a tabu search approach for the flow shop scheduling problem in this paper we propose a tabu search approach for solving the permutation flow shop scheduling problem the proposed implementation of the tabu search approach suggests simple techniques for generating neighborhoods of a given sequence and a combined scheme for intensification and diversification that has not been considered before these new features result in an implementation that improves upon previous tabu search implementations that use mechanisms of comparable simplicity also better results were obtained than those produced by a simulated annealing algorithm from the literature

robust mean field linear quadratic gaussian games with unknown l 2 disturbance this paper considers a class of mean field linear quadratic gaussian games with model uncertainty the drift term in the dynamics of the agents contains a common unknown function we take a robust

search with evolutionary ruin and stochastic rebuild a theoretic framework and a case study on exam timetabling this paper presents a state transition based formal framework for a new search method called evolutionary ruin and stochastic recreate which tries to learn and adapt to the changing environments during the search process it improves the performance of the original ruin and recreate principle by embedding an additional phase of evolutionary ruin to mimic the survival of the fittest mechanism within single solutions this method executes a cycle of solution decomposition evolutionary ruin stochastic recreate and solution acceptance until a certain stopping condition is met the solution decomposition phase first uses some problem specific knowledge to decompose a complete solution into its components and assigns a score to each component the evolutionary ruin phase then employs two evolutionary operators namely selection and mutation to destroy a certain fraction of the solution and the next stochastic recreate phase repairs the broken solution last the solution acceptance phase selects a specific strategy to determine the probability of accepting the newly generated solution hence optimisation is achieved by an iterative process of component evaluation solution disruption and stochastic constructive repair from the state transitions point of view this paper presents a probabilistic model and implements a markov chain analysis on some theoretical properties of the approach unlike the theoretical work on genetic algorithm and simulated annealing which are based on state transitions within the space of complete assignments our model is based on state transitions within the space of partial assignments the exam timetabling problems are used to test the performance in solving real world hard problems

randomized heuristics for the capacitated clustering problem in this paper we investigate the adaptation of the greedy randomized adaptive search procedure grasp and iterated greedy methodologies to the capacitated clustering problem ccp in particular we focus on the effect of the balance between randomization and greediness on the performance of these multi start heuristic search methods when solving this np hard problem the former is a memory less approach that constructs independent solutions while the latter is a memory based method that constructs linked solutions obtained by partially rebuilding previous ones both are based on the combination of greediness and randomization in the constructive process and coupled with a subsequent local search phase we propose these two multi start methods and their hybridization and compare their performance on the ccp additionally we propose a heuristic based on the mathematical programming formulation of this problem which constitutes a so called matheuristic we also implement a classical randomized method based on simulated annealing to complete the picture of randomized heuristics our extensive experimentation reveals that iterated greedy performs better than grasp in this problem and improved outcomes are obtained when both methods are hybridized and coupled with the matheuristic in fact the hybridization is able to outperform the best approaches previously published for the ccp this study shows that memory based construction is an effective mechanism within multi start heuristic search techniques

non permutation flow shop scheduling with order acceptance and weighted tardiness model the problem of non permutation flow shop scheduling with order acceptance the model is transformed to linear mip that is optimally solved by commercial solver theorems that are favorable for developing algorithms are presented an efficient two phase genetic algorithm tp ga is proposed the heuristic yields high quality non permutation solutions this paper studies the non permutation solution for the problem of flow shop scheduling with order acceptance and weighted tardiness fss oawt we formulate the problem as a linear mixed integer programming lmip model that can be optimally solved by ampl cplex for small sized problems in addition a non linear integer programming nip model is presented to design heuristic algorithms a two phase genetic algorithm tp ga is developed to solve the problem of medium and large sizes based on the nip model the properties of fss oawt are investigated and several theorems for permutation and non permutation optimum are provided the performance of the tp ga is studied through rigorous computational experiments using a large number of numeric instances the lmip model is used to demonstrate the differences between permutation and non permutation solutions to the fss oawt problem the results show that a considerably large portion of the instances have only an optimal non permutation schedule e g 43 3 for small sized and the proposed tp ga algorithms are effective in solving the fss oawt problems of various scales small medium and large with both permutation and non permutation solutions

cooperative metaheuristics for the permutation flowshop scheduling problem in this work we propose cooperative metaheuristic methods for the permutation flowshop scheduling problem considering two objectives separately total tardiness and makespan we use the island model where each island runs an instance of the algorithm and communications start when the islands have reached certain level of evolution that is communication is not allowed from the beginning of the execution subsequent ones occur when new better solutions are found we carry out an exhaustive comparison of the cooperative methods against the sequential counterparts running in completely comparable scenarios results have been carefully analysed by means of statistical procedures and we can conclude that the cooperative methods yield much better results than the sequential algorithms and state of the art methods running in the same number of processors but without communications the proposed cooperative schemes are easy to apply to other algorithms and problems

