.40 profit).

## Applications of OR; Contributed Session
TU 14:30 PM1 003

Maurizio Boccia maurizio.boccia@unina.it

Università di Napoli "Federico II"
Mancuso, Andrea, Università di Napoli "Federico II"; Masone, Adriano, Università di Napoli "Federico II"; Sterle, Claudio, Università di Napoli "Federico II"

*A Branch and Cut algorithm for the Flying Sidekick Traveling Salesman Problem*

Last mile logistics (LML) is one of the most important and expensive part of the freight distribution process in a supply chain. LML role is not going to change in the future since we are observing an always increasing shift away from physical stores to digital shopping. In this context, the integration of new distribution technologies in the delivery systems, specifically drones, has been investigated by several companies to reduce the LML costs. The most promising delivery system, in terms of emissions and completion time reduction, consists of a truck and a drone operating in tandem for the parcel delivery to the customers. These new drone-based delivery systems have led to the definition of new and complex decision and optimization problems for which operations research methodologies represent a valuable support tool. In this context, several contributions have appeared in the last years providing ILP and MILP formulations for these kinds of problems. Nevertheless, these formulations suffer from dimensional drawbacks which make their solution impracticable even on small instances. In this work, we propose an exact approach for one of these problems, the flying sidekick traveling salesman problem (FS-TSP) [3]. It is a variant of the TSP where routing decisions are integrated with customer-to-drone and customer-to-truck assignment decisions and truck-and-drone synchronization constraints. The objective is the minimization of the time required to serve all the customers, considering drone payload capacity and battery power constraints. Big-M constraints to take into account the synchronization issue, are used by almost all the formulations proposed in literature [2]. In [1][4] the synchronization constraints are tackled in a column generation fashion. In this work a compact formulation without Big-M constraints is presented and solved by using a Branch and Cut approach. The proposed method has been experienced on a large set of benchmark instances. Computational results show that it either is competitive or outperforms the best exact approach present in literature for the FS-TSP.

Applications of OR; Contributed Session
TU 14:50 PM1 003

Teresa Albini teresa.albini2@unisi.it

Università degli Studi di Siena
Brocchi, Andrea, Università degli Studi di Siena; Murgia, Gianluca, Università degli Studi di Siena; Pranzo, Marco, Università degli Studi di Siena

*Real-time optimization for a Digital Twin of a robotic cell with human operator*

Digital Twins (DTs) can support the simulation, planning, and optimization of the firms operations, but their adoption may be hindered by the role played by human operators. Indeed, differently from machines, human behaviours are largely characterized by nondeterministic nature, thus requiring that constant monitoring of the manufacturing system is accompanied by the development of real-time simulation and optimization algorithms. This paper presents the DT of a robotic cell for the manufacturing of Printed Circuit Boards (PCBs). The human operator oversees the management of the defective PCBs and the replenishment of the necessary materials for the cell but may also carry out some tasks otherwise performed by the robotic arm. The cell is autonomously optimized by the real time optimization algorithm keeping into account and adapting to the behaviour of the human operator. The optimization process guides the human operator by suggesting, without enforcing, the desired next moves. To deal with the uncertainty related to the human operator, we developed a simulation-optimization algorithm based on the Approximate Dynamic Programming framework. The algorithm evaluates the set of the available moves by simulating the behaviour of two independent agents (i.e., the robotic arm and the human operator) and selects the most promising moves for both these agents. Through an extensive experimental campaign and appropriate statistical analyses, we show how the productivity of the cell is scarcely affected by the behaviour of the human operator. These results may enrich the limited literature on DTs with human operators and provide useful insights to manufacturing companies interested in the implementation of robotic cells based on DTs.
TU 15:10 PM1 003

Riccardo Giusti riccardo.giusti@polito.it

Politecnico di Torino

Manerba, Daniele, Università degli Studi di Brescia; Crainic, Teodor

Gabriel, CIRRELT

*A time-space multi-network modelling approach for the Location-Transshipment Problem in Synchronmodal Logistics*

We study the tactical planning problem of a Logistics Service Provider (LSP) that must secure contracts with transshipment terminals for many months of operational activities. During that period the LSP needs to manage many customers origin-destination shipments through different types of services. The objective of the LSP is to minimize the costs for contracting and using the terminals plus the service costs to transport, handle, and store commodities. In the context of synchronmodal logistics [1], we consider truck, rail, barge, and ship as available transport modes to perform long-haul shipments. An important synchronmodality feature considered in our work regards the shipments flow synchronization addressed by considering penalties for late collection, early delivery, and late delivery. We first define a new MILP formulation variant of the classical Hub Location Problem [2], namely the Location-Transshipment Problem with Synchronized Multi-Commodity Flows. Then, we further model the problem using a time-space multi-network in which the time dimension and the time-dependent parameters are hidden within time-space nodes and arcs [3]. Given this model, we present an economic analysis to assess how much a more flexible environment, like the one required in the implementation of synchronmodality, can affect operational costs. For this aim, we compare different types of instances in which some cost parameters vary depending on how much terminals and customers are flexible. Moreover, we present a solution method based on cutting-planes to overcome the computational limits of using a commercial solver as a black-box tool. We will present the validation of our modeling and solving methodology through an extensive computational campaign. Note that the modelling approach adopted could be relevant for other multi-periodic hub location problems.

[1] Giusti, R., Manerba, D., Bruno, G., Tadei, R., 2019. Synchronmodal logistics: An overview of critical success factors, enabling technologies, and open research issues. Transportation Research Part E: Logistics and Transportation Review 129, 92110. [2] Alumur, S.A., Campbell, J.F., Contreras, I., Kara, B.Y., Marianov, V., OKelly, M.E., 2021. Perspectives on modeling hub location problems. European Journal of Operational Research 291, 117. [3] Crainic, T.G., Hewitt, M., Toulouse, M., Vu, D.M., 2016. Service network design with resource constraints. Transportation Science 50, 13801393.

Applications of OR; Contributed Session
TU 15:30 PM1 003

Carlo Filippi carlo.filippi@unibs.it

Università degli Studi di Brescia

*On crowd-shipping using public transport: MILP model and empirical evaluation*

Crowd-shipping is a promising shared mobility service that involve the delivery of goods using non-professional shippers [1]. One of the main goals of crowd-shipping initiatives is to reduce congestion and pollution in city centers. However, in most crowdshipping initiatives, the crowd rely on private motorized vehicles and hence the environmental benefits could be small, if not negative. Conversely, a crowd-shipping service relying on public transport should maximize the environmental benefits. Motivated by this observation, our aim is to model a crowd-shipping service based on public transport and to assess the potential economic impact of using bus- or metro-based crowd-shipping coupled with a traditional home delivery service. We consider a shipper that must deliver packages to customers located in an urban area served by a metro service using two delivery modes: home delivery and crowd-shipping. Home delivery is carried out by vehicles that visit customer locations; crowd-shipping is carried out by metro commuters using lockers located at the stations and supplied by the vehicles. A customer is compatible with crowd-shipping if her/his home is sufficiently close to a metro station and the required parcel is fitted for lockers. In this case, she/he can be served either by home delivery or by crowd-shipping. Otherwise, the customer must be served by home delivery. Essentially, the carrier has to decide: which customers to assign to crowd-shipping among those compatible with this delivery mode; how many vehicles are necessary to perform the delivery tasks; how to route the vehicles. We allow two crowd-shipment rewarding schemes: either fixed (possibly null) or proportional to the size of the package. The decision criterion for the carrier is total cost minimization. The resulting problem includes characteristics of the VRP with Occasional Drivers [2] and the VRP with Transshipment and Delivery Options [3]. We derive a MILP formulation including restrictions on the availability of crowd-shippers, locker capacity, and vehicle capacity. The model is implemented using Python with Gurobi solver and a computational study based on the municipalities of Brescia and Milan is performed. We get insights on the economic advantages that a metro-based crowd delivery option may have for a carrier, and we point out possible modeling and algorithmic developments.

[1] Le, T. V., Ukkusuri, S. V. (2019). Crowd-shipping services for last mile delivery: Analysis from American survey data. Transportation Research Interdisciplinary Perspectives, 1, 100008. [2] Archetti, C., Savelsbergh, M., Speranza, M. G. (2016). The vehicle routing problem with

Applications of OR; Contributed Session
occasional drivers. European Journal of Operational Research, 254(2), 472-480. [3] Vincent, F. Y., Jodiawan, P., Redi, A. P. (2022). Crowd-shipping problem with time windows, transshipment nodes, and delivery options. Transportation Research Part E: Logistics and Transportation Review, 157, 102545.
# OPTSM, Optimization in Public Transport and Shared Mobility; Invited Session

TU 14:10 PM1 Auditorium A

Tommaso Bosi tommaso.bosi@uniroma3.it

Roma Tre University, Department of Engineering Bigi, Federico, Department of Engineering, University of Luxembourg; D'Ariano, Andrea, Department of Engineering, Roma Tre University; Viti, Francesco, Department of Engineering, University of Luxembourg.

A MILP Model for the Wagon Shunt-in Shunt-out Problem in Rail Freight Transport

The European Union plans to double the freight rail traffic by 2050, both to cut pollution emissions and to mitigate the congestion by shifting traffic from road to rail networks. One of the challenges is to minimize the high costs associated with the shunting yard operations (including the cost of wagon maintenance), while maintaining an acceptable level of service. Due to the complexity of the studied problems, shunting operations are usually managed based on practitioners' experience. In this context, we propose a MILP model for wagon placing-in and taking-out operations on outbound and inbound trains along with a multi-objective Dijkstra algorithm (MDA), in which each arc bears a multidimensional vector of cost attributes, to deal with scalability limitations. Our methodology aims to minimize the number of shunting operations and, consequently, both the operating costs and the emissions of shunting locomotives. The proposed mathematical model considers the number of shunts as well as weighted delay terms of outbound trains in the objective function, while rolling stock maintenance and composition constraints are related to wagons. We propose the linearization of several constraints as well as a pre-processing phase to deal with the assumptions related to the fixed size of inbound and outbound trains. The MDA, developed in Python, represents each inbound train as a directed graph by adding weights on its arcs calculated by using the multi-objective function of the model. The algorithm finds the MultiObjective Shortest Path (MOSP) from the first wagon requiring maintenance to the last one. This path gives information on the wagons that must be shunted. To test the effectiveness of our methodology, we have considered the 2020 train timetable for freight trains in the Bettemburg Eurohub Sud Terminal (Luxembourg) and we have assessed different KPIs, linked both to tactical and strategical objectives, such as efficient wagon fleet management, to assign a smaller wagon pool to the shunting yard. Computational results show how the criteria for choosing which wagons should be taken-out from the inbound train and should be inserted in the outbound train might significantly impact the various

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
KPIs analyzed, in terms of time to shunt plus fixed and variable costs, that are related to depot costs and cost per shunt wagons availability in the shunting yard. The MILP model is used in the Antoine Project, financed by CFL (Société nationale des chemins de fer luxembourgeois), as an add-on tool to the Antoine event-based simulator. This simulator connects the MILP model with another mathematical model that, based on the shunting decisions resulting from the MILP model, exploits the potential of multiple placing-in policies.

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
TU 14:30 PM1 Auditorium A

Federico Bigi federico.bigi@uni.lu

University of Luxembourg

Bosi, Tommaso, Roma Tre University; Pineda-Jaramillo, Juan, Uni-
versity of Luxembourg; Viti, Francesco, University of Luxembourg;
D'Ariano, Andrea, Roma Tre University

A MILP Model for the Wagon Shunt-in Problem in Multimodal Rail
Freight Transport

In a context where Europe aims to become climate-neutral by 2050, freight trains will play a key role in this transition. By now, almost 78% of goods are transported by road, with double the freight train traffic expected in the next 30 years to reach carbon neutrality. Looking at an already overcrowded network system, the optimization of shunting operations, defined as the movement of multiple rolling stocks inside a shunting yard, has already proved to be impactful in terms of costs to be sustained by the companies, especially due to outbound trains' delays and cancellations. Moreover, due to the problem's complexity, the shunting operations are usually managed by practitioners in a sub-optimal way. Our study aims to formalize the shunt-in problem, defined as the modality to choose and place rail-cars stored in the shunting yard inside an outbound train given a certain demand of wagons. This demand is obtained by the relative shunt-out problem, defined as the problem of choosing which wagons have to be extracted from an inbound train T when a new composition has to be created for the corresponding outbound train. The basic shunt-in problem can be modeled as an ILP, specifically as a general set-partitioning problem, with the objective of minimizing the time required to complete all the shunt-in operations. For this problem, we define two sets of wagons: the wagons inside the inbound train that must be replaced, and the rail-cars in the shunting yard that are suitable to be shunted in. Each wagon from the shunting yard can be placed inside the freight train with a specific cost and respecting the composition request for the wagon types of the outbound train. The ILP model is then extended to a MILP, proposing different shunt-in policies expressed by weighted objective functions, such as the minimization of the actual mileage of wagons chosen to be shunted in. The suitability of a wagon in the shunting yard is related to maintenance and category constraints. The MILP is then solved via CPLEX solver and injected as an input in an event-based simulation framework developed by University of Luxembourg. Several analyses are carried out for the validation of these models, exploiting the 2020 rolling stock schedule used by the Luxembourg National Railway Company with a particular focus on the Intermodal terminal - EuroHub Sud, a combined rail-road transport terminal located in Bettembourg, Luxembourg, analyzing KPIs in terms of Feasibility, Service Level and Operations performed, focusing especially on the wagon fleet and delay of outbound trains. Results

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
show that different shunt-in policies can impact the overall percentage of delayed trains, number of wagons used and shunting operations to be performed.

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
TU 14:50 PM1 Auditorium A

Anna Livia Croella annalivia.croella@uniroma1.it

Sapienza University of Rome

Mannino, Carlo, SİNTEF; Ventura, Paolo, IASI

*Dynamic Discretization Discovery applied to train traffic re-scheduling*

Train scheduling is a critical activity in rail traffic management, both off-line (timetabling) and on-line (dispatching). Time-indexed formulations for scheduling problems are stronger than other classical formulations, like big-M. Moreover, they can be easily adapted to cope with complicating constraints and non-linear objectives. Unfortunately, their size grows usually very large with the size of the scheduling instance. As a consequence, time-indexed formulations are typically not fit to attack real-life instances of job-shop scheduling problems, especially when fast, online responses are required. Moreover, the approximation introduced by time discretization often leads to solutions which cannot be realized in practice. Dynamic Discretization Discovery (DDD), recently introduced by Boland for the continuous-time service network design problem, is a technique to keep at bay the growth of time-indexed formulations and thus response times and at the same time ensure the necessary modelling precision. Exploiting and extending the DDD paradigm, we develop a primal-dual approach to train dispatching and, more in general, to job-shop scheduling. The result is a restricted TI formulation and a procedure with running times comparable with the best alternatives presented in the literature on our real-life instances of train dispatching. Furthermore, the method implemented does not suffer by the approximation error introduced by a standard time discretization and seems to be very promising, not only in a railway context but, more generally, for the broader field of job-shop scheduling.

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
TU 15:10 PM1 Audtorium A

Pierre Hosteins pierre.hosteins@univ-eiffel.fr

University Gustave Eiffel

*Decomposition methods for an integrated rail-rail transshipment yard problem*

The optimised management of freight transshipment yards is a very complex problem resulting from the articulation of several difficult and intricate problems. Many yard resources must be scheduled, such as tracks, teams and cranes, so as to minimise the time required to load and unload containers on freight trains. Recently, a few works have tried to handle several transshipment yard subproblems within a single optimisation approach, particularly using mathematical programming. The work of Cichenski et al (2017) handles the separation of trains in bundles, the trains positioning on tracks and the placement of containers on outgoing trains. We propose to extend the MILP approach of Cichenski et al (2017) to consider the division of the tracks in different areas managed by the different cranes in order to take into account a more realistic objective function. Moreover, we propose to apply Benders Decomposition to the obtained MILP, after proving that many integer variables can be relaxed to continuous ones. Depending on the state of advancement, we will also discuss how to compare the obtained results with those of approaches which solve the respective subproblems sequentially, and how to integrate the remaining crane and shuttle cars scheduling problems.
TU 15:30 PM1 Auditorium A

Bianca Pascariu bianca.pascariu@uniroma3.it

Roma Tre University

Samà, Marcella, Roma Tre University; Pellegrini, Paola, Université Gustave Eiffel; D'Ariano, Andrea, Roma Tre University; Rodriguez, Joaquin, Université Gustave Eiffel; Pacciarelli, Dario, Roma Tre University

*Improving train punctuality by optimized train route selection in decision support systems*

The Train Routing Selection Problem (TRSP) is the combinatorial optimization problem of selecting the best train route alternatives, for each train in a rail network. Solving the TRSP aims to limit the number of rerouting variables of the train rescheduling problem, formalized as the real-time Rail Traffic Management Problem (rtRTMP) and intended to minimize train delays. In the TRSP, the benefit of using specific subsets of routes in the rtRTMP is assessed by considering estimations of costs due to scheduling decisions. The impact of TRSP solution on the rtRTMP has been analyzed in the literature by using RECIFE-MILP, a rtRTMP solver based on a MILP model formulation. In this paper, we propose the extension of the TRSP validity for the rtRTMP, regardless the specific model and solution approach used for the rtRTMP, and the objective function optimized. In addition to RECIFE-MILP, we consider for the rtRTMP the decision support system AGLIBRARY, developed at Roma Tre University, which solves an alternative graph model of the problem. We then propose the formulation in the TRSP of a selection of rtRTMP objectives functions, such as the minimization of the cumulative consecutive train delay, the train travel time, the number of delayed trains, and the maximum consecutive delay. We study the extent to which the TRSP effectiveness depends on the correlation between the TRSP and rtRTMP objective functions. The computational analysis is performed on a real case study: the line around the city of Rouen.