heuristic solution methods for the stochastic flow shop problem we investigate the stochastic flow shop problem with m machines and general distributions for processing times no analytic method exists for solving this problem so we looked instead at heuristic methods we devised three constructive procedures with modest computational requirements each based on approaches that have been successful at solving the deterministic counterpart we compared the performance of these procedures experimentally on a set of test problems and found that all of them achieve near optimal performance

strong stability for additive runge kutta methods space discretization of some time dependent partial differential equations gives rise to ordinary differential equations containing additive terms with different stiffness properties in these situ

linear quadratic mean field games with a major player the multi scale approach this paper considers linear quadratic lq mean field games with a major player and analyzes an asymptotic solvability problem it starts with a large scale system of coupled dynamic programming equations and applies a re scaling technique introduced in huang and zhou 2018 and huang and zhou 2020 to derive a set of riccati equations in lower dimensions the solvability of which determines the necessary and sufficient condition for asymptotic solvability we next derive the mean field limit of the strategies and the value functions finally we show that the two decentralized strategies can be interpreted as the best responses of a major player and a representative minor player embedded in an infinite population which have the property of consistent mean field approximations

an explicit one step multischeme sixth order method for systems of special structure abstract structure based partitioning of a system of ordinary differential equations is considered a general form of the explicit multischeme runge kutta type method for such systems is presented order conditions and simplifying conditions are written down an algorithm of derivation of the sixth order method with seven stages and reuse with two free parameters is given it embeds a fourth order error estimator numerical comparison to the dormand prince method with the same computation cost but of lower order is performed

construction of a multirate rodas method for stiff odes multirate time stepping is a numerical technique for efficiently solving large scale ordinary differential equations odes with widely different time scales localized over the components this technique enables one to use large time steps for slowly varying components and small steps for rapidly varying ones multirate methods found in the literature are normally of low order one or two focusing on stiff odes in this paper we discuss the construction of a multirate method based on the fourth order rodas method special attention is paid to the treatment of the refinement interfaces with regard to the choice of the interpolant and the occurrence of order reduction for stiff linear systems containing a stiff source term we propose modifications for the treatment of the source term which overcome order reduction originating from such terms and which we can implement in our multirate method

a comprehensive review and evaluation of permutation flowshop heuristics in this work we present a review and comparative evaluation of heuristics and metaheuristics for the well known permutation flowshop problem with the makespan criterion a number of reviews and evaluations have already been proposed however the evaluations do not include the latest heuristics available and there is still no comparison of metaheuristics furthermore since no common benchmarks and computing platforms are used the results cannot be generalised we propose a comparison of 25 methods ranging from the classical johnson s algorithm or dispatching rules to the most recent metaheuristics including tabu search simulated annealing genetic algorithms iterated local search and hybrid techniques for the evaluation we use the standard test of taillard eur j operation res 64 1993 278 composed of 120 instances of different sizes in the evaluations we use the experimental design approach to obtain valid conclusions on the effectiveness and efficiency of the different methods tested

heuristics for a flowshop scheduling problem with stepwise job objective function abstract in this work we introduce the flowshop scheduling problem with delivery dates and cumulative payoffs this problem is a variation of the flowshop scheduling problem with job release dates that maximizes the total payoff with a stepwise job objective function this paper contributes towards proposing a mathematical formulation for this new problem and an original constructive heuristic additionally we develop a new benchmark of 300 hard instances which are available in a public repository besides we provide primal and dual bounds for them extensive computational experiments were carried out taking into account classical constructive heuristics and hybrid local searches results show the merit of the ff heuristic when compared to other classical heuristics for flowshop scheduling problems additionally we compare an iterated local search ils an iterated greedy search igs and a biased random key genetic algorithm brkga both customized for the studied problem and a commercial mixed integer programming solver the comparison between these methods showed that the brkga starting with a solution from ff heuristic is able to find the best solutions in a very short period of time iterated local search and the commercial solver presented significantly worse results than the aforementioned methods

large population lqg games involving a major player the nash certainty equivalence principle we consider linear quadratic gaussian lqg games with a major player and a large number of minor players the major player has a significant influence on others the minor players individually have negligible impact but they collectively contribute mean field coupling terms in the individual dynamics and costs to overcome the dimensionality difficulty and obtain decentralized strategies the so called nash certainty equivalence methodology is applied the control synthesis is preceded by a state space augmentation via a set of aggregate quantities giving the mean field approximation subsequently within the population limit the lqg game is decomposed into a family of limiting two player games as each is locally seen by a representative minor player next when solving these limiting two player games we impose certain interaction consistency conditions such that the aggregate quantities initially assumed coincide with the ones replicated by the closed loop of a large number of minor players this procedure leads to a set of decentralized strategies for the original lqg game which is an varepsilon nash equilibrium