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
# MUOS, Multicriteria Optimization for sustainability; Invited Session

TU 14:10 PM1 Audtorium B

Lavinia Amorosi lavinia.amorosi@uniroma1.it

Sapienza University of Rome

De Santis, Marianna, Sapienza University of Rome

A criterion space search algorithm for bi-objective mixed integer linear programs

In this talk, we focus on bi-objective mixed integer linear programming problems (BOMIP) presenting a new algorithm able to detect the complete non-dominated set. The design of this exact method is motivated by multi-objective mixed integer linear models arising from real world applications and the need of the complete exploration of their Pareto frontiers. In particular, we mention an application in the energy sector related to the management and sizing of a battery storage system. The algorithm works in the criterion space, alternating the resolution of single objective mixed integer linear problems and bi-objective linear problems. We prove that, after a finite number of iterations, a list of points and segments, containing the Pareto frontier, is generated. This list is filtered by a post-processing procedure in order to eliminate potentially dominated regions of the image set.
TU 14:30 PM1 Audtorium B

Daniele Patria daniele.patria@uniroma1.it

Sapienza, University of Rome
De Santis, Marianna, Sapienza University of Rome; Eichfelder, Gabriele, TU Ilmenau; Warnow, Leo, TU Ilmenau

*Using Dual Bounds for Multiobjective Mixed Integer Quadratic Programming*

In this talk, we present an algorithmic framework for solving Multi-Objective Mixed Integer Convex Quadratic Programs (MOMICQP) with linear constraints. The framework is based on two phases. First, a branch-and-bound method is applied to detect promising integer fixings, that are needed to initialize the second phase, where the Pareto front of the (MOMICQP) is detected up to an according precision using the solver HyPaD. The branch-and-bound works by fixing subsets of variables to integer values. Lower bounds are computed by addressing the dual problems of the continuous relaxations of the restricted objective functions. A major advantage is that the expensive calculations are performed in a preprocessing phase so that the nodes in the branch-and-bound tree can be quickly enumerated. Suitable pruning strategies are presented. Experiments on biobjective instances and on instances with three objectives are shown.

MUOS, Multicriteria Optimization for sustainability; Invited Session
TU 14:50 PM1 Auditorium B

Justo Puerto puerto@us.es

Universidad de Sevilla

Pozo, Miguel A, Universidad de Sevilla; Roldan, Ignacio, Universidad de Sevilla

*The biobjective minimum-cost Perfect Matching and Chinese Postman Problems*

This paper analyzes the biobjective versions of the perfect matching problem and the Chinese postman problem. We consider supported and non-supported non-dominated solutions of both problems resorting to scalarization methods and different two phase strategies. We also study the issue of finding the entire set of non-dominated solutions of the Chinese postman problem by solving the corresponding biobjective matching problems and prove that unlikely the single objective case, in general, this strategy does not provide the correct solution of the biobjective problem. We derive sufficient conditions that ensure under which conditions one can expect to solve the biobjective Chinese postman problem by solving matching problems. Extensive computational results are reported assesing the usefulness of our approaches.
TU 15:10 PM1 Auditorium B

Marianna De Santis mdesantis@diag.uniroma1.it

University of Rijeka, Faculty of Maritime Studies
Luca, Benvenuti, DIAG, Università di Roma La Sapienza; Alberto,
De Santis, DIAG, Università di Roma La Sapienza; Daniele, Patria,
DIAG, Università di Roma La Sapienza

*Designing sustainable diet plans by solving a tri-objective 0-1 linear problem*

In this talk, we present a tri-objective 0-1 linear model, built to design nutritionally adequate and healthy diet plans, minimizing their environmental impact. The diet plans refer to two-week full-board menus for nursing homes and we consider the carbon, water and nitrogen footprints as conflicting objectives to be minimized. Energy and nutrient contents are constrained in suitable ranges suggested by the dietary recommendation of health authorities. In order to compute the non-dominated solutions of the tri-objective 0-1 linear model an algorithm that combines the epsilon-constrained method and suitably defined weighted sum scalarizations is devised. We analyze our method and prove that it is able to detect the complete Pareto front within a finite number of iterations. Results obtained on real world data are reported and discussed.

MUOS, Multicriteria Optimization for sustainability; Invited Session
# OUUTA, Optimization under Uncertainty: Theory and Applications; Invited Session

TU 16:30 PM2 001

Andrea Spinelli andrea.spinelli@guest.unibg.it

Università degli Studi di Bergamo
Maggioni, Francesca, Università degli Studi di Bergamo

A Robust Optimization Model for Nonlinear Support Vector Machine

In this contribution we present a novel optimization approach for Support Vector Machine (SVM), with the aim of separating two sets of points by means of a nonlinear decision boundary. Our approach extends the deterministic and linear predictor proposed in [1] to a nonlinear classifier by including a kernel function in the model. Moreover, we consider the case in which training data are plagued by uncertainty. To tackle the problem, we formulate a robust optimization model that generalizes the technique proposed in [2] to a class of uncertainty sets bounded by a p-norm and by including a nonlinear classifier [3]. The deterministic model and its robust counterpart reduce both to linear programs which can be shown to be computationally tractable. Preliminary numerical results on real-world datasets show the performance of the proposed approach.

[1] Liu, X., Potra, F.A., 2009. Pattern separation and prediction via linear and semidefinite programming. Stud. Inform. Control 18, 7182. [2] Faccini, D., Maggioni, F., Potra, F.A., 2022. Robust and distributionally robust optimization models for linear support vector machine. Comput. Oper. Res., to appear. [3] Trafalis, T.B., Gilbert, R.C., 2006. Robust classification and regression using support vector machines. Eur. J. Oper. Res. 173, 893909.
TU 16:50 PM2 001

Edoardo Fadda edoardo.fadda@polito.it, daniele.gioia@polito.it

Department of Mathematical Sciences Giuseppe Luigi Lagrange, DISMA, Politecnico di Torino

Daniele Giovanni, Gioia, Department of Mathematical Sciences Giuseppe Luigi Lagrange, DISMA, Politecnico di Torino; Paolo, Brandimarte,

Department of Mathematical Sciences Giuseppe Luigi Lagrange, DISMA, Politecnico di Torino

*Robust Approaches for a Two-Stage Assembly-to-Order Problem.*

Assembly to order is a production strategy where components are man-
ufactured under demand uncertainty and end items are assembled only
after demand is realized. Risk-neutral approaches aim to maximize the
expected profit. However, this approach may fail if heavy-tailed or multi-
modal distributions are likely to generate significant disruptions or if the
shrinking life of products is considered. Conversely, risk-averse models
may tackle these problems. In the paper, we deal with an assembly-
to-order problem, modeled as a two-stage stochastic linear programming
problem considering the introduction of a classical risk measure from fi-
nance: the conditional value-at-risk. We examine the characteristics and
the performance of the model by means of a large number of out-of-sample
scenarios.
TU 17:10 PM2 001

Patrizia Beraldi patrizia.beraldi@unical.it

Department of Mechanical, Energy and Management Engineering,
University of Calabria

Sara, Khodaparasti, Department of Mechanical, Energy and Man-
agement Engineering, University of Calabria

*Dynamic Pricing in the Electricity Retail Market: A Stochastic Bi-Level Approach*

This paper investigates the dynamic pricing problem in the retail mar-
ket and propose a bi-level approach to define time-differentiated electric-
ity rates which are announced with short advance. The pricing decisions
are affected by the procurement plan that the retailer defines also ex-
ploiting the local energy system composed by Photovoltaic panels and
a battery storage device. In the proposed bi-level formulation, the re-
tailer acts as leader deciding first about the electricity rates, whereas the
consumer acts as follower, reacting to the announced tariff changing the
consumption pattern. To account for the inherent uncertainty affecting
the main parameters entering the decision process a stochastic formula-
tion is proposed. By exploiting the structure of the problem a single level
reformulation is provided. Preliminary numerical results carried out on a
real case study are presented and discussed.
# HCM, Health Care Management; Invited Session

TU 16:30 PM2 002

Marco Roma marco.roma@unifi.it

DINFO Università degli Studi di Firenze
Cappanera, Paola, DINFO Università degli Studi di Firenze; Ga-
vanelli, Marco, DE Università di Ferrara; Nonato, Maddalena, DE
Università di Ferrara

*Mid term scheduling of medical staff at a hospital network by An-
swer Set Programming: a case study*

This study deals with a staff scheduling problem concerning physicians working at few hospitals belonging to a local area network. Due to the pandemic situation, these hospitals have been subject to several reorganizations in terms of both staff and services allocation. These changes have exacerbated previous strains to manually provide working schedules able to cover the service, meet legal requirements, and be perceived as a fair workload allocation. On the one hand, the problem shares the features of classical scheduling problems, i.e., a set of tasks, which repeat on a weekly basis, must be assigned to a set of workers according to a set of rules, possibly meeting a few criteria. On a regular basis, service can be covered without overtime. Since physicians get paid a fixed monthly salary, any feasible schedule has the same monetary cost for the administration. Therefore, the primary focus is not on cost rather than on feasibility. On the other hand, beside the challenges posed by feasibility constraints, fairness related issues sharply arise in the mid term. In fact, while working time is constrained by law, differences arise because of the kinds of tasks in the physician rosters. Since the variety of tasks is high and each physician has different skills, achieving fairness by simply rotating tasks among different people is not viable. In particular, there are no two identical professional profiles, so that a rotation is to be directly mapped on to specific individual. Moreover, because of this diversity, a priori there is no ideal workload threshold whose distance from may return a measure of fairness. Indeed, more elaborated attributes should be measured to make a comparison possible, taking into account also the spatial distribution of the activities. In our proposal, fairness is sought off by diversification in the short term and possibly achieved in the long one. To this aim, service must be scheduled over a mid term time period, such as few months, long enough to allow a certain degree of diversification within the schedule of each physician, as well as a fair distribution of the heaviest tasks (such as week end duties and night shifts) among all physicians. Long planning horizons, though, increase the problem size, which poses a challenge on the solution process performance. Moreover, beside compulsory requirements, many soft preferences are present (such as do not assign night shifts to older physicians). These tend to confine

## HCM, Health Care Management; Invited Session
the returned solutions into a narrow field, which goes to the detriment of variety and, in turn, of fairness achievement. We propose to tackle the problem by Answer Set Programming, as it easily handles preferences and soft constraints. The aim is to provide the Hospital administration with a flexible tool that is easy to use and to customize, i.e., by fixing some shift assignment to someone or by changing priorities, to be leveraged for conflict resolution as well as to promptly react to sudden organizational changes. In the presentation we will focus on various modeling options regarding fairness representation, and how to enforce it over time. In particular, we will discuss a mathematical formulation for the objective function, which in the ASP environment is realized by way of soft constraints with different priority and weight, and will present results based on real data.

HCM, Health Care Management; Invited Session
TU 16:50 PM2 002

Christian Piermarini christian.piermarini@uniroma1.it

Dipartimento di Ingegneria Informatica, Automatica e Gestionale
Roma, Massimo, Dipartimento di Ingegneria Informatica, Automat-
ica e Gestionale

*The Ambulance Diversion phenomenon in an Emergency Depart-
ment network: a case study*

The Emergency-Department (ED) overcrowding problem is regularly regarded as the main subject of many healthcare management-oriented studies. Such works are generally carried out by the means of a model of the patient-flow within a single ED, without considering the possibilities offered by the cooperation among EDs. In this article, such solution is examined and an ED network model is developed, focusing on the Ambulance Diversion problem. Then, the resulting Discrete Event Simulation (DES) model is studied employing a Simulation-Based Optimization (SBO) approach. Various scenarios are considered to analyze the first-aid network under different conditions, in order to obtain optimal operative performances without carrying unsustainable resource costs. As a case study, six EDs in the Lazio region of Italy were considered to build the network. The results show the obtained performances for each diversion policy, both in terms of patient waiting time and costs for the service providers. Moreover, a brand-new interface for the communication between the DES model and the Derivate-Free algorithm has been set up in our implementation, in order not to rely on external software.

HCM, Health Care Management; Invited Session
# Applications of OR; Contributed Session

TU 16:30 PM2 003

Gianfranco Guastaroba gianfranco.guastaroba@unibs.it

Department of Economics and Management, University of Brescia
Morandi, Valentina, University of Brescia; Speranza, M. Grazia,
University of Brescia

*Designing optimal paths in large crowded events*

There are several practical situations where the number of people simultaneously allowed in a specific area needs to be limited over time below a predefined threshold. This is often related to safety reasons, or the physical capacity of the venue. Well-known examples are shopping malls, theme parks, large expositions, and international events. In such situations, providing directions to people regarding where and when to go, as well as tracking where people are over time, can help to avoid overcrowding and provide people with a better and safer experience. Note that this has been a critical issue during the pandemic caused by the SARS-CoV-2 virus. In this talk, we present the Crowd Avoiding Routing (CAR) problem, which we define as follows. We consider a multi-period setting defined over a finite planning horizon. The planning horizon is discretized into a number of equally spaced time periods, each corresponding to, e.g., one minute, ten minutes, or one hour. We consider an environment where a set of physical points is given. We assume that this set comprises one entry point, one exit point, and a set of locations that provide a service. Examples of the latter are shops available in a mall, attractions in a theme park, or pavilions in a large exposition. Each of such locations is associated with a fixed capacity and a predetermined service time. We are given a set of requests, where each request is associated with a weight, a preferred start time, a maximum time available for the visit, and a set of desired locations. The weight of a request represents the amount of capacity consumed if that request visits a location. We assume that it is not mandatory to visit all the desired locations associated with a request, but a selection can be made if the capacity of some locations is not sufficient to accommodate simultaneously all requests. We also allow that a request stands in line before entering a location if the capacity available of the latter is not sufficient. In such a case, the request stands in line until a sufficient number of other requests, whose service started previously, leave the location. The CAR problem calls for determining an optimal set of coordinated paths, one per each request, so that the total number of desired locations not selected and the total time spent queuing is minimized. The main constraints of the problem are that the length of each path, that includes the travel, service, and queue times, must not be larger than the maximum time available of the associated request; and that, at any time period, the capacity of each location cannot be violated. Based

Applications of OR; Contributed Session
on a time-space network representation, we cast the CAR problem as a
Mixed-Integer Program (MIP) and introduce a set of valid inequalities
to strengthen the mathematical formulation. Computational experiments
are given where the MIP is solved by means of a general-purpose solver on
a set of instances generated by the authors. We discuss the computational
effectiveness of the valid inequalities proposed, and present some insights
on the potential benefits that can be achieved by using the solutions of
the CAR problem as a tool to support decision-making processes.
TU 16:50 PM2 003

Martina Luzzi martina.luzzi@unical.it

Department of Mechanical, Energy and Management Engineering,
University of Calabria

Guerriero, Francesca, Department of Mechanical, Energy and Man-
agement Engineering, University of Calabria; Macrina, Giusy, De-
partment of Mechanical, Energy and Management Engineering, Uni-
versity of Calabria; Triki, Chefi, Department of Engineering for In-
novation, University of Salento, Lecce, Italy

An auction mechanism in restaurant business

An auction is a popular sales practice, in which every potential cus-
tomer, called bidder, expresses an offer, named bid, for a particular prod-
uct that is usually sold to the person who offers the highest price, (i.e., the
winner of the auction). Although the auction mechanism is currently ap-
plied in many fields including procurement, luxury goods, electricity, art
and rare collectibles, public-works contracts and sale of natural-resource
rights, there are still some business where auction could be applied in an
innovative and profitable way. In this study we focus on the application of
auction mechanism, through a web platform, to the restaurant business.
In particular, we propose some optimization models and strategies, aimed
at winners determination and revenue maximization. Different types of
auction mechanisms, like first price auctions, second price auctions and
dynamic auctions, are implemented and tested. In addition, we consider
several features of the restaurant business, such as the possibility to com-
bine more tables to allocate larger groups of customers and the duration
of the meal, hence, considering the tables as a renewable resource. Pre-
liminary computational results have shown that the application of auction
strategies to restaurant business is an effective way to achieve revenues.

[1] Guerriero F., Miglionico G., and Olivito F. "Strategic and oper-
ational decisions in restaurant revenue management." European Journal
of Operational Research 237.3 (2014): 1119-1132. [2] Talluri Kalyan T.,
and Van Ryzin Garrett J. The theory and practice of Revenue Manage-
ment. Springer (2004). [3] Triki C. "Using combinatorial auctions for
the procurement of occasional drivers in the freight transportation: A
case-study." Journal of Cleaner Production 304 (2021): 127057.
TU 17:10 PM2 003

Veronica Mosca veronica.mosca1996@libero.it

University of Calabria

Guerriero, Francesca, University of Calabria; Matteucci, Massimil-
iano, PAC 2000A Conad Group

*Optimising the order picking process: CONAD case study*

The order picking is one of the most expensive and laborious operation
in a warehouse. Optimising the picking activities involves several aspects
that could be improved, such as the packing, layout design, storage assign-
ment, zoning, batching, and routing. In this work we address the problem
of optimising the picking activities of an existent warehouse of PAC 2000A
CONAD (Consorzio Nazionale Dettaglianti) group. CONAD is an Ital-
ian cooperative system of entrepreneurs which operates the largest super-
market chains in Italy, and PAC 2000A is its biggest cooperative. After
analysing the current process adopted by the company, and outlining the
best practices, we focus on the re-optimisation of the process, proposing
several strategies aiming at providing more efficient and effective picking
solutions.
TU 17:30 PM2 003

Petra Groelj University of Ljubljana, Biotechnical Faculty
Tjaa, midovnik, University of Ljubljana, Biotechnical Faculty

*Decision makers weights of importance based on the projection measure in DEMATEL*

EMATEL (Decision Making Trial and Evaluation Laboratory) is a method for identifying and evaluating the relationships between factors in a complex system, divided into cause and effect factors. Digraphs can help visualize the direction and strength of the relationships, while influence matrices represent them numerically. The results of the analysis of the interdependence between factors can be represented by the causal diagrams. A group of experts with different knowledge and experience should be involved in decision-making to better grasp all the important aspects of complex real world problems and to solve them satisfactorily. To improve the decisions, different importance of decision makers (DMs) should be taken into account. Subjective weights based on experts positions and objective weights based on different mathematical methods are two different approaches used in applications. In order to successfully manage the differences in DMs opinions that can lead to difficulties in the decision-making process, objective methods based on the similarity of DMs opinions are one way to assign importance weights to DMs. Although there are many studies that use the group DEMATEL, most assume that DMs are equally important. In order to contribute to more satisfactory and powerful group decision making, we present a new approach to derive objective weights of DMs in DEMATEL. It is based on the projection method that considers the distance and angle between two vectors. Its generalization to the matrices can be a suitable distance measure between two matrices representing the opinions of DMs. Although several projection measures have been proposed in the literature, we show that they are not suitable for DEMATEL. We present a new DProj method adapted for DEMATEL influence matrices. Larger DProj values indicate higher similarity between matrices. Based on DProj, we define the importance weights of DMs, with larger weights indicating greater closeness between DMs opinions and promoting higher agreement between DMs. To validate DProj-DEMATEL, some examples from the literature are given. To compare the results from the literature with the results of DProj-DEMATEL, the normalized Manhattan distance between the individual and group influence matrices is measured. The results show that DProj-DEMATEL is suitable for use in applications.

Applications of OR; Contributed Session
# OPTSM, Optimization in Public Transport and Shared Mobility; Invited Session

TU 16:30 PM2 Auditorium A

Majid Soolaki M.Soolaki@westminster.ac.uk

University of Westminster

Gurtner, Gérald, University of Westminster; Bolic, Tatjana, University of Westminster; Delgado, Luis, University of Westminster

*New mathematical model for extended arrival management capabilities*

The Extended arrival management (E-AMAN) concept is based on starting the arrival traffic sequencing earlier than is the case by the arrival management (AMAN). The E-AMAN extends the horizon at which to start sequencing from the airport terminal area further upstream, to enable more smooth traffic management through speeding up, or slowing down arriving flights. Current application of E-AMAN at Heathrow, with the horizon at 350NM reduces delay, operational costs, CO2 emission and smooths delivery of arrival traffic to the runways. Here we propose an E-AMAN model that extends to 500NM. More specifically, the model incorporates three horizons: Tactical Horizon (100NM), Command Horizon (500NM), and Data Horizon (600NM). When a flight enters Data Horizon, the flight intentions are sent to the E-AMAN. When a flight enters Command Horizon, the optimizer is run to find optimal slot for that flight at the runway. Compared to previous optimisation processes, the E-AMAN takes into account the cost of delay and fuel for the airline instead of delay alone, and uses information on the distribution time of arrival to manage uncertainty (e.g. due to wind). Based on the optimal slot assigned, the E-AMAN issues a command to the flight, that can be to maintain initial speed, to speed up, or to slow down. It also assigns minutes of holding if delay cannot be absorbed during cruise. We will present some evidence of the efficiency of the optimisation process, in particular compared to a baseline scenario where the E-AMAN takes only delay into account and no uncertainty. We will show how this efficiency changes in different conditions, in particular relative to wind uncertainty.

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
TU 16:50 PM2 Auditorium A

David Garcia-Heredia garciaherediad@ryanair.com

Ryanair Labs

Alonso-Ayuso, Antonio, Universidad Rey Juan Carlos; Laguna, Manuel, University of Colorado Boulder; Molina, Elisenda, Universidad Complutense de Madrid

*Metaheuristic algorithm for the Air Traffic Flow Management problem*

One of the biggest challenges that the global air traffic industry is currently facing is the saturation of the airspace and airports. That is, the mismatch between capacity (number of flights that want to be operated) and demand (what can be operated attending to safety conditions).

On a daily basis, this saturation problem mainly arises because of short-term factors such as weather, which can negatively affect flight conditions. When saturation issues are detected, the current practice is to modify the flight plan of some aircraft a few hours before their execution. That way, all the scheduled flights can proceed at the expense of some of them suffering some delay or having to fly a longer route. These modifications are included in what is denoted as Air Traffic Flow Management (ATFM).

Thus, the ATFM problem is about proposing the reschedule of some flights a few hours before their execution so: 1) the overall cost is minimized and, 2) safety (capacity) conditions are respected in airports and air sectors at all times.

To that end, we present here an integer programming formulation that permits MIP solvers to tackle large ATFM instances within minutes. The formulation is based on 4D graphs, resulting in most of the constraints being facets of the polytope. The decisions considered to modify the flight plans include ground and air delays, changes in the speed of the aircraft, and alternative routes.

For the largest instances arising in practice, we present a parallelizable matheuristic algorithm. The algorithm, capable of providing near-optimal solutions within minutes, consists of three phases: (1) generation of feasible solutions, (2) combination of solutions, and (3) solution improvement. In the three phases, the structure of the mathematical formulation proposed is largely exploited.

A large computational experience, which shows the goodness of the formulation and algorithm proposed, is presented.

Optimization in Public Transport and Shared Mobility 2 - Airline Optimization

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
TU 17:10 PM2 Auditorium A

Guglielmo Lulli guglielmo.lulli@unimib.it

University of Milano-Bicocca & Lancaster University management
School

De Giovanni, Luigi, university of Padova; Lancia, Carlo, University of Milano-Bicocca

*Solving the European Air Traffic Flow Management Problem*

The air traffic industry is a strategically important sector of the overall world economy. Although air travel is currently one of the economy's sectors most affected by the COVID-19

epidemic, there is a general agreement among experts that the sector will recover. Indeed, all the major R & D programmes for modernizing the air transport systems around the world are continuing with their plan and long-term objectives, and perhaps even reinforcing the focus on resilient and network-based operations. One of the cornerstones of these initiatives is the implementation of the ICAO Trajectory Based Operations concept. Moreover, in the attempt of better satisfying airspace users' business objective and enabling a more collaborative decision-making environment in the air traffic flow management decision process, the concept of trajectory preference has been widely discussed.

In this talk, we present a novel data-driven optimization approach for air traffic flow management (ATFM). The proposed approach allows resolving demand-capacity imbalances while considering airspace users preferences. The model assigns a feasible 4D trajectory and a possible ground delay to each flight. The proposed approach has been tested on instances extracted from the Eurocontrol data repository. With more than 32000 flights considered, we solved the largest instances of the ATFM problem available in the literature in short computational times that are reasonable for practical application. As a by-product, we highlight the trade-off between preferences and delays as well as the potential benefit of the proposed approach.

The proposed approach has the potential of becoming the main engine of air traffic flow management tools.

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
TU 17:30 PM2 Auditorium A

Luigi De Giovanni luigi.degiovanni@unipd.it

Dipartimento di Matematica 'Tullio Levi-Civita' - Università di Padova
Lulli, Guglielmo, Lancaster University Management School and Di-
partimento di Informatica Sistemistica e Comunicazione - Università
degli Studi di Milano Bicocca

*Data-driven kernel search for trajectory based air traffic flow management*

In the Air Traffic Flow Management (ATFM) problem, we want to assign a flight plan to each scheduled flight, taking both the network manger's and the airspace users' perspectives into account: on the one side, safe operations and efficient use of airspace are required, on the other side, we have to consider the airspace users flying preferences [1]. In this talk, we explicitly consider routes' preference into account and, to this aim, we propose a trajectory based ATFM modeling framework, where a set of alternative flight plans is directly extracted from air traffic data repositories by means of data analytics. We thus build consistent trajectory option sets (in the spirit of [2]) and, moreover, we learn the preference of each flight for each option [3]. We propose an assignment formulation for the ATFM, where binary variables select a trajectory option and a delay for each flight, constraints limit total delays and airspace congestion, and the objective function maximizes airspace users preferences. Realistic daily instances lead to prohibitively large Integer Linear Programming models, and we consider kernel search inspired matheuristics: they solve a sequence of models restricted to a suitable variable subset and, at each iteration, a kernel of variables is expanded by a further bucket. We compare different implementations where buckets are a-priori defined based on a linear relaxation, or they are dynamically determined by machine learning techniques. In particular, a tree classifier, trained on reduced-size instances, selects the next bucket by considering features of the candidate variables, the current solution and the search state. Preliminary computational results show that appropriate configurations of the methods are able to solve realistic daily instances within limited optimality gap and acceptable running times.

[1] Dal Sasso, V., Djeumou Fomeni, F., Lulli, G., Zografos, K.: Incorporating stakeholders priorities and preferences in 4D trajectory optimization. Transportation Research Part B 117:594609, 2018. [2] Estes, A.S, Ball, M.O.: Alternative Resource Allocation Mechanisms for the Collaborative Trajectory Options Program (CTOP). In Thirteenth USA/Europe Air Traffic Management Research and Development Seminar, 1-9, 2019. [3] Lancia, C., De Giovanni, L., Lulli, G.: Data analytics for trajectory selection and preference-model extrapolation in the European airspace. In: The OR2018 Proceedings. Springer, 1-7, 2018.

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
# AMUO, Advances in Multiobjective Optimization; Invited Session

TU 16:30 PM2 Auditorium B

Marco Boresta marco.boresta@uniroma1.it

Sapienza Università di Roma / IASI-CNR
Giovannelli, Tommaso, Lehigh University; Lucidi, Stefano, Sapienza Università di Roma; Roma, Massimo, Sapienza Università di Roma

*Multi-objective simulation-based optimization using a machine learning-based mathematical programming model*

We present a novel approach to solving a multi-objective simulation-based optimization problem that employs Artificial Neural Networks (ANN) to approximate the objective function whose values are obtained by running a simulation model. This method involves replacing such objective function with a metamodel with the structure of a Multilayer Perceptron, allowing the use of gradient-based methods to solve the optimization problem. The Pareto Frontier is then generated by solving a series of single-objective problems, with the objective function obtained as a weighted combination of the different conflicting objectives.

We test this approach on a real problem for the Emergency Department (ED) of a large Italian hospital which is significantly affected by the phenomenon of overcrowding: the ED of Policlinico Umberto I in Rome, Italy, one of the largest EDs in Europe. We compare its performance to that of a globally convergent Derivative-Free (DF) method on the same data and with the same budget of function evaluations. The results are encouraging, demonstrating that the ANN approach has several advantages over the DF approach, such as a significant reduction in computation time, the generation of a Pareto Frontier with more distinct, better distributed points, and higher robustness to changes in the problem statement.
TU 16:50 PM2 Auditorium B

Giampaolo Liuzzi liuzzi@diag.uniroma1.it

DIAG - Sapienza

Giovannelli, Tommaso, Lehigh University; Lucidi, Stefano, Sapienza

Univ. di Roma; Rinaldi, Francesco, Univ. di Padova

*A derivative-free approach to mixed integer constrained multiobjective nonsmooth optimization*

In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box. Furthermore, we consider the case where a subset of the variables can only take integer values. We propose a new linesearch-based solution method and show that it converges to a set of stationary points for the problem. For what concerns the continuous variables, we employ a strategy for the estimation of the Pareto frontier recently proposed in the literature and which takes advantage of dense seuqnces of search directions. The subset of variables that must assume dicrete values are dealt with using primitive directions appropriately modified to take into account the presence of more than one objective functions. Numerical results obtained with the proposed method on a set of test problems and comparison with other solution methods show the viability and efficiency of the proposed approach.
TU 17:10 PM2 Auditorium B

Gabriele Eichfelder gabriele.eichfelder@tu-ilmenau.de

Technische Universität Ilmenau
Leo, Warnow, Technische Universität Ilmenau

*A new approach to solve multi-objective mixed-integer convex optimization problems*

We propose a new numerical method for solving multi-objective mixed-integer convex optimization problems. The algorithm determines a covering of the whole set of nondominated solutions which is the image set of efficient solutions, also known as Pareto frontier. It works mainly in the image space and can thus handle larger numbers of variables.

In multi-objective mixed-integer convex optimization multiple convex objective functions need to be optimized simultaneously while some of the variables are only allowed to take integer values. We present an approach to compute an enclosure of the nondominated set of such optimization problems by calculating lower and upper bound sets. For obtaining this covering, we decompose the multi-objective mixed-integer convex optimization problem into several multi-objective continuous convex optimization problems, which we refer to as patches. Then, we iteratively compute and improve enclosures of the nondominated sets of those patches to finally combine them to obtain an enclosure of the nondominated set of the multi-objective mixed-integer convex optimization problem with a certain width as quality guarantee. Additionally, we introduce a mechanism to reduce the number of patches that need to be considered in total by using linear relaxations.
TU 17:30 PM2 Auditorium B

Pierluigi Mansueto pierluigi.mansueto@unifi.it

University of Florence

Lapucci, Matteo, University of Florence

*A Quasi-Newton Approach for Large Scale Multi-Objective Optimization*

We propose a Limited Memory Quasi-Newton method for large scale unconstrained multi-objective optimization. The algorithm approximates the combinations of the objective functions Hessians through positive definite matrices, whose formula is similar to the one of the L-BFGS method for scalar optimization. By means of a Wolfe line search, our method is well defined even for non-convex optimization problems. We compare the performance of the proposed algorithm with other state-of-the-art Newton and Quasi-Newton approaches, showing its effectiveness and strengths with respect to the competitors.
Keynote

TU 19:00 PM3 Museo degli Innocenti

Anna Nagurney nagurney@isenberg.umass.edu

Isenberg School of Management, University of Massachusetts Amherst,
(U.S.A.)

Labor and Supply Chain Networks: It's All About People

The COVID-19 pandemic, climate change, conflicts and wars have dra-
matically illustrated the importance of labor in supply chain networks in
numerous economic sectors, from agriculture to healthcare. In this talk, I
will discuss our research on the inclusion on labor in supply chains both in
optimization and game theory frameworks to elucidate the impacts of dis-
ruptions of labor in terms of availability as well as productivity on product
flows, prices, and the objective functions of organizations, both profit and
nonprofit ones. I will also highlight what can be done to ameliorate neg-
ative impacts and will discuss the power of setting appropriate wages on
supply chain links from production and transportation to storage and the
ultimate distribution to points of demand. The use of international mi-
grants to alleviate shortages will be discussed and the impacts of the war
on Ukraine on global supply chains. The inclusion of labor in blood ser-
vice supply chains in healthcare and in humanitarian organization models
for disaster preparedness and response will also be highlighted. I will con-
clude with some of our experiences in influencing policy in the pandemic.