tabu enhanced iterated greedy algorithm a case study in the quadratic multiple knapsack problem abstract iterated greedy search is a simple and effective metaheuristic for combinatorial problems its flexibility enables the incorporation of components from other metaheuristics with the aim of obtaining effective and powerful hybrid approaches we propose a tabu enhanced destruction mechanism for iterated greedy search that records the last removed objects and avoids removing them again in subsequent iterations the aim is to provide a more diversified and successful search process with regards to the standard destruction mechanism which selects the solution components for removal completely at random we have considered the quadratic multiple knapsack problem as the application domain for which we also propose a novel local search procedure and have developed experiments in order to assess the benefits of the proposal the results show that the tabu enhanced iterated greedy approach in conjunction with the new local search operator effectively exploits the problem knowledge associated with the requirements of the problem considered attaining competitive results with regard to the corresponding state of the art algorithms

a class of interference induced games we consider a multi agent system with linear stochastic individual dynamics and individual linear quadratic ergodic cost functions the agents partially observe their own states their cost functions and initial statistics are a priori independent but they are coupled through an interference term the mean of all agent states entering each of their individual measurement equations while in general for a finite number of agents the resulting optimal control law may be a non linear function of the available observations we establish that for certain classes of cost and dynamic parameters optimal separated control laws obtained by ignoring the interference coupling are asymptotically optimal when the number of agents goes to infinity thus forming for finite n an nash equilibrium more generally though optimal separated control laws may not be asymptotically optimal and can in fact result in unstable overall behavior thus we consider a class of parameterized decentralized control laws whereby the separated kalman gain is treated as the arbitrary gain of a luenberger like observer system stability regions are characterized and the nature of optimal cooperative control policies within the considered class is explored numerical results and an application example for wireless communications are reported

decentralized tracking type games for multi agent systems with coupled arx models asymptotic nash equilibria a class of decentralized tracking type games is considered for large population multi agent systems mas the agents are described by stochastic discrete time auto regressive models with exogenous inputs arx models and coupled together through their individual dynamics and performance indexes by terms of the unknown population state average psa the performance index of each agent to minimize is a stochastic long term averaged group tracking type functional in which there is a nonlinear term of the unknown psa the control law is decentralized and implemented via the nash certainty equivalence principle by probability limit theory under mild conditions it is shown that a the estimate of the psa is strongly consistent b the closed loop system is stable almost surely and the stability is independent of the number n of agents c the decentralized control law is an asymptotic nash equilibrium almost surely or in probability according to the property of the nonlinear coupling function in the performance indexes

comparison of the asymptotic stability properties for two multirate strategies this paper contains a comparison of the asymptotic stability properties for two multirate strategies for each strategy the asymptotic stability regions are presented for a 2x2 test problem and the differences between the results are discussed the considered multirate schemes use rosenbrock type methods as the main time integration method and have one level of temporal local refinement some remarks on the relevance of the results for 2x2 test problems are presented

mean field linear quadratic control uniform stabilization and social optimality abstract this paper is concerned with uniform stabilization and social optimality for general mean field linear quadratic control systems where subsystems are coupled via individual dynamics and costs and the state weight is not assumed with the definiteness condition for the finite horizon problem we first obtain a set of forward backward stochastic differential equations fbsdes from variational analysis and construct a feedback type control by decoupling the fbsdes for the infinite horizon problem by using solutions to two riccati equations we design a set of decentralized control laws which is further proved to be asymptotically social optimal some equivalent conditions are given for uniform stabilization of the systems in different cases respectively finally the proposed decentralized controls are compared to the asymptotic optimal strategies in previous works

a restricted lagrangean approach to the traveling salesman problem we describe an algorithm for the asymmetric traveling salesman problem tsp using a new restricted lagrangean relaxation based on the assignment problem ap the lagrange multipliers are constrained so as to guarantee the continued optimality of the initial ap solution thus eliminating the need for repeatedly solving ap in the process of computing multipliers we give several polynomially bounded procedures for generating valid inequalities and taking them into the lagrangean function with a positive multiplier without violating the constraints so as to strengthen the current lower bound upper bounds are generated by a fast tour building heuristic when the bound strengthening techniques are exhausted without matching the upper with the lower bound we branch by using two different rules according to the situation the usual subtour breaking disjunction and a new disjunction based on conditional bounds we discuss computational experience on 120 randomly generated asymmetric tsp s with up to 325 cities the maximum time used for any single problem being 82 seconds this is a considerable improvement upon earlier methods though the algorithm discussed here is for the asymmetric tsp the approach can be adapted to the symmetric tsp by using the 2 matching problem instead of ap