Keynote
# EQVA, Equilibria, variational models and applications; Invited Session

WE 10:00 AM1 001

Valerio Giuseppe Sasso sasso.1808011@studenti.uniroma1.it

Roma Tre University

Lorenzo, Lampariello, Roma Tre University; Simone, Sagratella,

Roma Tre University

*Nonsmooth Hierarchical Multi Portfolio Selection*

We focus on the case of a financial service provider having to manage different clients accounts via assigning them to multiple managers. In this multi-agent scenario, we introduce sparsity-enhancing terms in the objectives of both clients and managers. The resulting decision problem can be modeled as a hierarchical GNEP that is Jointly-Convex with nonsmooth objectives. We study the main theoretical properties of this multi-agent problem, and show that it is solvable under mild conditions.
WE 10:20 AM1 001

Mauro Passacantando mauro.passacantando@unipi.it

Department of Computer Science, University of Pisa
Raciti, Fabio, Department of Mathematics and Computer Science,
University of Catania

*A finite convergence algorithm for solving network games with strategic complements and bounded strategies*

We propose a new algorithm for solving a class of network games with strategic complements and bounded strategies. The algorithm is based on the sequential solution of linear systems of equations and we prove that it finds the Nash equilibrium of the game after a finite number of iterations. The new algorithm is then applied to a social network model of juvenile delinquency which has been investigated recently, where we also consider random perturbations of some data. Preliminary numerical results show the efficiency of the algorithm.

EQVA, Equilibria, variational models and applications; Invited
Session
WE 09:00 AM1 001

Francesco Caruso francesco.caruso@unina.it

University of Naples "Federico II"

Maria Carmela, Ceparano, University of Naples "Federico II"; Jacque-
line, Morgan, University of Naples "Federico II" and CSEF

*A general method for selecting subgame perfect Nash equilibria in
two-player Stackelberg games*

Two-player Stackelberg games may have multiple Subgame Perfect Nash Equilibria (henceforth SPNEs), especially when the optimal reaction of the follower to any choice of the leader is not always unique. In this presentation we investigate the issue of selection of SPNEs in two-player Stackelberg games by exploiting perturbations of the payoff functions of the game. To achieve such a goal, since the limit of "perturbed" SPNEs is not necessarily an SPNE of the initial game even for classic perturbations, first we show how to produce an SPNE starting from a sequence of SPNEs of perturbed games. This result allows to define a general selection method for SPNEs that can accommodate various behaviors of the players. More precisely, under mild assumptions on the data of the game we prove that perturbations relying on a Tikhonov regularization, on an adverse-to-move behaviour and on an altruistic behaviour fit the general method and we present the specific selection results associated to such perturbations. On the one hand, as regards to the Tikhonov regularization and the adverse-to-move behaviour, we extend or recover the results showed by Morgan and Patrone [Advances in Dynamic Games, 2006] and by Caruso, Ceparano and Morgan [Dyn. Games Appl., 2019]. On the other hand, concerning the altruistic behaviour, we present a new specific selection method for SPNEs based on the slightly altruistic approach introduced by De Marco and Morgan [J. Optim. Theory Appl., 2008] for simultaneous-move games. Finally, we illustrate by examples that the general method carried out under the three different "behaviours" just mentioned can select different SPNEs.

EQVA, Equilibria, variational models and applications; Invited
Session
WE 09:20 AM1 001

Giandomenico Mastroeni giandomenico.mastroeni@unipi.it

Department of Computer Science, University of Pisa, Largo B. Pontecorvo 3, 56127 - Pisa, Italy

Pellegrini, Letizia, Department of Economics, University of Verona,
Via Cantarane, 24, 37129 - Verona; Peretti, Alberto, Department
of Economics, University of Verona, Via Cantarane, 24, 37129 -
Verona, Italy

*A decomposition method for a linear problem with complementarity constraints*

We consider a linear programming problem in which a complementarity type constraint is considered in addition. The complementarity constraint in the feasible region causes the lack of the classic properties that are usually important to obtain the standard optimality conditions, as convexity and constraint qualifications. To overcome this difficulty, we propose a decomposition method of the given problem in a sequence of parameterized linear problems, that aim to force complementarity. Once we obtain an optimal solution of one of the parameterized problems, exploiting duality results, we are able to generate a suitable cut that allows us to eliminate a set of parameterized problems which are not worthwhile to be considered. The procedure continues until there are no further parameterized problems to be considered or until a feasible value of the objective function is sufficiently close to some lower bound for the optimal value. We present an example of application of the proposed technique and some computational experiments.

EQVA, Equilibria, variational models and applications; Invited
Session
WE 09:40 AM1 001

Annamaria Barbagallo annamaria.barbagallo@unina.it

Department of Mathematics and Applications R. Caccioppoli", Uni-
versity of Naples Federico II

Serena Guarino, Lo Bianco, Department of Agricultural Sciences,
University of Naples Federico II

*A general Cournot-Nash equilibrium principle and applications to the COVID-19 pandemic*

The paper deals with the study of an oligopolistic market equilib-
rium problem in which each firm produces several commodities and both
production and demand excesses occur. The equilibrium definition is pre-
sented by means of a general Cournot-Nash equilibrium principle. Such a
condition is characterized by a tensor variational inequality. Hence, the
existence and uniqueness of equilibrium solution can be established by
using theoretical results on tensor variational inequalities.
# KNAP, Knapsack Problems; Invited Session

WE 10:00 AM1 002

Ulrich Pferschy ulrich.pferschy@uni-graz.at

University of Graz

Scatamacchia, Rosario, Politecnico di Torino

## On a knapsack game

Given a standard 0-1 knapsack problem, we consider the following sequential game played by two players A and B in consecutive rounds. As in a subset sum game previously considered in the literature, the items are partitioned between the two players. In each round both players submit simultaneously one of their items to a neutral decider who chooses the more efficient item (w.r.t. profit to weight ratio) and packs it into the knapsack. The losing item can be resubmitted in a later round. We are looking for a strategy of one player, say B, who aims to maximize the total profit of its packed items, when the item set is known. It can be shown that for an arbitrary strategy of A, every strategy of B may perform arbitrarily bad. However, if A follows a list strategy, i.e. submits items according to a fixed ordering (omitting the submission of items that would violate the capacity constraint), then we can show that the best response of B will always be a list strategy of items sorted in decreasing order of efficiencies. If also the list of A is sorted in decreasing order of efficiencies, then the computation of the submitted items for such an optimal response strategy of B can be done by an Integer Linear Programming (ILP) model or by a pseudopolynomial time dynamic program. A dynamic program can also be given for the more general case of an arbitrarily sorted list of A. However, in polynomial time not even a response with constant approximation ratio can be reached. The problem seems to be more difficult, if the losing item of every round is permanently discarded.
WE 10:20 AM1 002

Laura Galli laura.galli@unipi.it

Dipartimento di Informatica, Università di Pisa
Giulia, Ansuini, Dipartimento di Matematica, Università di Pisa;
Antonio, Frangioni, Dipartimento di Informatica, Università di Pisa;
Giovanni, Nardini, Dipartimento di Ingegneria dell'Informazione, Uni-
versità di Pisa; Giovanni, Stea, Dipartimento di Ingegneria dellIn-
formazione, Università di Pisa

Bi-dimensional Assignment in 5G Periodic Scheduling

We consider a scheduling application in 5G cellular networks, where base stations serve periodic tasks by allocating conflict-free portions of the available spectrum, in order to meet their traffic demand. The problem has a combinatorial structure featuring bi-dimensional periodic allocations of resources. We consider four variants of the problem, characterized by different degrees of freedom. Two types of formulations are presented and tested on realistic data, using a general-purpose solver.

KNAP, Knapsack Problems; Invited Session
WE 09:00 AM1 002

Iskander Aliev alievi@cardiff.ac.uk

Cardiff University

*Sparse integer points in knapsack polyhedra and beyond*

We will overview recent results on the sparsity of integer points in the standard form knapsack polyhedra. Specifically, let P be a knapsack polyhedron, defined by a linear equation $ax=b$, where x is nonnegative and the vector a is integer. Suppose that P contains integer points. We are interested in estimating the minimum size of the support of an integer point in P. When P is a polytope, we establish a surprising transference result that links the sparsity with distances of integer points to the vertices of P. Perhaps unexpectedly, known bounds are weaker for unbounded knapsack polyhedra.

KNAP, Knapsack Problems; Invited Session
WE 09:20 AM1 002

Adam Letchford a.n.letchford@lancaster.ac.uk

Lancaster University

Galli, Laura, University of Pisa

Cutting Planes for the Multiple Knapsack Assignment Problem

The Multiple Knapsack Assignment Problem (MKAP) was introduced by Kataoka and Yamada in 2014. In the MKAP, we have *m* knapsacks and *n* items. The *i*-th knapsack has a capacity *c*ᵢ. The *j*-th item has a profit *p*ⱼ and a weight *w*ⱼ. Moreover, the set of items is partitioned into *r* subsets or classes. Each knapsack can contain items from at most one class. The objective is to assign each knapsack to a class, and to select a set of items of maximum total profit, such that the total weight of the items assigned to any given knapsack does not exceed the capacity of that knapsack.

The MKAP has applications in the purchasing of goods and their
subsequent transportation by air, rail or water. It includes the multiple
knapsack problem and the assignment problem as special cases. We derive
several families of cutting planes (i.e., strong valid linear inequalities) for
the MKAP. We also present some exact and heuristic separation routines
for them. Some encouraging computational results are also presented.

KNAP, Knapsack Problems; Invited Session
WE 09:40 AM1 002

Alberto Locatelli alberto.locatelli@unimore.it

University of Modena and Reggio Emilia

Cacchiani, Valentina, Alma Mater Studiorum University of Bologna;
Iori, Manuel, University of Modena and Reggio Emilia; Martello, Sil-
vano, Alma Mater Studiorum University of Bologna

Knapsack problems - An Overview of Recent Advances

A systematic research on the knapsack problem and its many variants started in the Fifties. It produced, over the next fifty years, an impres- sive number of scientific results, making this field a very relevant area of combinatorial optimization. The two seminal books devoted to this area, by Martello and Toth in 1990 and by Kellerer, Pferschy, and Pisinger in 2004, include in total about 700 bibliographic entries. In this presenta- tion, structured in two parts, we cover the developments appeared in this field after the publication of the latter volume, until Summer 2021.

Part I is devoted to problems whose goal is to optimally assign items to a single knapsack. Besides the classical knapsack problems (binary, sub- set sum, bounded, unbounded, change-making), we review problems with special constraints (setups, multiple-choice, conflicts, precedence, sharing, compartments) as well as relatively recent fields of investigation, like ro- bust and bilevel problems. Part II covers multiple, multidimensional (vec- tor and geometric), and quadratic knapsack problems, but also presents a succinct treatment of online and multiobjective knapsack problems.

The two parts are based on over 450 different papers, mostly appeared after 2004, the publication year of the latter of the two classical books specifically dedicated to these topics. Recent research has produced a good number of new exact algorithms, but there is still room for improvement on many problem variants. The publication dates of most reviewed articles (over 70% of the articles in the bibliography appeared in the last decade) indicate that all the main variants and generalizations of these problems still undergo intensive analysis and hence are attractive research areas to researchers interested in pursuing investigations in this fascinating area.

KNAP, Knapsack Problems; Invited Session
# NODAI, Numerical optimization for data analysis and imaging; Invited Session

WE 10:00 AM1 003

Cesare Molinari cecio.molinari@gmail.com

UNIGE

Mathurin Massias, Lorenzo Rosasco, Silvia Villa, Cristian Vega

*Iterative regularization for convex regularizers*

Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in modern machine learning, where it provides both a new perspective on algorithms analysis, and significant speed-ups compared to explicit regularization. In this talk, we propose and study the first iterative regularization procedure able to handle biases described by non smooth and non strongly convex functionals, prominent in low-complexity regularization. Our approach is based on a primal-dual algorithm of which we analyze convergence and stability properties, even in the case where the original problem is unfeasible. The general results are illustrated considering the special case of sparse recovery with the 1 penalty. Our theoretical results are complemented by experiments showing the computational benefits of our approach.
WE 10:20 AM1 003

Simone Rebegoldi simone.rebegoldi@unifi.it

Università di Firenze

Stefania, Bellavia, Università di Firenze; Natasa, Krejic, University
of Novi Sad; Benedetta, Morini, Università di Firenze

*Stochastic trust-region methods with subsampling for finite-sum minimization problems*

We propose some novel stochastic first-order trust-region methods with function and gradient approximations for solving finite-sum minimization problems. At each iteration, the proposed methods approximate the function and the gradient by sampling, employing adaptive sample sizes that may vary from one iteration to the other. The core idea of these methods lies in the definition of an appropriate merit function, which combines the subsampled objective function with a measure of the distance of the sample size from its maximum value. The trust-region step is indeed accepted or rejected according to whether a sufficient decrease condition on the aforementioned merit function holds or not. We investigate the convergence in probability of these methods, showing that the gradient converges to zero with probability one under some appropriate probabilistic requirements on the function and gradient estimates. Furthermore, we provide some worst-case complexity results to achieve a certain accuracy in the gradient norm. We also report numerical results on nonconvex binary classification problems, which confirm that the proposed algorithms achieve an adequate accuracy way before the maximum sample size is reached, and without requiring a problem-dependent tuning of the involved parameters.

NODAI, Numerical optimization for data analysis and imaging;
Invited Session
WE 09:00 AM1 003

Elena Morotti elena.morotti4@unibo.it

Università di Bologna

Davide, Evangelista, University of Bologna, Italy; Elena Loli, Pic-
colomini, University of Bologna, Italy

*A new converging approach for learnt optimization with applications
to imaging*

Image processing and image reconstruction are active research fields
that have been recently revolutionized by the advent of convolutional neu-
ral networks, as deep learning-based schemes often yield superior results
than classical optimization approaches. However, their ability to actually
compute the inverse problem solution is still discussed in the literature.
This talk presents a new scheme, called RISING, embedding deep learn-
ing tools in an optimization approach. Numerical results and theoretical
aspects will be discussed, showing that RISING preserves the convergence
properties of iterative solvers and also exploits the accuracy and flexibil-
ity of data-driven approaches, while fitting constraints due to large-scale
problem applications.

NODAI, Numerical optimization for data analysis and imaging;
Invited Session
WE 09:20 AM1 003

Margherita Porcelli margherita.porcelli@unibo.it

University of Bologna

Domitilla, Brandoni, University of Bologna; Valeria, Simoncini, Uni-
versity of Bologna

*A spectral PALM algorithm for Dictionary Learning*

Dictionary Learning (DL) is one of the leading sparsity promoting
techniques in the context of image classification, where the "dictionary"
matrix D of images and the sparse matrix X are determined so as to rep-
resent a redundant image dataset. The resulting constrained optimization
problem is nonconvex and non-smooth, providing several computational
challenges for its solution. To preserve multidimensional data features,
various tensor DL formulations have been introduced, adding to the prob-
lem complexity. We present a new alternating algorithm for the solution
of the DL problem both in the matrix and tensor frameworks; in the
latter case a new formulation based on Tensor-Train decompositions is
also introduced. The new method belongs to the Proximal Alternating
Linearized Minimization (PALM) algorithmic family, with the inclusion
of second order information to enhance efficiency. The numerical perfor-
mance of the new method will be discussed on the image classification of
several benchmark datasets.

NODAI, Numerical optimization for data analysis and imaging;
Invited Session
WE 09:40 AM1 003

Monica Pragliola monica.pragliola@unina.it

University of Naples Federico II
di Serafino, Daniela, University of Naples Federico II

*Automatic parameter selection for the TGV regularizer in image restoration under Poisson noise*

We address the image restoration problem under Poisson noise corrup-
tion. The Kullback-Leibler divergence, which is typically adopted in the
variational framework as data fidelity term in this case, is coupled with the
second-order Total Generalized Variation (TGV²). The TGV² regularizer
is known to be capable of preserving both smooth and piece-wise constant
features in the image, however its behavior is subject to a suitable set-
ting of the parameters arising in its expression. We propose a hierarchical
Bayesian formulation of the original problem coupled with a Maximum
A Posteriori estimation approach, according to which the unknown image
and parameters can be jointly and automatically estimated by minimizing
a given cost functional. The minimization problem is tackled via a scheme
based on the Alternating Direction Method of Multipliers, which also in-
corporates a procedure for the automatic selection of the regularization
parameter by means of a popular discrepancy principle. Computational
results show the effectiveness of our proposal.