two branch and bound algorithms for the permutation flow shop problem abstract the objective of this paper is to present two exact methods for the permutation flow shop problem the first method is based on immediate selections and optimal adjustments of heads and tails the second method consists in recursively enumerating jobs potentially processed first inputs and jobs which would be processed last outputs on machines it is found that this second method gives better results than the first however the first method becomes more efficient when initial heads and tails are added

a fast tabu search algorithm for the permutation flow shop problem abstract a fast and easily implementable approximation algorithm for the problem of finding a minimum makespan in the permutation flow shop is presented the algorithm is based on a tabu search technique with a specific neighborhood definition which employs a block of jobs notion computational experiments up to 500 jobs and 20 machines show its excellent numerical properties

the weighted independent domination problem integer linear programming models and metaheuristic approaches abstract this work deals with the so called weighted independent domination problem which is an np hard combinatorial optimization problem in graphs in contrast to previous work this paper considers the problem from a non theoretical perspective the first contribution consists in the development of three integer linear programming models second two greedy heuristics are proposed finally the last contribution is a population based iterated greedy metaheuristic which is applied in two different ways 1 the metaheuristic is applied directly to each problem instance and 2 the metaheuristic is applied at each iteration of a higher level framework known as construct merge solve and adapt to sub instances of the tackled problem instances the results of the considered algorithmic approaches show that integer linear programming approaches can only compete with the developed metaheuristics in the context of graphs with up to 100 nodes when larger graphs are concerned the application of the populated based iterated greedy algorithm within the higher level framework works generally best the experimental evaluation considers graphs of different types sizes densities and ways of generating the node and edge weights

a variable iterated greedy algorithm for the traveling salesman problem with time windows this paper presents a variable iterated greedy algorithm for solving the traveling salesman problem with time windows tsptw to identify a tour minimizing the total travel cost or the makespan separately the tsptw has several practical applications in both production scheduling and logistic operations the proposed algorithm basically relies on a greedy algorithm generating an increasing number of neighboring solutions through the use of the idea of neighborhood change in variable neighborhood search vns algorithms in other words neighboring solutions are generated by destructing a solution component and re constructing the solution again with variable destruction sizes in addition the proposed algorithm is hybridized with a vns algorithm employing backward and forward 1 opt local searches to further enhance the solution quality the performance of the proposed algorithm was tested on several benchmark suites from the literature experimental results confirm that the proposed algorithm is either competitive to or even better than the best performing algorithms from the literature ultimately new best known solutions are obtained for 38 out of 125 problem instances of the recently proposed benchmark suite whereas 15 out of 31 problem instances are also further improved for the makespan criterion

multirate generalized additive runge kutta methods this work constructs a new class of multirate schemes based on the recently developed generalized additive runge kutta gark methods sandu and gunther siam j numer anal 53 1 17 42 2015 multirate schemes use different step sizes for different components and for different partitions of the right hand side based on the local activity levels we show that the new multirate gark family includes many well known multirate schemes as special cases the order conditions theory follows directly from the gark accuracy theory nonlinear stability and monotonicity investigations show that these properties are inherited from the base schemes provided that additional coupling conditions hold

record breaking optimization results using the ruin and recreate principle a new optimization principle is presented solutions of problems are partly but significantly ruined and rebuilt or recreated afterwards performing this type of change frequently one can obtain astounding results for classical optimization problems the new method is particularly suited for more complex optimization problems discontinuous ones problems with hard to find admissible solutions problems with complex objectives or many constraints the method is an all purpose heuristic numerical results are given for the traveling salesman problem for the vehicle routing problem with time windows and for network optimization numerical evidence for the quality of the proposed principle is given for most of the instances of a research library of problems the ruin and recreate r r implementation achieved the best published results for many instances better or much better solutions could be found

opinion dynamics in social networks through mean field games emulation mimicry and herding behaviors are phenomena that are observed when multiple social groups interact to study such phenomena we consider in this paper a large population of homogeneous social networks each such network is characterized by a vector state a vector valued controlled input and a vector valued exogenous disturbance the controlled input of each network aims to align its state to the mean distribution of other networks states in spite of the actions of the disturbance one of the contributions of this paper is a detailed analysis of the resulting mean field game for the cases of both polytopic and mathcal l 2 bounds on controls and disturbances a second contribution is the establishment of a robust mean field equilibrium that is a solution including the worst case value function the state feedback best responses for the controlled inputs and worst case disturbances and a density evolution this solution is characterized by the property that no player can benefit from a u

a simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem over the last decade many metaheuristics have been applied to the flowshop scheduling problem ranging from simulated annealing or tabu search to complex hybrid techniques some of these methods provide excellent effectiveness and efficiency at the expense of being utterly complicated in fact several published methods require substantial implementation efforts exploit problem specific speed up techniques that cannot be applied to slight variations of the original problem and often re implementations of these methods by other researchers produce results that are quite different from the original ones in this work we present a new iterated greedy algorithm that applies two phases iteratively named destruction were some jobs are eliminated from the incumbent solution and construction where the eliminated jobs are reinserted into the sequence using the well known neh construction heuristic optionally a local search can be applied after the construction phase our iterated greedy algorithm is both very simple to implement and as shown by experimental results highly effective when compared to state of the art methods

multi objective sequence dependent setup times permutation flowshop a new algorithm and a comprehensive study abstract the permutation flowshop scheduling problem has been thoroughly studied in recent decades both from single objective as well as from multi objective perspectives to the best of our knowledge little has been done regarding the multi objective flowshop with pareto approach when sequence dependent setup times are considered as setup times and multi criteria problems are important in industry we must focus on this area we propose a simple yet powerful algorithm for the sequence dependent setup times flowshop problem with several criteria the presented method is referred to as restarted iterated pareto greedy or ripg and is compared against the best performing approaches from the relevant literature comprehensive computational and statistical analyses are carried out in order to demonstrate that the proposed ripg method clearly outperforms all other algorithms and as a consequence it is a state of art method for this important and practical scheduling problem

an iterated greedy heuristic for the sequence dependent setup times flowshop problem with makespan and weighted tardiness objectives iterated greedy ig algorithms are based on a very simple principle are easy to implement and can show excellent performance in this paper we propose two new ig algorithms for a complex flowshop problem that results from the consideration of sequence dependent setup times on machines a characteristic that is often found in industrial settings the first ig algorithm is a straightforward adaption of the ig principle while the second incorporates a simple descent local search furthermore we consider two different optimization objectives the minimization of the maximum completion time or makespan and the minimization of the total weighted tardiness extensive experiments and statistical analyses demonstrate that despite their simplicity the ig algorithms are new state of the art methods for both objectives

a new heuristic method for the flow shop sequencing problem abstract a new heuristic method is presented for solving the m machine n job flow shop scheduling problem this method named spirit is composed of two phases the first finds an initial sequence using an analogy with the travelling salesman problem and the second tries to improve this solution using taboo search techniques the results of the heuristic are compared with those from other well known methods

an iterated greedy heuristic for a market segmentation problem with multiple attributes this research has been supported by the mexican national council for science and technology conacyt through grants cb2005 01 48499y and cb2011 01 166397 and a scholarship for graduate studies and by the universidad autonoma de nuevo leon through its scientific and technological research support program paicyt grants ca1478 07 ce012 09 it511 10 and ce331 15 ruben ruiz is partially supported by the spanish ministry of economy and competitiveness under the project scheyard optimization of scheduling problems in container yards no dpi2015 65895 r financed by feder funds we would like to thank rafael frinhani richard fuchshuber and their corresponding research teams for providing us the source code of their algorithms to carry out the corresponding tests furthermore we are grateful to the editor and the four anonymous reviewers for their careful reading of our manuscript and their constructive comments and suggestions which helped us improve its quality

social optima in mean field lqg control centralized and decentralized strategies we study a class of linear quadratic gaussian lqg control problems with n decision makers where the basic objective is to minimize a social cost as the sum of n individual costs containing mean field coupling the exact socially optimal solution determining a particular pareto optimum requires centralized information for each agent and has high implementational complexity as an alternative we subsequently exploit a mean field structure in the centralized optimal control problem to develop decentralized cooperative optimization so that each agent only uses its own state and a function which may be computed offline the resulting set of strategies asymptotically achieves the social optimum as n a key feature in this scheme is to let each agent optimize a new cost as the sum of its own cost and another component capturing its social impact on all other agents we also discuss the relationship between the decentralized cooperative solution and the so called nash certainty equivalence based solution presented in previous work on mean field lqg games

tabu search for non permutation flowshop scheduling problem with minimizing total tardiness abstract this paper deals with the non permutation flowshop problem which means that the job sequences are allowed to be different on machines the objective function is minimizing the total tardiness firstly three mixed integer linear programming milp models for non permutation flowshop problems are described and then are analyzed and assessed their relative effectiveness secondly two tabu search based algorithms denoted by lh1 and lh2 are proposed to solve the complicated non permutation flowshop problems the algorithms are constructed on specific neighborhood structures which enable the searching method effective finally the performance is evaluated against taillard s famous benchmark computational experiments show that the proposed algorithms lh1 and lh2 are significantly superior to the l ts algorithm and the percentages of improved permutation flowshop instances by lh1 and lh2 algorithms are about 87 8 and 98 3 with respect to total tardiness respectively the non permutation schedules also have achieved significant improvement in four different scenarios of due dates consequently average percentage improvement api is 14 52 for flowshop problems with low tardiness factors it is evident that exploring non permutation schedule is effective and necessary for low tardiness factors