NODAI, Numerical optimization for data analysis and imaging;
Invited Session
# OPTSM, Optimization in Public Transport and Shared Mobility; Invited Session

WE 10:00 AM1 Auditorium A

Marcella Samà marcella.sama@uniroma3.it

Roma Tre University

Meloni, Carlo, Sapienza Università di Roma; Pranzo, Marco, Università di Siena

*Risk evaluation considering uncertain dwell times of real-time Railway Traffic Management solutions*

While trains travel in railway networks, disturbances may arise and corrective decisions to minimize delay propagation may be necessary to solve conflicting track requests. This problem is known in the literature as the real-time Railway Traffic Management Problem (rtRTMP) and its solutions represent plans of operations that minimize delay propagation due to unexpected disturbances. However, uncertainty may still affect such plans and their expected quality. We propose a new approach for assessing the risk of onset or worsening of delays associated to an rtRTMP solution when dwell times are uncertain and only an interval representation of them is known to the scheduler. To this aim, the Conditional-Value-at-Risk of the maximum train delay is adopted as risk index. We address both modeling and computational issues, developing and testing a graph-based model to use with an innovative numerical method to obtain a real-time risk evaluation for rtRTMP solutions. The proposed approach is applied on a real case study analyzing the effects of uncertainties of different severity. Promising computational results enable to use the methodology to deal with the rtRTMP taking into account the uncertainty on the involved activities and the risk attitude of the decision-makers at operational level.
WE 09:00 AM1 Auditorium A

Lorenzo Castelli castelli@units.it

University of Trieste

Brugnara, Irene, University of Trieste; Pesenti, Raffaele, University

Ca' Foscari of Venice

*A distributed market mechanism for an efficient and equitable resource assignment*

Air traffic resources consisting in airports and airspace volumes have a
limited capacity in terms of number of aircraft that can enter the resource
in a given period of time. The factor determining capacity is the amount
of traffic that can be safely handled by air traffic controllers.

In the current European Air Traffic Flow Management (ATFM) sys-
tem, when an imbalance between traffic demand and available capacity is
foreseen in an airport or airspace volume, the Network Manager can im-
pose an ATFM regulation, which limits the rate of aircraft that can enter
the regulated resource in a given period of time. This ATFM measure
is achieved by delaying the departure of flights from their origin airport.
ATFM delays are imposed to flights through an ATFM slot, a 15-minute
tolerance time window that flights have to comply with for departure. In
the case a flight is subject to multiple regulations, the delay on the most
constraining regulation is applied.

In the current system, ATFM slots are assigned to flights according to
a First Come First Served (FPFS) principle. Since ATFM delays represent
a cost for airlines, remarkable cost savings are possible by considering a
different assignment of ATFM slots which takes into account the different
impact that delays have on costs for airlines.

We introduce a model which extends the concept of ATFM slot to the
concept of time window, allowing to effectively deal with a network of
interacting regulations. The model aims at minimising the total cost of
delay of a time window assignment to flights and is based on an integer
programming problem. It consists in a market-based mechanism between
flights and the Network Manager to trade time windows, which fulfill
the properties of individual rationality (every participating airline has
a non-negative profit from the mechanism) and weak budget-balanced
(the mechanism requires no external subsidisation). Equity is guaranteed
by considering the FPFS assignment as an endowment guaranteed to all
flights and allocated for free.

The proposed market mechanism can be implemented in a distributed
manner which prevents the disclosure of confidential information by air-
lines, and is based on the Lagrangian relaxation of the integer optimisation
problem, solved through the subgradient algorithm.

We present some computational experiments conducted to test the
model on some real instances of air traffic data.

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
WE 09:20 AM1 Auditorium A

Valentina Morandi VALENTINA.MORANDI1@UNIBS.IT

Università degli Studi di Brescia
Enico, Angelelli, Università degli Studi di Brescia; Maria Grazia, Speranza, Università degli Studi di Brescia

*Optimization models for fair horizontal collaboration in demand- responsive transportation*

The advances in information and communication technology are chang-
ing the way people move. Companies that offer demand-responsive trans-
portation services have the opportunity to reduce their costs and increase
their revenues through collaboration, while at the same time reducing
the environmental impact of their operations. We consider the case of
companies, offering a shared taxi service, that are involved in horizon-
tal collaboration and present mixed integer linear programming (MILP)
models for the optimization of their routes that embed constraints aimed
at balancing the workload exchange. These constraints bound the imbal-
ance in terms of travelled time and/or served customers to be less than
thresholds agreed in advance by the companies. We also present a heuris-
tic algorithm for the solution of the MILP models. The computational
results show the good performance of the heuristic and the benefits, to
each company, of the collaboration.

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
WE 09:40 AM1 Auditorium A

Recipient of the Verizon Connect Italy grant

Marta Leonina Tessitore marta.tessitore@uniroma3.it

Roma Tre University

Sartor, Giorgio, SINTEF; Mannino, Carlo, SINTEF; Samà, Mar-
cella, Roma Tre University; Pacciarelli, Dario, Roma Tre University

Identifying Railway Timetable Fragility

In dense railway traffic, the delay of a single train may propagate in a domino effect over the entire network. During the last decade, several approaches have been proposed to measure and improve timetable robustness. Robustness usually refers to the timetables ability to restore punctuality following disturbed traffic situations and therefore prevent delays from spreading over the network. Existing robustness measures, however, are not always useful for perfectly understanding how the robustness of a timetable could be increased. The challenge we are trying to tackle is therefore to identify the weaknesses of a timetable, i.e., the sections of each train schedule that are more likely to generate knock-on delays. In order to do this, we developed a MILP model that computes the maximum delay a train can incur in each section of its schedule such that all trains will still arrive at their final station on-time. We define a section of a schedule as fragile if this maximum allowed delay is less than a few minutes. The model considers the optimal dispatching of trains rather than using a simulation tool based on heuristic algorithms as it is common in robustness related work. The model is based on the work of Lamorgese and Mannino (2015) for practical real-time train scheduling, which employs an exact decomposition approach combined with a row-generation scheme. This newly introduced concept of fragility is complementary to that of robustness, in the sense that it can help route planners identify which parts of a timetable to focus on for reducing knock-on delays. We test this approach on real-life scenarios from a busy railway line in Norway.

[1] Lamorgese, L., Mannino, C., 2015. An Exact Decomposition Approach for the Real-Time Train Dispatching Problem. Operations Research, 63(1), 48-64 [2] Lusby, R. M., Larsen, J., Bull, S., 2018. A Survey on Robustness in Railway Planning. European Journal of Operational Research, 266(1), 1-15
# Global Optimization; Invited Session

WE 10:00 AM1 Auditorium B

Leo Liberti liberti@lix.polytechnique.fr

LIX CNRS Ecole Polytechnique, Institut Polytechnique de Paris Benedetto, Manca, Dip. Matematica and Informatica, Universita degli Studi di Cagliari; Pierre-Louis, Poirion, RIKEN Center for Advanced Intelligence Project, Tokyo, Japan; Antoine, Oustry, LIX CNRS Ecole Polytechnique, Institut Polytechnique de Paris

*Random projections for semidefinite programming*

Random projections can reduce the dimensionality of point sets while keeping approximate congruence. Applying random projections to optimization problems raises many theoretical and computational issues. Most of the theoretical issues in the application of random projections to conic programming were addressed in [1]. This paper focuses on semidefinite programming.
WE 09:00 AM1 Auditorium B

Filippo Pecci f.pecci14@imperial.ac.uk

Imperial College London

Stoianov, Ivan, Imperial College London

*A global optimization framework for resilient water distribution networks*

Resilience and sustainability are key objectives for critical infrastructure systems, which society relies upon for water, energy, and food supply. Optimization has the potential to play a vital role in supporting the design and operation of next generation infrastructure systems, improving resilience, reducing CO2 emissions, and efficiently integrating renewable energy sources. The complexity of these large interconnected systems has grown to the level that modelling and optimization are needed to improve their resilience and sustainability in face of climate change, urbanisation, and fast growing population.

This is especially relevant for optimal design-for-control of nonlinear network systems, where the flow through the network is driven by a potential, and the potential loss across a link is a nonlinear function of the flow rate. These optimization problems combine continuous decision variables (e.g. pipe flow rates), with discrete decision variables (e.g. location of control actuators). Together with nonconvex constraints modelling systems dynamics, they result in large-scale Mixed Integer Nonlinear Programs (MINLPs). Despite significant progress in optimization algorithms and availability of computational power, it is still not possible to solve most MINLPs that arise when considering large and complex nonlinear network systems.

Water distribution networks (WDNs) are critical infrastructure facing unprecedented challenges due to increasing water demand, climate change, and more stringent economic and environmental constraints. The main operational objectives for water utilities include the reduction of water leaks, and the reduction of probability of pipe bursts. These objectives are achieved through pressure management, which is implemented by installing and operating pressure control valves. To benefit from advances in technological, modelling, and control solutions, it is necessary to simultaneously optimize both valve locations and their operational settings. The problem of optimal placement and operation of pressure control valves in WDNs belongs to the framework of optimal design-for-control of non-linear network systems. Hence, it poses significant computational challenges to optimization solvers.

The results reported in this work show that off-the-shelf global optimization solvers can fail to compute feasible solutions for this optimal design-for-control problem. Therefore, we propose a tailored branch and bound algorithm relying on polyhedral relaxations of the potential loss constraints, optimization-based bound-tightening, and heuristics to gen-

Global Optimization; Invited Session
erate good quality feasible solutions with bounds on their level of sub-optimality. The developed algorithm is implemented to optimally place and operate PCVs to minimize different operational objectives, including Average Zone Pressure (AZP) and Pressure Variability with the Zone (PVZ). The tailored branch and bound algorithm enables the joint optimization of location and operational settings of pressure control valves in WDNs. This allows water utilities to implement integrated and efficient schemes for pressure management, in order to minimize leakage and probability of pipe bursts. Finally, we discuss further work and possible extensions to the framework of multiobjective optimization and water quality management.

Global Optimization; Invited Session
WE 09:20 AM1 Auditorium B

Immanuel Bomze immanuel.bomze@univie.ac.at

University of Vienna

Rinaldi, Francesco, Univ.Padova; Zeffiro, Damiano, Univ.Padova

Fast Cluster Detection in Networks by First Order Optimization

Cluster detection plays a fundamental role in the analysis of data. In this paper, we focus on the use of *s*-defective clique models for network-based cluster detection and propose a nonlinear optimization approach that efficiently handles those models in practice. In particular, we introduce an equivalent continuous formulation for the problem under analysis, and we analyze some tailored variants of the FrankWolfe algorithm that enable us to quickly find maximal *s*-defective cliques. The good practical behavior of those algorithmic tools, which is closely connected to their support identification properties, makes them very appealing in practical applications. The reported numerical results clearly show the effectiveness of the proposed approach.
WE 09:40 AM1 Auditorium B

Marco Locatelli marco.locatelli@unipr.it

Università degli Studi di Parma
Consolini, Luca, Università degli Studi di Parma

Sharp and fast bounds for the Celis-Dennis-Tapia problem

In the Celis-Dennis-Tapia (CDT) problem a quadratic function is min-
imized over a region defined by two strictly convex quadratic constraints.
Recently, it has been proved that the problem can be solved in polynomial
time. However, all known polynomial-time algorithms are computation-
ally expensive, since the degree of the polynomial in the complexity results
is rather high. Moerover, differently from other quadratic problems such
as the classical trust region problem or the trust region problem with
an additional linear inequality, no exact convex relaxation for the CDT
problem is known.

In this work we re-derive a necessary and sufficient optimality con-
dition for the exactness of the dual Lagrangian bound (equivalent to the
Shor relaxation bound in this case). Starting from such condition, we pro-
pose to strengthen the dual Lagrangian bound by adding one or two linear
cuts to the Lagrangian relaxation. Such cuts are obtained from support-
ing hyperplanes of one of the two constraints. Thus, they are redundant
for the original problem, but they are not for the Lagrangian relaxation.
For the case of a single cut we also propose a procedure to detect the
best possible cut, i.e., the one delivering the best possible bound. Inter-
estingly, such best bound is computationally equivalent to the SOC-RLT
bound proposed in [1], although up to now we do not have a theoretical
proof of equivalence.

The computational experiments show that the new bounds are effective
and require limited computing times. In particular, one of the proposed
bounds is exact for all but one of the 212 hard instances of the CDT
problem presented in [1].

[1] S.Burer, K.M. Anstreicher, Second-oder-cone constraints for ex-
tended trust-region subproblems, SIAM J. Optim., 23(1), 432-451 (2013)
RAVIEP, Recent Advances in Variational Inequal-
ities and Equilibrium Problems; Invited Session

WE 11:30 AM2 001

Maria Bernadette Donato mbdonato@unime.it

Department of Economics, University of Messina
Villanacci, Antonio, Department of Economics and Management,
University of Firenze

*Variational inequalities, maximal elements and economic equilib-
rium problems*

Our main goal is to provide conditions under which the solution sets
to a maximal problem and to a generalized variational inequality prob-
lem coincide and are nonempty. In choice theory, individual actors are
assumed to have preferences on a set of alternatives, i.e., a binary relation
on a choice set. Individuals choose a subset of the choice set using such
preferences. The preference relation is often assumed to be transitive and
complete. In the present talk, we consider the case of preferences without
completeness and transitivity. In this context, the individual look for an
element in the choice set which is not strictly preferred by any other ele-
ment in the set, i.e., a maximal element. The way we use to find maximal
elements is to follow a variational inequality approach. Finally, we apply
the obtained results to get a proof of the existence of equilibria in general
equilibrium models.
WE 11:50 AM2 001

Daniele Sciacca daniele.sciacca@unipa.it

University of Catania

Colajanni, Gabriella, University of Catania; Daniele, Patrizia, Uni-
versity of Catania; Nagurney, Anna, 2Department of Operations and
Information Management, Isenberg School of Management, Univer-
sity of Massachussets, Department of Electrical and Computer En-
gineering, University of Hartford

*Disaster Management with UAVs and 5G technology: a Three-Stage Stochastic network-based Optimization Model*

In a disaster situation, whether natural or man-made, slow-onset or
sudden-onset, an efficient and efficacious management is paramount and
can assist in the saving of lives, the reduction of pain and suffering, and
the protection and restoration of infrastructure. 5G technology and Un-
manned Aerial Vehicles (UAVs) have emerged as powerful tools for dis-
aster management which allow service providers and decision-makers to
restore connectivity and provide much needed services in disaster areas.
In this talk, we propose a three-stage stochastic optimization model in
which each of the three stages represents a phase of disaster manage-
ment: the preparedness, the response, and the recovery/reconstruction
phase. Furthermore, managers need to consider multiple disaster scenar-
ios with different probabilities of occurrence so as to be able to minimize
the potential losses. The optimization model is based on a multi-level
network made up of users and devices on the ground, which require 5G
services, the controller UAVs, which handle requests for services, and a
fleet of UAVs, which execute the services. The proposed model allows
providers to satisfy service requests (favoring those with higher priority)
while minimizing the overall cost and by determining the optimal flows
and the optimal management of additional resources. A variational for-
mulation of the proposed optimization model, ensuring the existence of
a solution, and a numerical example, validating the effectiveness of the
proposed model, are provided.
WE 12:10 AM2 001

Sergio Grammatico s.grammatico@tudelft.nl

Delft University of Technology

*Generalised Nash equilibrium seeking under partial information*

We consider the generalised Nash equilibrium (GNE) problem under
partial-decision information, i.e., where each player can only observe the
decisions of its neighbours, while its cost function possibly depends on the
actions of some other players. For this class of equilibrium problems, we
study fully distributed, proximal-point and projected-pseudo-gradient al-
gorithms. Finally, we discuss the numerical performance of our algorithms
that can be accelerated via over-relaxation and inertial schemes.
WE 12:30 AM2 001

Jacqueline Morgan morgan@unina.it

Department of Economics and Statistics & CSEF, University of
Naples Federico II

M.Beatrice, Lignola, Department of Mathematics and Applications

R. Caccioppoli University of Naples Federico II

Viscosity solutions in multi-leader-common-follower games

Two-stage games with multiple leaders having pessimistic behavior and one common follower are considered. These games may fail to have pessimistic solutions, even if the leader payoffs are linear and the optimal reaction of the follower to the leaders strategies is unique. In a suitable class of such games, approximate and viscosity solutions are introduced and are proven to exist under appropriate conditions, in line with the results obtained by the authors in J. Optim. Theory Appl., 173 (2017) for one-leader-one-follower games with a pessimistic leader, also called weak Stackelberg games or pessimistic bilevel optimization problems.
Finance; Contributed Session

WE 11:30 AM2 002

Adolfo Hilario-Caballero ahilario@isa.upv.es

Universitat Politècnica de València

Ana García-Bernabeu (UPV), José Vicente Salcedo (UPV), David

Pla-Santamaria (UPV)

*A preference directions-based approach to integrate sustainability in portfolio selection*

This contribution develops a new proposal to include investor; pref-
erences in both the efficient frontier estimation and the decision-making
phase using the concept of preference directions. In the optimization phase
of a portfolio selection problem, sustainability criteria or ESG criteria are
integrated as a third objective using the elitist algorithm ev-MOGA. The
advantage of this algorithm is that it generates a uniformly distributed effi-
cient surface. By including the third objective the problem of determining
the preferred portfolio is transported to the space of three dimensions. In
this context, the investors optimal portfolio is the most preferred risk/re-
turn/ESG trade-off in the mean-variance-ESG surface. To include the
investors preferences in the optimal portfolio construction process, two
ways can be chosen: (i) A priori: the optimization problem is redefined
at the efficient surface estimation stage by including the preference direc-
tions without the need to modify the algorithm; (ii) A posteriori: at the
decision-making stage the preference directions change the way the Eu-
clidean norm (distance between the ideal and the frontier) is calculated.
As a result, the region of interest is reduced and refocused in a way that
facilitates decision-making for the nvestor. Keywords: Sustainable in-
vestments, Decision-maker39;s preferences, Multiobjective optimization,
MOEAs.
WE 11:50 AM2 002