local search methods for the flowshop scheduling problem with flowtime minimization abstract flowshop scheduling is a very active research area this problem still attracts a considerable amount of interest despite the sheer amount of available results total flowtime minimization of a flowshop has been actively studied and many effective algorithms have been proposed in the last few years new best solutions have been found for common benchmarks at a rapid pace however these improvements many times come at the cost of sophisticated algorithms complex methods hinder potential applications and are difficult to extend to small problem variations replicability of results is also a challenge in this paper we examine simple and easy to implement methods that at the same time result in state of the art performance the first two proposed methods are based on the well known iterated local search ils and iterated greedy ig frameworks which have been applied with great success to other flowshop problems additionally we present extensions of these methods that work over populations something that we refer to as population based ils pils and population based ig piga respectively we calibrate the presented algorithms by means of the design of experiments doe approach extensive comparative evaluations are carried out against the most recent techniques for the considered problem in the literature the results of a comprehensive computational and statistical analysis show that the presented algorithms are very effective furthermore we show that despite their simplicity the presented methods are able to improve 12 out of 120 best known solutions of taillard s flowshop benchmark with total flowtime criterion

accelerated tabu search for no wait flowshop scheduling problem with maximum lateness criterion abstract for the no wait flowshop scheduling problem with maximum lateness criterion properties are developed to speed up three kinds of basic operations generating candidate solutions i e the insertion of a new job into a partial sequence and the insertion and exchange neighborhood moves the properties reduce the time to evaluate a candidate from o nm to o 1 and simplify the implementation of the heuristics based on the basic operations by evaluating candidates before their generation the properties also reduce from o n 3 m to o n 2 the time complexity of well known neh heuristic and the complete evaluation of the insertion and exchange neighborhoods tabu search ts is applied to the considered problem since ts tries to find the best neighbor of the current solution in each iteration and therefore can much benefit from the speedups three different ways to use insertion and exchange neighborhoods are compared in ts computational experiments show that the speedups are more helpful as job number increases and all proposed ts algorithms are more effective and robust than the existing algorithms although two and single neighborhood ts algorithms are not significantly different two neighborhood ts algorithms are more preferable

mean field production output control with sticky prices nash and social solutions this paper presents an application of mean field control to dynamic production optimization with sticky prices and adjustment costs both noncooperative and cooperative solutions are considered by solving auxiliary limiting optimal control problems subject to consistent mean field approximations two sets of decentralized strategies are obtained and further shown to asymptotically attain nash equilibria and social optima respectively a numerical example is given to compare market prices firms outputs and costs under the two solution frameworks

shifting representation search for hybrid flexible flowline problems this paper considers the hybrid flexible flowline scheduling problem with a set of additional restrictions and generalizations that are common in practice these include precedence constraints sequence dependent setup times time lags machine eligibility and release times there are many potential solution representations for this problem ranging from simple and compact to more complex and complete typically when choosing the degree of detail of the solution representation a tradeoff can be found between efficiency of the algorithm and the size of the search space several adaptations of existing methods are introduced memetic algorithm iterated local search iterated greedy as well as a novel algorithm called shifting representation search srs this new method starts with an iterated greedy algorithm applied to a permutation version of the problem and at a given time switches to an iterated local search on the full search space as far as we know this shift of the solution representation is new in the scheduling literature experimental results and statistical tests clearly prove the superiority of srs compared with classical and existing methods

a generalized structure approach to additive runge kutta methods this work considers a general structure of the additively partitioned runge kutta methods by allowing for different stage values as arguments of different components of the right hand side an order conditions theory is developed for the new formulation of generalized additive methods and stability and monotonicity investigations are carried out the paper discusses the construction and properties of implicit explicit and implicit implicit methods in the new framework the new approach named gark introduces additional flexibility when compared to traditional partitioned runge kutta formalism and therefore offers additional opportunities for the development of flexible solvers for systems with multiple scales or driven by multiple physical processes

scheduling to minimize the sum of weighted flowtime and weighted tardiness of jobs in a flowshop with sequence dependent setup times abstract efficient heuristics for scheduling jobs in a static flowshop with sequence dependent setup times of jobs are presented in this paper the objective is to minimize the sum of weighted flowtime and weighted tardiness of jobs two heuristic preference relations are used to construct a good heuristic permutation sequence of jobs thereafter an improvement scheme is implemented once and twice on the heuristic sequence to enhance the quality of the solution an existing heuristic a random search procedure and a greedy local search are used as benchmark methods for relatively evaluating the proposed heuristics an extensive performance analysis has shown that the proposed heuristics are computationally faster and more effective in yielding solutions of better quality than the benchmark procedures