Eduardo Pipicelli eduardo.pipicelli@unina.it

Department of Industrial Engineering, University of Naples Federico
II

S., Baldassarre, Department of Industrial Engineering, University
of Naples Federico II; G., Bruno, Department of Industrial Engi-
neering, University of Naples Federico II; M., Cavola, Department
of Industrial Engineering, University of Naples Federico II

*A mathematical model to locate Services of General Economic Interest*

Services of General Economic Interest (SGEI) are services of public
interest whose provision is ruled by public authorities to guarantee ac-
cessibility levels for users and fair competition among service providers.
Therefore, locating SGEI in a given territory implies the definition of
adequate criteria driving the decision-making process. In this context,
Facility Location Models (FLMs) can play a crucial role as a decision
support tool to simulate regulatory frameworks and identify practical so-
lutions. In this work, we propose a mathematical model for the location of
such services, including constraints about users spatial accessibility while
considering a dispersion criterion to ensure fair market competition. We
apply the model to a real problem concerning the locations of pharmacies
in the city of Pamplona (Navarre, Spain). The obtained results show the
capability of the model to produce meaningful scenarios that can support
the definition of appropriate regulatory frameworks.
WE 12:10 AM2 002

Ana Garcia-Bernabeu angarber@upv.es

Universitat Politecnica de Valencia
Adolfo, Hilario-Caballero, Universitat Politecnica de Valencia; José
Vicente, Salcedo, Universitat Politecnica de Valencia; Francisco,
Salas-Molina, Universitat Politecnica de Valencia

Approaches to ESG - Integration in Portfolio Optimization using MOEAs

Against a backdrop of growing collective awareness of sustainability, the financial sector plays a key role in aligning financial flows with a path towards sustainable development. In this research, we focus on the process of integrating environmental, social, and governance (ESG) criteria, which will lead to a better reorientation of investments towards socially and environmentally useful projects. With this aim, we approach the ESG-Integration problem in portfolio selection using a recently proposed evolutionary multiobjective optimization procedure called evMOGA. This new approach significantly improves over exact methods and allows a better assessment of financial and ESG criteria tradeoffs. As an application example, we compute the M-V-ESG non-dominated surface for ESG motivated investors who want to assess the tradeoffs among the three criteria.
# NODAI, Numerical optimization for data analysis and imaging; Invited Session

WE 11:30 AM2 003

Ambra Catozzi ambra.catozzi@unipr.it

Università degli Studi di Parma
Benfenati, Alessandro, Università di Milano

*Bacterial Colonies Segmentation via Variational Approaches*

Digital image processing can be a crucial tool to automate and improve the analysis of plate culture of microorganisms, such as bacteria, molds and fungi. After taking a sample from the investigated environment, the main objective is to study its development within a specific growth medium in potential colonies. The number of plates to examine is usually large, hence the costs in terms of time and resources grows fast; we propose to combine image segmentation techniques with mathematical tools, such as the Mumford-Shah or Blake-Zisserman functionals (see Numerical minimization of a second-order functional for image segmentation, M. Zanetti, V. Ruggiero. M. Miranda, 2016), for the development of an automatic colonies detector. A possible dataset is composed of RGB images of plates; a pre-processing phase on the original data enables to crop the uninteresting parts of an image and to enhance the contrast without losing any significant information or properties, reducing the computational time. Thus, a variational approach enables to highlight the edges in the image, by identifying colonies of microorganisms with respect to the whole plate. Furthermore, the performance of the proposed approach is evaluated on a set of real images with respect to state-of-the-art techniques (see A comprehensive review of image analysis methods for microorganism counting: from classical image processing to deep learning approaches, J. Zhang et al., 2021). Session: "Numerical optimization for data analysis and imaging" [NODAI].
WE 11:50 AM2 003

Francesco Colibazzi francesco.colibazzi2@unibo.it

University of Bologna

Lazzaro, Damiana, University of Bologna; Morigi, Serena, University of Bologna; Samorè, Andrea, University of Bologna

*Learning regularized Gauss-Newton methods*

We consider variational networks for a class of nonlinear-ill-posed least squares inverse problems. These problems are addressed by regularized Gauss-Newton type optimization algorithms where the regularization is learned by a neural network. Two different data-driven approaches will be investigated. First, we present a learned-regularizer integrated into an unrolled Gauss-Newton network. As an alternative approach, we derive a proximal regularized quasi-Newton (PRQN) method and we unfold the PRQN into a deep network which consists of a cascade of multiple proximal mappings. Therefore the proximal operator is learned directly through a variable metric denoiser network. As a practical application, we show how our methods have been successfully applied to solve the parameter identification problem in elliptic PDEs, such as the nonlinear Electrical Impedance Tomography inverse problem.

NODAI, Numerical optimization for data analysis and imaging;
Invited Session
WE 12:10 AM2 003

Giorgia Franchini giorgia.franchini@unimore.it

UNIMORE

Porta, Federica, UNIMORE; Ruggiero, Valeria, UNIFE; Trombini, Ilaria, UNIPR

*A line search based proximal stochastic gradient algorithm with dynamical variance reduction for finite-sum optimization problems*

Many optimization problems arising from machine learning applica-
tions can be cast as the minimization of a regularized finite-sum. When
dealing with large-scale machine learning issues, the computation of the
full gradient of the finite-sum functional can be prohibitively expensive.
For this reason, proximal stochastic gradient methods have been exten-
sively studied in the optimization area in the last decades. It is well
known in the literature that a proper strategy to select the hyperparam-
eters of the method (i.e., the set of parameters a-priori selected) and, in
particular, the steplength and the mini batch size is needed to guarantee
convergence properties and good practical performance. In this work we
develop a proximal stochastic gradient algorithm which is based on two
main ingredients: the steplength is automatically selected by means of a
proper line search procedure and the variance of the stochastic gradients
is dynamically reduced along the iterative procedure through an adaptive
subsampling strategy. No need of periodical full gradient computation is
required. An extensive numerical experimentation in training a binary
classifier highlights that the proposed approach appears robust with re-
spect to the setting of the hyperparameters and competitive compared to
state-of-the-art methods.

NODAI, Numerical optimization for data analysis and imaging;
Invited Session
WE 12:30 AM2 003

Recipient of the Verizon Connect Italy grant

Marta Lazzaretti marta.lazzaretti@edu.unige.it

DIMA, Università di Genova - Lab I3S, UCA CNRS INRIA
Estatico, Claudio, DIMA Università di Genova; Calatroni, Luca,
Lab I3S UCA CNRS INRIA

*Iterative regularisation and modular-proximal algorithms in $L^{p^{(\cdot)}}$ spaces for imaging problems*

Solving imaging inverse problems by means of a variational approach requires some crucial choices: the modelling of the data-fidelity term whose structural form depends on the noise statistics, the use of a suitable regularisation (penalty) term typically promoting sparsity of the solution in some sense, and, when the formulation is given in an infinite-dimensional framework, the solution space. The latter choice is often overlooked due to the technical challenges it poses w.r.t. to the underlying metric and topological properties. However, it might have a critical effect on the quality of the computed solution due to its 'implicit' regularisation properties. We focus our attention on the non-standard choice of variable exponent Lebesgue spaces $L^{p^{(\cdot)}}$ as solution spaces. Such Banach spaces are defined in terms of a point-wise variable exponent inducing a specific shift-variant norm and intrinsic space-variant properties. Choosing $L^{p^{(\cdot)}}$ as a solution space corresponds to promote a spatially adaptive solution smoothness. We first show how this modelling improves the accuracy of the reconstructions with respect to standard $L^2$ and $L^p$ spaces with a constant exponent $p \in (1,2)$ by considering at first the so-called dual method, e.g. an iterative regularisation (Landweber) algorithm suited to the Banach spaces scenario, minimising the data term.

We then consider more complex, structured, problems, defined in terms of the sum of a smooth and convex fidelity, and a proper, l.s.c., convex, typically non-smooth penalty. Optimisation problems of this form are frequently encountered in signal and image processing and usually tackled with forward-backward splitting algorithms, where a gradient descent step w.r.t. the smooth part is alternated with a proximal step associated to the non-smooth part. The use of analogous strategies for minimising composite functionals in $L^{p^{(\cdot)}}$ is more challenging since due to the Banach setting, which requires the use of new definition of both gradient and proximal steps due to the lack of the Riesz identification between the solution space and its dual. To do so, we propose a proximal gradient algorithm where the gradient step is performed in the dual space and the proximal step, rather than depending on the natural but non-separable $L^{p^{(\cdot)}}$ norm, is defined in terms of its separable modular function, which allows for the

NODAI, Numerical optimization for data analysis and imaging;
Invited Session
efficient computation of algorithmic iterates, and by means of a Bregman-
like distance, which is more suitable to the Banach space geometry rather
than the usual $L^2$-norm. We analyse the algorithms convergence rate in
function values, showing its dependence on the smoothness of both the
functional and the space. Some numerical tests highlight the flexibility
of the space $L^{p(\cdot)}$ for exemplar deconvolution and mixed noise removal
problems are reported, showing improved reconstruction accuracy, faster
convergence speed and reduced computational costs of the proposed algo-
rithm in comparison with analogous ones defined in standard $L^p$ spaces.
# OPTSM, Optimization in Public Transport and Shared Mobility; Invited Session

WE 11:30 AM2 Auditorium A

Federico Naldini federico.naldini@univ-eiffel.fr

COSYS-ESTAS Université Gustave Eiffel

Pellegrini, Paola, COSYS-LEOST Université Gustave Eiffel; Rodriguez, Joaquin, COSYS-ESTAS Université Gustave Eiffel

*Practical deployment of real-time railway traffic management algorithms: impact of process meta-parameters*

Railway traffic is often afflicted by unforeseen perturbations causing so-called primary delays. As a result, impacted trains utilize some track sections later than planned. This may impact neighboring trains in that may not be allowed to proceed at their planned speed due to the onset of conflicts triggering restrictive signals. The consequent unplanned slow-downs or stops may cause delay propagation, as secondary delay. Dispatchers can counteract this by quick and effective train re-timing, re-routing and re-ordering decisions. In the literature, this is known as the real-time Railway Traffic Management Problem (rtRTMP). RECIFE-MILP is an optimization algorithm for the rtRTMP that may be used as a decision support tool for dispatchers. In the literature, the impact of rtRTMP algorithms on traffic is seldom assessed considering an actual possible deployment framework. This can be done considering a railway simulator to replace reality and using an optimization algorithm for making traffic management decisions. To further increase the realism of the assessment, a closed-loop framework can be set up, in which optimization is repeated periodically to take into account the actual traffic state as time evolves. In this work, we assess the performance of RECIFE-MILP when used in closed-loop with a state-of-the-art railway simulator named Open-Track. We consider various infrastructures modeled microscopically, real timetables and realistic traffic perturbations. In particular, we perform a sensitivity analysis on the most relevant closed-loop meta-parameters, to understand their impact on the quality of the traffic management decisions implemented over time. For example, we vary the time horizon concerning the decisions to be taken and the frequency at which a new rtRTMP solution is to be computed. The results show how the best meta-parameter configuration depends on the characteristics of the case study considered.

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
WE 11:50 AM2 Auditorium A

Giorgio Sartor giorgio.sartor@sintef.no

SINTEF

Kloster, Oddvar, SINTEF; Luteberget, Bjørnar, SINTEF; Mannino, Carlo, SINTEF; Schulz, Christian, SINTEF

*Large-scale real-time dispatching in the Greater Oslo area*

We present the results of a 4 year project aimed at developing a prototype for large-scale real-time dispatching in the Greater Oslo area, which includes all lines incident to Oslo central station up to a 100 km radius. The prototype was developed in collaboration with Bane NOR, the Norwegian railway infrastructure manager, which also provided us with real-time information about train positions and timetables. The underlying algorithm is based on a MILP approach introduced in Lamorgese and Mannino (2015), then extended in Bach et al. (2019), and here extensively updated to support the additional complexity of the Greater Oslo area. It combines an exact micro-macro decomposition approach with a sophisticated column-and-row-generation scheme. The model is able to consider almost every action a human dispatcher is able to perform, such as rerouting in stations, overtakes, and slow-downs. And it takes into consideration almost all operational constraints, including safety margins, platform lengths, slopes, train weight, etc.

The prototype consists of a decision support tool available via web GUI to train dispatchers seated at Oslo. The tool receives real-time information about the current traffic situation and displays the optimal future schedules for all trains for the next 6 hours through an interactive train graph. Dispatchers are allowed to interact with the tool by providing specific constraints or preferences, and therefore test what-if scenarios. For example, if a platform in a station is not available for the rest of the day due to a signal failure, the algorithm is able to adapt and recompute all future schedules in a matter of seconds.

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
WE 12:10 AM2 Auditorium A

Xiajie Yi xiajie.yi@railenium.eu

IRT Railenium

Marlière, Grégory, Univ. Gustave Eiffel; Pellegrini, Paola, Univ. Gustave Eiffel; Rodriguez, Joaquin, Univ. Gustave Eiffel; Pesenti, Raffaele, Università Ca Foscari Venezia

*Coordinated perturbation management in railway traffic*

Due to perturbations (i.e., an unexpected, degraded operation, technical failures, etc), a common problem faced by traffic controllers is that timetables for trains are not necessarily operated as they were initially planned. This paper deals with a coordinated train rerouting and rescheduling problem to minimise the impact of such a perturbation, e.g., to minimise delay propagation. This problem is often faced by traffic controllers at regional railway control centres. The problem of efficiently rerouting and rescheduling trains is known in the literature as real-time Railway Traffic Management Problem (rtRTMP). Typically, the railway network is divided into non-overlapping control areas. Regional control centres coordinate several control areas, and a coordinator manages each control centre. In this contribution, we call a track connecting between two control areas a border section. If a multiple track line connects two control areas, we represent them as multiple border sections. Besides, a border section can be traversed in either one or two directions. In many control centres, the real-time railway traffic management is organised into two decision levels. At a higher level, a coordinator makes decisions on the overall network making abstraction of operational details. At the lower level, a dispatcher manages train schedules and routes in his own control area to fit with coordinator decisions. Indeed, to optimise the overall system performance and ensure decision coherence, the coordinator may impose constraints to dispatchers. We hereby refer to the problems tackled at the lower and higher levels as dispatching and coordination problems, respectively. As far as we are aware, only few papers focus on the coordination of traffic management across different control areas. In this study, we propose an iterative algorithm to solve the coordinated traffic management problem in networks including multiple control areas.

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
WE 12:30 AM2 Auditorium A

Joaquin Rodriguez joaquin.rodriguez@univ-eiffel.fr

Université Gustave Eiffel

Ferrari, Alessandro, Università di Udine; Sobieraj Richard, Sonia,

Université Gustave Eiffel; Pellegrini, Paola, Université Gustave Eif-
fel

*Train-based instance reformulation in real-time Railway Traffic Management*

Railway timetables are designed to allow smooth traffic operations. Nonetheless, when unexpected events occur delays may arise, and timetables may have to be modified to limit their propagation: trains may be rerouted or may have to respect specific passing orders in critical parts of the network. The real-time Railway Traffic Management Problem (rtRTMP) is the problem of minimizing the impact of unexpected events through rerouting and rescheduling. In the literature, several optimization algorithms have been proposed for tackling the rtRTMP (Cacchiani et al., 2012). In its classic representation, an instance of this problem includes information on the network topology, the timetable, and the expected traffic perturbation. Depending on network topology and train characteristics, a large number of alternative routes may be available for each train, and this typically has a negative impact on the performance of rtRTMP algorithms. In this work, we propose and assess a novel way for modeling instances aiming to allow algorithms to better deal with large numbers of rerouting possibilities. The novel modeling is based on a train-based instance reformulation. The motivation for this decomposition is the observation that train alternative routes often partially overlap. In the novel modeling, we split single trains with several partially overlapping routes into multiple trains with shorter and non-overlapping routes. The multiple trains deriving from a single split one are modeled as different trains performed by the same rolling-stock. Hence, algorithms will impose the route of each train to depart where the route of the previous train arrives, and departure and arrival times to be coherent. For example, consider a network including three stations with four platforms each, and a single track connecting stations. A train allowed to stop at any of these platforms will have 64 alternative routes. Of these routes, 16 will overlap in the first part as they will be passing through the first platform at the first station. Three disjoint sets of overlapping routes can also be defined for the other three platforms at the first station. In the novel modeling, we split this train into four new ones: the first goes from the origin to the first station, the second from the first to the second station, and so on. The first train will have four alternative routes, one reaching each platform. The second train will have 16, to connect each platform of the first station to each platform of the second. The third and the fourth trains will have 16 and 4 routes respectively. In a thorough experimental analysis

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
based on French case studies with different network and timetable char-
acteristics, we assess the impact of the train-based instance reformulation
when solving instances through RECIFE-MILP (Pellegrini et al., 2015),
a state-of-the-art rtRTMP algorithm. We show that the novel modeling
never worsens the algorithm performance and strongly improves them in
instances with specific characteristics.

[1] V. Cacchiani, D. Huisman, M. Kidd, L. Kroon, P. Toth, L. Veelen-
turf and J. Wagenaar, 2014. An overview of recovery models and algo-
rithms for real-time railway rescheduling. Transp. Res. Part B Methodol.
63, 1537. [2] P. Pellegrini, G. Marlière, R. Pesenti, and J. Rodriguez,
2015. RECIFE-MILP: an effective MILP-based heuristic for the real-time
railway traffic management problem. Intelligent Transportation Systems,
IEEE Transactions on, 16(5):26092619.
# Teaching Session

WE 11:30 AM2 Auditorium B

**Roberto Musmanno** Department of Mechanical, Energy and Management Engineering
Gianpaolo Ghiani, Univ del Salento; Gibert Laporte, HEC Montréal
(Canada)

*Introduction to Logistics Systems Management with Microsoft Excel and Python Examples*

We present the updated new edition of the award-winning introduc-
tory textbook on logistics system management. It provides an in-depth
introduction to the methodological aspects of planning, organization, and
control of logistics for organizations in the private, public and non-profit
sectors. Based on the authors extensive teaching, research, and indus-
trial consulting experience, this classic textbook is used in universities
worldwide to teach students the use of quantitative methods for solving
complex logistics problems. Fully updated and revised, the third edition
places increased emphasis on the complexity and flexibility required by
modern logistics systems. In this context, the extensive use of data, de-
scriptive analytics, predictive models, and optimization techniques will
be invaluable to support the decisions and actions of logistics and supply
chain managers. Throughout the book, brand-new case studies and nu-
merical examples illustrate how various methods can be used in industrial
and service logistics to reduce costs and improve service levels. The book:
- includes new models and techniques that have emerged over the past
decade;

- describes methodologies for logistics decision making, forecasting, lo-
logistics system design, procurement, warehouse management, and freight
transportation management;

- includes end-of-chapter exercises, Microsoft Excel files and Python com-
puter codes for each algorithm covered;

- includes access to a companion website with additional exercises, links to
video tutorials, and supplementary teaching material. Introduction to Lo-
gistics Systems Management with Microsoft Excel and Python Examples

- Third Edition remains an essential textbook for senior undergraduate and graduate students in engineering, computer science, and management science courses. It is also a highly useful reference for academic researchers and industry practitioners alike.
WE 11:45 AM2 Auditorium B

Eugenia Taranto eugenia.taranto@unict.it

Department of Mathematics and Computer Science, University of
Catania, Viale Andrea Doria 6, 95125 Catania, Italy
Gabriella, Colajanni, Department of Mathematics and Computer
Science, University of Catania, Viale Andrea Doria 6, 95125 Cata-
nia, Italy; Alessandro, Gobbi, Department of Mechanical and in-
dustrial Engineering, University of Brescia, Via Branze 38, 25123
Brescia, Italy; Marinella, Picchi, IIS Antonietti, Via Paolo VI, 3,
25049, Iseo, Italy; Alice, Raffaele, Department of Computer Science,
University of Verona, Strada Le Grazie 15, 37134 Verona, Italy

*Operations Research at high school: its impact on modelling skills and beyond*

Operations Research (OR) is a branch of applied mathematics usually
taught at the university level. Anyway, in recent years, various initiatives
have been developed to introduce OR to secondary school students [1].
In addition to these initiatives, since March 2021 we have been carrying
out the teaching experimentation ROAR (Real Applications of Operations
Research), a three-year project consisting of three teaching units, designed
for three-year secondary school students. In particular, we already tested
the first teaching unit in a Grade-10 class. We completely reported the
design and the implementation of this first part in [2, 3]. In this con-
tribution, we intend to focus more on the results of these experiments,
with an emphasis on the didactical aspects. The Grade-10 class worked
in collaborative mode, divided into groups of 4-5 students. During the
several activities, they were asked to formalise several optimization prob-
lems with two or more variables, by applying Linear, Integer, Binary, or
Mixed Integer Programming. They also computed the optimal solutions
of these problems by using digital technologies, such as GeoGebra and the
add-in Solver of Microsoft Excel. All the meetings of the experiment were
video-recorded. By watching these videos, it was possible to reconstruct
the modelling processes implemented by the students, by using the mod-
elling cycle described in [4]. Specific modes of action of peer collaboration
[5] and discrete techno-mathematical fluency [6] also emerged. Moreover,
an initial and a final questionnaire were administered to the students, in
order to be able to analyse a possible evolution of their competences from
the entrance to the end of the experiment. Qualitative and quantitative
analysis on all collected data show first how it is appropriate to include OR
and its typology of problems in regular school mathematics lectures. Sec-
ondly, how modelling and problem-solving skills, developed through OR,
can be fostered by implementing a collaborative way of working, also by
making use of digital technologies. Last but not least, how such activities
can have a positive impact on students understanding and appreciation
of OR as well as mathematics in general.

Teaching Session
[1] Raffaele, A., Gobbi, A.: Teaching Operations Research Before University: A Focus on Grades 912. SN Oper. Res. Forum 2, 13 (2021).
[2] Colajanni, G., Gobbi, A., Picchi, M., Raffaele, A., Taranto, E. (2021). Teaching OR before University: the ROAR Experience (Part I). Book of Abstracts of the 50th Annual Meeting of AIRO Italian Operations Research Society, pp. 186-187. Roma, Italy.
[3] Colajanni, G., Gobbi, A., Picchi, M., Raffaele, A., Taranto, E.: An Operations Research based Teaching Unit for Grade 10: The ROAR Experience, Part I. INFORMS Transactions on Education (2022). To appear.
[4] Kaiser, G., Bracke, M., Göttlich, S., Kaland, C. (2013). Authentic complex modelling problems in mathematics education. Educational interfaces between mathematics and industry (pp. 287297). Springer.
[5] Weinberger, A., Stegmann, K., Fischer, F., Mandl, H. (2007). Scripting argumentative knowledge construction in computer-supported learning environments. Scripting computer-supported collaborative learning (pp. 191211). Springer.
[6] Jacinto, H., Carreira, S. (2017). Mathematical problem solving with technology: The techno-mathematical fluency of a student-with-GeoGebra. International Journal of Science and Mathematics Education, 15 (6), 11151136.
WE 12:00 AM2 Auditorium B

Claudio Sterle claudio.sterle@unina.it

University "Federico II" of Naples - Department of Electrical Engineering and Information Technology

Boccia, Maurizio, University "Federico II" of Naples - Department of
Electrical Engineering and Information Technology; Masone, Adri-
ano, University "Federico II" of Naples - Department of Electrical
Engineering and Information Technology; Sforza, Antonio, Univer-
sity "Federico II" of Naples - Department of Electrical Engineering
and Information Technology

*OPS4Math project: teaching optimization and problem solving at Secondary Schools*

Nowadays, the teaching of science, technology, engineering and math-
ematics, i.e., the so called STEM disciplines, represents a relevant topic
of discussion given their boosting role for the economic growth of any
developed and developing country. Several initiatives have been imple-
mented worldwide to foster students interest towards STEM disciplines.
These initiatives are based on the awareness that mathematics is essential
for scientific and technological advancement: it trains to reasoning and re-
фlection, stimulates logical capabilities and intuition, improve investigation
attitude. Most of them recognize also that mathematical problem solv-
ing represents an effective way to support teachers and students in their
teaching and learning activities, respectively. However, most of these ini-
tiatives are more focused on teaching mathematics for problem-solving
rather than teaching mathematics through problem solving. Thus, they
do not reflect directly in actions devoted to the insertion of problem solv-
ing in school curricula, thus confirming the mismatch between the math-
ematics education provided by school and university and the required
problem-solving skills. This work is aimed at presenting a project pro-
viding a contribution in filling this gap. It is devoted to the presentation
OPS4Math Optimization and Problem Solving for Teaching of Mathe-
matics, a training project for Secondary School teachers organized by the
University Federico II of Naples, financed by Italian Ministry of Univer-
sity and Research (D.D. 1662 del 22.10.2020), and supported by Campa-
nia Regional Education Office. The project driving idea, resembling the
teaching mathematics through problem solving approach, consists in op-
erating a reversal of the didactic perspective in classical curricula: starting
from phenomena/problems to introduce concepts of data, variables, rela-
tionships and functions in an appealing way, providing new materials for
mathematic teachers of Secondary School. We present project organiza-
tion, structure and aims, to give useful hints for its replication at national
and international level.

Teaching Session
WE 12:15 AM2 Auditorium B

Alessandro Gobbi alessandro.gobbi@unibs.it

Department of Mechanical and industrial Engineering, University of Brescia, Via Branze 38, 25123 Brescia, Italy

Gabriella, Colajanni, Department of Mathematics and Computer Science, University of Catania, Viale Andrea Doria 6, 95125 Catania, Italy; Marinella, Picchi, IIS Antonietti, Via Paolo VI, 3, 25049, Iseo, Italy; Alice, Raffaele, Department of Computer Science, University of Verona, Strada Le Grazie 15, 37134 Verona, Italy; Eugenia, Taranto, Department of Mathematics and Computer Science, University of Catania, Viale Andrea Doria 6, 95125 Catania, Italy

*Teaching OR before University: the ROAR Experience (Part II)*

Ricerca Operativa Applicazioni Reali (ROAR, i.e., Real Applications of Operations Research) [1, 2] is a three-year learning path for secondary school students, also inspired by a few similar initiatives which dissemi-nate Operations Research (OR) before university level [3]. ROAR relies on active learning and constructionism [4], by offering examples and prob-lems closely connected with students everyday life or with the Italian real-ity. The implementation of ROAR started in Spring 2021 as a three-year project-work fitting into a Percorso per le Competenze Trasversali e lOri-entamento (Path for Transversal Skills and Orientation), activated at the scientific high school IIS Antonietti in Iseo (Brescia, Italy). We reported the design, the implementation, and the results of the first teaching unit addressed to Grade 10 in [2]. In this talk, we describe how we carried out a teaching experiment of the second unit to the same students (now Grade 11), from January to April 2022. In particular, we show how we introduced graph theory and network applications, by starting from real situations and problems, such as social and transportation networks. Similar to the previous unit, we relied on collaborative learning (by dividing the stu-dents into groups), and the use of digital technologies. Differently, in this second unit, we focused on solving problems by applying both mathemat-ical modelling and algorithms. Thus, we introduced the students to well known procedures, such as Kruskals and Dijkstra's algorithms, but we also discussed the mathematical models of the Shortest Path Problem and the Travelling Salesman Problem. Moreover, we assigned a challenge to the groups as a final project, by applying competitive learning [5, 6] to in-crease students motivation and engagement. In particular, we asked them to find a solution for three instances of a Vehicle Routing Problem con-cerning the home delivery of groceries from a hypothetical supermarket chain. The groups had one month to submit their best solutions found, computed by developing their own heuristic algorithms and/or applying any tools or techniques we taught them during these two teaching units of ROAR. We analyse the results and feedback received from both stu-dents and teachers. Finally, we anticipate some topics of the third and

Teaching Session
last teaching unit of ROAR, addressed to Grade 12, that we will conduct
in Autumn 2022 with the same students.

[1] Colajanni, G., Gobbi, A., Picchi, M., Raffaele, A., & Taranto, E. (2021). Teaching OR before University: the ROAR Experience (Part I). Book of Abstracts of the 50th Annual Meeting of AIRO Italian Operations Research Society, pp. 186-187. Roma, Italy. [2] Colajanni, G., Gobbi, A., Picchi, M., Raffaele, A., Taranto, E.: An Operations Research based Teaching Unit for Grade 10: The ROAR Experience, Part I. INFORMS Transactions on Education (2022). To appear. [3] Raffaele, A., Gobbi, A.: Teaching Operations Research Before University: A Focus on Grades 912. SN Oper. Res. Forum 2, 13 (2021). [4] Papert, S: Constructionism: A New Opportunity for Elementary Science Education. MIT, Media Laboratory, Epistemology and Learning Group (1986). [5] Johnson, D.W., Johnson, R.T., Holubec E.J. (1986). Circle of Learning: Cooperation in the classroom. Edina MN: Interaction Book Company. [6] Cohen, E.G. (1994). Restructuring the classroom: Condition for productive small groups. Review of Educational Research, 64(1): 1-35.
WE 12:30 AM2 Auditorium B

Daniela Ambrosino ambrosin@economia.unige.it

University of Genova

Sciomachen, Anna, University of Genova

*Projects for getting a taste of problem solving and mathematics in high school*

The University of Genova, in particular, the Department of economics and business studies (DIEC) is going on the realization of paths related to the POT (Piani di Orientamento e Tutorato) thanks to a project ScopriTalento. This project is coordinated by the University of Torino, and other four Italian Universities are involved in it. The aim of the project ScopriTalento is to direct students in the search for their skills and abilities. The idea is to use new and active teaching methods. Project works are used in the projects that involve a group of students either of the same class as in the project Explora or of different classes as in the Summer school. The Explora project is for students in the third class of the high school. Tutors, university students, prepared to work in the classroom permit to operate with a peer to peer education. Tutors meet students and teach them the basic information for understanding the organization of companies operating in the market. Then a second meeting is organised in the company, that usually presents a problem to solve. Coming back to school, the students- helped by tutors- analyse the problem and try to solve it by using the more adequate tool. In our case, we stress the importance of well understanding the problem, the decisions to take and the main aim of guiding the decision-maker. We propose decision theory and simple operation research approaches, we learn them to represent the problem in spreadsheet excel and to find a solution, a good solution. In the last meeting, students and tutors prepare a video for the company, students propose a solution. The summer school project concerns the realization of a summer school with the aim of presenting to the students some concepts related to the companies’ organizations and some instruments useful to solve problems for being competitive in the market. Some labs are proposed, and a team game is organized. Each team can choose its preferred field. At the end of summer school, each team presents its work and a winner is identified by the teachers. Some examples of the activities realized by students will be presented.
Keynote

WE 14:30 PM0 Auditorium A

Dimitris Bertsimas dbertsim@mit.edu

MIT, Sloan School of Management, Cambridge, MA (U.S.A.)

HAIM: Holistic AI for Medicine

Artificial intelligence (AI) systems hold great promise to improve health-
care over the next decades. Specifically, AI systems leveraging multiple
data sources and input modalities are poised to become a viable method to
deliver more accurate results and deployable pipelines across a wide range
of applications. In this work, we propose and evaluate a unified Holistic
AI in Medicine (HAIM) framework to facilitate the generation and testing
of AI systems that leverage multimodal inputs. Our approach uses gen-
eralizable data pre-processing and machine learning modeling stages that
can be readily adapted for research and deployment in healthcare envi-
ronments. We evaluate our HAIM framework by training and character-
izing 14,324 independent models based on MIMIC-IV-MM, a multimodal
clinical database (N=34,537 samples) containing 7,279 unique hospital-
izations and 6,485 patients, spanning all possible input combinations of
4 data modalities (i.e., tabular, time-series, text, and images), 11 unique
data sources and 12 predictive tasks. We show that this framework can
consistently and robustly produce models that outperform similar single-
source approaches across various healthcare demonstrations (by 6-33%),
including 10 distinct chest pathology diagnoses, along with length-of-stay
and 48-hour mortality predictions. We also quantify the contribution of
each modality and data source using Shapley values, which demonstrates
the heterogeneity in data modality importance and the necessity of multi-
modal inputs across different healthcare- relevant tasks. The generalizable
properties and flexibility of our Holistic AI in Medicine (HAIM) frame-
work could offer a promising pathway for future multimodal predictive
systems in clinical and operational healthcare settings.