iterated greedy for the maximum diversity problem abstract the problem of choosing a subset of elements with maximum diversity from a given set is known as the maximum diversity problem many algorithms and methods have been proposed for this hard combinatorial problem including several highly sophisticated procedures by contrast in this paper we present a simple iterated greedy metaheuristic that generates a sequence of solutions by iterating over a greedy construction heuristic using destruction and construction phases extensive computational experiments reveal that the proposed algorithm is highly effective as compared to the best so far metaheuristics for the problem under consideration

heuristics for the flow line problem with setup costs this paper presents two new heuristics for the flowshop scheduling problem with sequence dependent setup times sdsts and makespan minimization objective the first is an extension of a procedure that has been very successful for the general flowshop scheduling problem the other is a greedy randomized adaptive search procedure grasp which is a technique that has achieved good results on a variety of combinatorial optimization problems both heuristics are compared to a previously proposed algorithm based on the traveling salesman problem tsp in addition local search procedures are developed and adapted to each of the heuristics a two phase lower bounding scheme is presented as well the first phase finds a lower bound based on the assignment relaxation for the asymmetric tsp in phase two attempts are made to improve the bound by inserting idle time all procedures are compared for two different classes of randomly generated instances in the first case where setup times are an order of magnitude smaller than the processing times the new approaches prove superior to the tsp based heuristic for the case where both processing and setup times are identically distributed the tsp based heuristic outperforms the proposed procedures

solving the flowshop scheduling problem with sequence dependent setup times using advanced metaheuristics abstract this paper deals with the permutation flowshop scheduling problem in which there are sequence dependent setup times on each machine commonly known as the sdst flowshop the optimisation criteria considered is the minimisation of the makespan or cmax genetic algorithms have been successfully applied to regular flowshops before and the objective of this paper is to assess their effectiveness in a more realistic and complex environment we present two advanced genetic algorithms as well as several adaptations of existing advanced metaheuristics that have shown superior performance when applied to regular flowshops we show a calibration of the genetic algorithm s parameters and operators by means of a design of experiments doe approach for evaluating the proposed algorithms we have coded several if not all known sdst flowshop specific algorithms all methods are tested against an augmented benchmark based on the instances of taillard the results show a clear superiority of the algorithms proposed especially for the genetic algorithms regardless of instance type and size

scheduling open shops with parallel machines to minimize total completion time this paper explores scheduling a realistic variant of open shops with parallel machines per working stage since real production floors seldom employ a single machine for each operation the regular open shop problem is very often in practice extended with a set of parallel machines at each stage the purpose of duplicating machines in parallel is to either eliminate or to reduce the impact of bottleneck stages on the overall shop efficiency the objective is to find the sequence which minimizes total completion times of jobs we first formulate the problem as an effective mixed integer linear programming model and then we employ memetic algorithms to solve the problem we employ taguchi method to evaluate the effects of different operators and parameters on the performance of memetic algorithm to further enhance the memetic algorithm we hybridize it with a simple form of simulated annealing as its local search engine to assess the performance of the model and algorithms we establish two computational experiments the first one is small sized instances by which the model and general performance of the algorithms are evaluated the second one consists of large sized instances by which we further evaluate the algorithms

a scatter search algorithm for the distributed permutation flowshop scheduling problem abstract the distributed permutation flowshop problem has been recently proposed as a generalization of the regular flowshop setting where more than one factory is available to process jobs distributed manufacturing is a common situation for large enterprises that compete in a globalized market the problem has two dimensions assigning jobs to factories and scheduling the jobs assigned to each factory despite being recently introduced this interesting scheduling problem has attracted attention and several heuristic and metaheuristic methods have been proposed in the literature in this paper we present a scatter search ss method for this problem to optimize makespan ss has seldom been explored for flowshop settings in the proposed algorithm we employ some advanced techniques like a reference set made up of complete and partial solutions along with other features like restarts and local search a comprehensive computational campaign including 10 existing algorithms together with statistical analyses shows that the proposed scatter search algorithm produces better results than existing algorithms by a significant margin moreover all 720 known best solutions for this problem are improved

some efficient heuristic methods for the flow shop sequencing problem abstract in this paper the best heuristic methods known up to now are compared to solve the flow shop sequencing problem and we improve the complexity of the best one next this problem is applied to taboo search a new technique to solve combinatorial optimization problems and computational experiments are reported finally a parallel taboo search algorithm is presented and experimental results show that this heuristic allows very good speed up