Keynote
RAVIEP, Recent Advances in Variational Inequal-
ities and Equilibrium Problems; Invited Session

WE 15:40 PM1 001

Sofia Giuffrè sofia.giuffre@unirc.it

DIIES, Mediterranea University of Reggio Calabria
Attilio, Marcianò, DIIES, Mediterranea University of Reggio Calabria

*On the equivalence between constrained variational problems*

The talk deals with nonlinear monotone variational inequalities with gradient constraints. In particular, using a new strong duality principle, we prove the equivalence of the problem under consideration with a double obstacle problem and with a Lagrange multiplier problem.
WE 16:00 PM1 001

Domenico Scopelliti domenico.scopelliti@unibs.it

University of Brescia, Brescia, Italy

Quasi-variational problems with non-self map on Banach space

This talk focuses on the study of generalized quasi-variational inequality problems with a non-self constraint map. For such problems, the concept of the projected solution needs to be introduced. The main result deals with the existence of such solutions on real Banach spaces. Then, we introduce the concept of the projected solution for a multistage stochastic generalized quasi-variational inequality, and the existence of such a solution is provided. These theoretical results are applied in studying an electricity market with renewable power sources.
WE 16:20 PM1 001

Fabio Raciti fabio.raciti@unict.it

Department of Mathematics and Computer Science, University of
Catania

Mauro, Passacantando, Department of Computer Science, Univer-
sity of Pisa

*A multiclass network international migration model under shared regulations*

In this note we extend a previously proposed model of international
human migration by introducing the possibility that some of the destina-
tion countries agree to establish a common upper bound on the migratory
flows they are willing to accept jointly. In this framework, we propose a
new equilibrium definition and prove its equivalence to a suitably defined
variational inequality. Some numerical examples show that the flow dis-
tribution under joint regulations can differ from those corresponding to
a situation where each government autonomously establishes migration
bounds
WE 16:40 PM1 001

Georgia Fargetta georgia.fargetta@phd.unict.it

Department of Mathematics and Computer Science, University of
Catania

Laura, Scriminali, Department of Mathematics and Computer Sci-
ence, University of Catania

*Time-Dependent Generalized Nash Equilibria in Social Media Platforms*

In this paper, we develop a dynamic network model of the competi-
tion of digital contents on social media platforms, assuming that there is a
known and fixed upper bound on the total amount of views. In particular,
we consider a two-layer network consisting of creators and viewers. Each
creator seeks to maximize the profit by determining views and likes. The
problem is formulated as a time-dependent generalized Nash equilibrium
for which we provide the associated evolutionary variational inequality,
using the variational equilibrium concept. We also discuss a possible dif-
ferential game formulation. Finally, using a discrete-time approximation
of the continuous time adjustment process, we present a numerical exam-
ple.
Applications; Contributed Session

WE 15:40 PM1 002

Vladimír Holý vladimir.holy@vse.cz

Prague University of Economics and Business

Tomanová, Petra, Prague University of Economics and Business

*High-Frequency Analysis of Price Clustering and Instantaneous Volatility*

In finance, an increased occurrence of specific prices is known as price clustering. This phenomenon is widely observed and well-documented for various financial instruments and markets. In the literature, however, it is rarely incorporated into price models. We focus on a particular type of price clustering – an increased occurrence of specific multiples of the tick size. For example, stocks on the NYSE and NASDAQ exchanges are traded with precision to one cent but multiples of five cents and ten cents occur much more often in prices. Such behavior is explained by several types of agents trading only in specific multiples of the tick size resulting in an increased occurrence of these multiples in prices.

We propose a discrete dynamic model relating price clustering to the distribution of prices and study the high-frequency behavior of price clustering. We model prices using a mixture of several double Poisson distributions with specific supports corresponding to agents trading in different multiples of the tick size. This mixture distribution has a location parameter, a dispersion parameter, and parameters determining portions of trader types. In our model, we introduce time variation to all these parameters. We assume the location parameter to be equal to the last observed price resulting in zero expected returns. Furthermore, we assume the dispersion parameter to depend on the last trade duration and to follow dynamics of generalized autoregressive score (GAS) models, in a similar fashion as generalized autoregressive conditional heteroskedasticity (GARCH) models. Finally, we assume the trader portion parameters to be driven by the volatility process and other variables such as the price, the last trade duration, and the volume. The resulting observation-driven model is estimated by the maximum likelihood method.

In an empirical study of the 30 Dow Jones Industrial Average (DJIA) stocks, we find that higher instantaneous volatility leads to weaker price clustering at the ultra-high frequency. This is in sharp contrast with our results at low frequencies which show that daily realized volatility has a positive impact on price clustering. The degree of aggregation therefore plays a pivotal role in the relation between price clustering and volatility. While high daily realized volatility correlates with high price clustering, high instantaneous volatility has the opposite effect. We conclude that volatility on lower frequency affects dominantly low-frequency traders through the resolution hypothesis, which states that the source of price

Applications; Contributed Session
clustering is the uncertainty. In contrast, volatility on higher frequency affects only high-frequency traders who do not tend to price clustering. Our approach can be used to improve various price models in high-frequency trading and risk management.
WE 16:00 PM1 002

Chiara Turbian turbian@math.unipd.it

Dipartimento di Matematica Tullio Levi-Civita, Università di Padova
Luigi De Giovanni, Univ di Padova, Nicola Gastaldon, Salvagnini
Italia

A Two-Dimensional Bin Packing Problem with Precedence Con-
straints in the Sheet Metal Industry

We consider an optimization problem of practical relevance arising in
Salvagnini Italia, a multinational corporation in the sheet metal industry
that produces computer numerical control (CNC) machines designed to
cut and bend the sheet metal. We focus on cutting machines and we face
the problem of determining efficient cutting layouts, that is, given a set
of rectangular items to be cut, we want to place them in the available
material sheets with the objective

of minimizing the waste. This problem falls into the well-known area of
Two-Dimensional Bin Packing Problems (2DBPP) and, given its possible
application

in multiple fields, several variants have been proposed during the last
decades in the Operations Research literature. Nevertheless, the problem
under study presents a set of attributes that, to the best of our knowledge,
has never been considered yet. More precisely, we take into account the
following practical aspects, coming from the specific cutting technology:
two items can either share a side (common cut) or need to be placed at
a given minimum distance, and the same may be imposed between an
item and the sheets border; 90 degrees rotation is allowed and each item
may have mandatory or forbidden placement areas; a hard (resp. soft)
precedence may be assigned to each item, meaning that a production order
has to be determined for material sheets and items with higher precedence
need to (resp. should, the waste being the same) be produced before the
others; optional items are also considered.

We devise a Mixed Integer Linear Programming (MILP) model able
to inte- grate the different attributes. Moreover, in order to pursue a
secondary objective

of proposing an as compact as possible cutting layout, we present a
post-process optimization based on a Strip Packing MILP formulation.
The proposed models have been solved on preliminary instances of practi-
cal relevance by means of Cplex. Results indicates that the packing model
well

integrates the new practical features and that, in combination with
the post- process optimization, it returns solutions that fully match the
companys needs.

Keywords. 2D-Bin Packing, Sheet Metal Industry, Precedence Con-
straints, Mixed Integer Linear Programming. References.

[1] M. Dell'Amico, J. C. Diaz, M. Iori, The Bin Packing Problem with

Applications; Contributed Session
Precedence Constraints, Operations Research 60:6, 1491-1504 (2012).

[2] D. Pisinger, M. Sigurd, The Two-Dimensional Bin Packing Problem with Variable Bin Sizes and Costs, Discrete Optimization 2, 154-167 (2005).
WE 16:20 PM1 002

Sara Ceschia sara.ceschia@uniud.it

DPIA, University of Udine

Di Gaspero, Luca, DPIA University of Udine; Schaerf, Andrea, DPIA University of Udine

*Educational Timetabling: Problems, Benchmarks, and State-of-the-Art Results*

We propose a survey of the research contributions on the field of Educational Timetabling with a specific focus on "standard" formulations and the corresponding benchmark instances. We identify six of such formulations and we discuss their features, pointing out their relevance and usability. Other available formulations and datasets are also reviewed and briefly discussed. Subsequently, we report the main state-of-the-art results on the selected benchmarks, in terms of solution quality (upper and lower bounds), search techniques, running times, statistical distributions, and other side settings. Finally, we consider the issue of reliability of the results claimed in the literature, stressing the importance of the presence of instance and solution checkers, so as to provide against possible errors and misunderstandings. To this aim, we developed a web application, named OptHub (https://opthub.uniud.it), that allows users to check and upload both new instances and solutions.

Applications; Contributed Session
# Machine Learning; Contributed Session

WE 15:40 PM1 003

Michele Barbato michele.barbato@unimi.it

Università degli Studi di Milano

Ceselli, Alberto, Università degli Studi di Milano

Simultaneous Feature Selection and Outlier Detection: New MILP Formulation and an Experimental Study

Let $p^1 = (a^1, r_1), p^2 = (a^2, r_2), \dots, p^k = (a^k, r_k)$ be points of $\mathbb{R}^{d+1}$ satisfying $r_i = \omega a^i + \zeta + \varepsilon_i$ for every $i = 1, 2, \dots, k$, where $\omega \in \mathbb{R}^d$ is a features vector, $\zeta \in \mathbb{R}$ and $\varepsilon_1, \varepsilon_2, \dots, \varepsilon_k$ are random errors. The simultaneous feature selection and outlier detection (SFSOD) problem (1) is

$$ \min_{(w,z,s) \in \mathbb{R}^d \times \mathbb{R} \times \{0,1\}^k} \left\{ \sum_{i=1}^k (1-s_i) \ell(r_i - a^i w_i - z) : \|w\|_0 \le d_0 \text{ and } \|s\|_0 \le k_0 \right\}. $$

Above, $\ell(\cdot)$ is a generic loss function, the 0-norm $\|\cdot\|_0$ counts the nonzero entries of its argument and $d_0$ and $k_0$ are given integral budget values. The SFSOD with $\ell(x) = x^2$ has been recently treated in several works from a mixed-integer optimization perspective and it is particularly relevant for linear regression problems having high-dimensionality and exhibiting high data corruption: an optimal solution $(\hat{w}, \hat{z}, \hat{s})$ to (1) with $\ell(x) = x^2$ corresponds to a hyperplane $\hat{H} = \{(x, y) \in \mathbb{R}^{d+1}: y = \hat{w}x + \hat{z}\}$ such that: 1) at most $k_0$ points $p^i$ with $s_i = 1$ are discarded from the dataset as outliers; 2) $H$ optimizes the least-square criterion with respect to the non-outlier points; 3) the feature vector $\hat{w}$ is sparse, involving at most $d_0$ features. In this work we consider the least absolute deviation (LAD) setting, corresponding to $\ell(x) = |x|$ and making the objective of (1) a bilinear function. We propose a linearization for the bilinear terms in the objective of (1) based on disjunctive arguments. Although the disjunctive linearization presented here is applied to the SFSOD problem, it is valid whenever bilinear terms involving binary factors are to be linearized. Our linearization involves big-$M$ values, thus we experimentally study the impact of their magnitude on the qualitative and computational performance of MIP models for the SFSOD. Moreover, we show that the linear relaxation of the proposed disjunctive-based linearization is always as good as linear relaxations of MILP models for the SFSOD already present in the literature and that it can be strictly stronger when the involved big-$M$ values are tight enough. Finally, we computationally show that the LAD setting is competitive in terms of both performance and predictive power with respect to the least-square criterion.

## Machine Learning; Contributed Session
WE 16:00 PM1 003

Paula Brito mpbrito@fep.up.pt

FEP, Universidade do Porto & LIAAD-INESC TEC
A. Pedro, Duarte Silva, Catolica Porto Business School

*Multivariate Discriminant Analysis of Distributional Data*

In this work we consider data where individual units are described by distributions. Distributional data may result from the aggregation of large amounts of open/collected/generated data, or may be directly available in a structured or unstructured form, describing the variability of some features. In recent years, different approaches have been investigated and methods proposed for the analysis of such data. We present parametric probabilistic models for numerical distributional variables building upon previous models for interval-valued variables. The proposed models are based on the representation of each distribution by a location measure and inter-quantile ranges, for given quantiles. Multivariate Normal distributions are assumed for the whole set of indicators, considering alternative structures of the variance-covariance matrix. For all cases, maximum likelihood estimators of the corresponding parameters are derived. This framework is applied to the problem of identifying internet traffic redirection (attacks), both in a two-class (regular vs irregular traffic) and a five-class (regular, and four distinct relays) formulations. Results show that the proposed approach has an excellent classification performance in the problem at hand. Furthermore, the restricted covariance configurations allow for parsimonious classification rules.

Machine Learning; Contributed Session
WE 16:20 PM1 003

Alberto Ceselli alberto.ceselli@unimi.it

Università degli Studi di Milano, Dipartimento di Informatica
Elia, Togni, Università degli Studi di Milano, Dipartimento di In-
formatica

*Mathematical Programming and Machine Learning for a Task Allocation Game*

We consider a combinatorial game proposed in the literature, motivated by the arising paradigm of crowdworking. It consists in assigning tasks to worker agents whose behaviour details are unknown. The game proceeds in rounds. At the end of each of them, the player is given a feedback on the effect of the choices which have been made, including an overall score and a reputation value obtained by each worker agent. The game is meant to be solved by pure player intuition. We analyze instead the effect of using quantitative models. We evaluate the effectiveness of regression models, which are trained round by round, in predicting worker agents performance. We also experiment on suggesting users choice by optimization models, in which regressors are re-encoded as parts of a mathematical program, and merged in a generalized assignment formulation. We present a computational evaluation on a dataset collected from a real online gaming system.
WE 16:40 PM1 003

Annabella Astorino annabella.astorino@icar.cnr.it

ICAR, Consiglio Nazionale delle Ricerche
Avolio, Matteo, Dipartimento di Matematica e Informatica, Università della Calabria, Italy; Fuduli, Antonio, Dipartimento di Matematica e Informatica, Università della Calabria, Italy

*Spherical and Polyhedral separation approaches for Multiple Instance Learning*

We extend the spherical and polyhedral separation approaches to the Multiple Instance Learning (MIL) paradigm. MIL constitutes a kind of weak supervised classification, where, differently from the traditional supervised learning scenario, each example to be classified, is not represented by a fixed-length vector of features but by a bag of feature vectors called instances. In the training phase the classification labels are only provided for each entire bag whereas the labels of the instances inside them are unknown. The final task is to learn a model that predicts the labels of the new incoming bags together with the labels of the instances inside them.

We address the MIL problem in the case of two types of instances and two types of bags (positive and negative) through spherical and polyhedral approaches. The idea is to generate a spherical or a polyhedral separation surface such that, for each positive bag, at least one of its instances is inside the sphere or the polyhedron and all the instances of each negative bag are outside.

In particular, we propose to iteratively separate the bags by means of successive maximum-margin spheres (whose number is automatically determined) or maximum-margin polyhedral surfaces, obtained for both the cases by solving successive linear programs. Moreover only for the polyhedral case we come out with a nonlinear nonconvex nonsmooth optimization model of DC (Difference of Convex) type that we solve by adapting the DCA algorithm.

The results of our implementations on a number of benchmark classification datasets are presented.
OPTSM, Optimization in Public Transport and
Shared Mobility; Invited Session

WE 15:40 PM1 Auditorium A

Matteo Petris matteo.petris@inria.fr

Univ. Lille, Inria, CNRS, Centrale Lille, UMR 9189 CRISTAL, F-59000 Lille, France

Naldini, Federico, COSYS-ESTAS, Univ Gustave Eiffel, IFSTTAR,  
Univ Lille, F-59650 Villeneuve d'Ascq, France; Pellegrini, Paola,  
COSYS-LEOST, Univ Gustave Eiffel, IFSTTAR, Univ Lille, F-  
59650 Villeneuve d'Ascq, France; Pesenti, Raffaele, Department  
of Management, Università Ca' Foscari Venezia, Cannaregio 873,  
30121 Venice, Italy

Extracting series-parallel subnetworks in rail infrastructures - benefits and limits

Managing the railway traffic in real-time after a perturbing event oc-
curs is a difficult task by itself: the best possible train routing and/or
scheduling decisions have to be quickly made to minimise delay propa-
gation. This problem is known as real-time Railway Traffic Management
Problem (rt-RTMP). The topology of the underlying railway infrastruc-
tures plays an important role when solving the rt-RTMP. Indeed, several
state-of-the-art optimisation methods are able to produce good quality so-
lutions in reasonable time, in particular if the underlying infrastructure is
rather simple, e.g., a single line with passing loops. Conversely, they may
struggle to do so when the infrastructure yields a very complex topology.
As an example, if the network involves many parallel tracks and switches
to pass from one to another, the number of routes to consider when eval-
uating rerouting may explode, bringing with it the problem instance size.
Indeed, the effort to manage the traffic sharpens if the infrastructure is
described microscopically. In this study, we evaluate the possibility of
sacrificing some portions of the railway infrastructure to mitigate the
complexity of its topology when solving the rt-RTMP. Specifically, we
consider extracting subnetworks from the infrastructure that can be mod-
elled as series-parallel graphs. We motivate the choice of this particular
topology with two main reasons. First, several NP-complete graph theory
problems, such as finding of the minimum vertex cover and the maximum
matching, are solvable in polynomial time on series-parallel graphs. Sec-
ond, extracting series-parallel subnetworks can be done in linear time with
respect to the size of the original network. Our objective is to assess the
benefits and limits of solving the rt-RTMP on a series-parallel subnetwork
instead of solving it on the entire infrastructure. Specifically, we want to
empirically verify whether simplifying the topology of the network yields a
good trade-off between the computational time decrease, feasibility issues

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session
and solution quality.

OPTSM, Optimization in Public Transport and Shared Mobility;
Invited Session