on heuristic solutions for the stochastic flowshop scheduling problem abstract we address the problem of scheduling jobs in a permutation flowshop when their processing times adopt a given distribution stochastic flowshop scheduling problem with the objective of minimization of the expected makespan for this problem optimal solutions exist only for very specific cases consequently some heuristics have been proposed in the literature all of them with similar performance in our paper we first focus on the critical issue of estimating the expected makespan of a sequence and found that for instances with a medium large variability expressed as the coefficient of variation of the processing times of the jobs the number of samples or simulation runs usually employed in the literature may not be sufficient to derive robust conclusions with respect to the performance of the different heuristics we thus propose a procedure with a variable number of iterations that ensures that the percentage error in the estimation of the expected makespan is bounded with a very high probability using this procedure we test the main heuristics proposed in the literature and find significant differences in their performance in contrast with existing studies we also find that the deterministic counterpart of the most efficient heuristic for the stochastic problem performs extremely well for most settings which indicates that in some cases solving the deterministic version of the problem may produce competitive solutions for the stochastic counterpart

multirate runge kutta schemes for advection equations explicit time integration methods can be employed to simulate a broad spectrum of physical phenomena the wide range of scales encountered lead to the problem that the fastest cell of the simulation dictates the global time step multirate time integration methods can be employed to alter the time step locally so that slower components take longer and fewer time steps resulting in a moderate to substantial reduction of the computational cost depending on the scenario to simulate s osher r sanders numerical approximations to nonlinear conservation laws with locally varying time and space grids math comput 41 1983 321 336 h tang g warnecke a class of high resolution schemes for hyperbolic conservation laws and convection diffusion equations with varying time and pace grids siam j sci comput 26 4 2005 1415 1431 e constantinescu a sandu multirate timestepping methods for hyperbolic conservation laws siam j sci comput 33 3 2007 239 278 in air pollution modeling the advection part is usually integrated explicitly in time where the time step is constrained by a locally varying courant friedrichs lewy cfl number multirate schemes are a useful tool to decouple different physical regions so that this constraint becomes a local instead of a global restriction therefore it is of major interest to apply multirate schemes to the advection equation we introduce a generic recursive multirate runge kutta scheme that can be easily adapted to an arbitrary number of refinement levels it preserves the linear invariants of the system and is of third order accuracy when applied to certain explicit runge kutta methods as base method

the two machine sequence dependent flowshop scheduling problem abstract this paper considers the static two machine flowshop scheduling problem where the setup times of jobs depend on immediately preceding jobs and shows that the problem is np complete it is shown that permutation schedules for this problem do not always minimize makespan conditions are specified which will prove the optimality of a permutation schedule four efficient approximate algorithms are proposed to find approximate schedules for the problem and are empirically evaluated to assess their effectiveness in finding a minimum makespan permutation schedule

iterated greedy local search methods for unrelated parallel machine scheduling abstract this work deals with the parallel machine scheduling problem which consists in the assignment of n jobs on m parallel machines the most general variant of this problem is when the processing time depends on the machine to which each job is assigned to this case is known as the unrelated parallel machine problem similarly to most of the literature this paper deals with the minimization of the maximum completion time of the jobs commonly referred to as makespan c max many algorithms and methods have been proposed for this hard combinatorial problem including several highly sophisticated procedures by contrast in this paper we propose a set of simple iterated greedy local search based metaheuristics that produce solutions of very good quality in a very short amount of time extensive computational campaigns show that these solutions are most of the time better than the current state of the art methodologies by a statistically significant margin

an additive bounding procedure for the asymmetric travelling salesman problem in this paper new lower bounds for the asymmetric travelling salesman problem are presented based on spanning arborescences the new bounds are combined in an additive procedure whose theoretical performance is compared with that of the balas and christofides procedure 1981 both procedures have been imbedded in a simple branch and bound algorithm and experimentally evaluated on hard test problems

social optima in mean field linear quadratic gaussian models with markov jump parameters this paper investigates social optima of mean field linear quadratic gaussian lqg control models with markov jump parameters the common objective of the agents is to minimize a social cost the cost average of the whole society in the cost functions there are coupled mean field terms first we consider the centralized case and get a parameterized equation of mean field effect then we design a set of distributed strategies by solving a limiting optimal control problem in an augmented state space subject to the consistency requirement for mean field approximation it is shown that the set of distributed strategies is asymptotically team optimal and the asymptotically optimal social cost value can be obtained explicitly the optimal social average cost is compared with the optimal individual cost in mean field games by virtue of the explicit expressions and the difference is further illustrated by a numerical example

an energy stable runge kutta method for convex gradient problems abstract we propose a class of runge kutta methods which provide a simple unified framework to solve the gradient flow of a convex functional in an unconditionally energy stable manner stiffly accurate runge kutta methods are high order accurate in terms of time and also assure the energy stability for any time step size when they satisfy the positive definite condition we provide a detailed proof of the unconditional energy stability as well as unique solvability of the proposed scheme we demonstrate the accuracy and stability of the proposed methods using numerical experiments for a specific example

large population cost coupled lqg problems with nonuniform agents individual mass behavior and decentralized varepsilon nash equilibria we consider linear quadratic gaussian lqg games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs a state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv nash equilibrium property a stability property of the mass behavior is established and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques