the similarity problem for j nonnegative sturm liouville operators abstract sufficient conditions for the similarity of the operator a 1 r x d 2 d x 2 q x with an indefinite weight r x sgn x r x are obtained these conditions are formulated in terms of titchmarsh weyl m coefficients sufficient conditions for the regularity of the critical points 0 and of j nonnegative sturm liouville operators are also obtained this result is exploited to prove the regularity of 0 for various classes of sturm liouville operators this implies the similarity of the considered operators to self adjoint ones in particular in the case r x sgn x and q l 1 r 1 x d x we prove that a is similar to a self adjoint operator if and only if a is j nonnegative the latter condition on q is sharp i e we construct q 1 l 1 r 1 x d x such that a is j nonnegative with the singular critical point 0 hence a is not similar to a self adjoint operator for periodic and infinite zone potentials we show that j positivity is sufficient for the similarity of a to a self adjoint operator in the case q 0 we prove the regularity of the critical point 0 for a wide class of weights r this yields new results for forward backward diffusion equations

reoptimization approaches for the vehicle routing problem with stochastic demands we consider the vehicle routing problem with stochastic demands vrpsd under reoptimization we develop and analyze a finite horizon markov decision process mdp formulation for the single vehicle case and establish a partial characterization of the optimal policy we also propose a heuristic solution methodology for our mdp named partial reoptimization based on the idea of restricting attention to a subset of all the possible states and computing an optimal policy on this restricted set of states we discuss two families of computationally efficient partial reoptimization heuristics and illustrate their performance on a set of instances with up to and including 100 customers comparisons with an existing heuristic from the literature and a lower bound computed with complete knowledge of customer demands show that our best partial reoptimization heuristics outperform this heuristic and are on average no more than 10 13 away from this lower bound depending on the type of instances

the merchant subtour problem we consider the problem of a travelling merchant who makes money by buying commodities where they are cheap and selling them in other places where he can make a profit the merchant ships commodities of his own choice in a van of fixed capacity given the prices of all the commodities in all of the places and the cost of driving from one place to another the problem the merchant faces each day is to select a subset of the cities that he can visit in a day and to determine the order in which the cities are visited such that the total profit is maximised we call this problem the merchant subtour problem the msp models the pricing problem of a rather complex pickup and delivery problem that was given to us by the dutch logistics company van gend loos we show that a special case of the msp has a totally unimodular constraint matrix this knowledge enables us to develop a tabu search algorithm for finding good feasible solutions to the msp and a branch and price and cut algorithm for solving the msp to optimality the relaxations solved in each node of the branch and bound tree are strengthened by lifted knapsack inequalities lifted cycle inequalities and mod k cuts we present computational results on data sets derived from our main instance of the van gend loos pickup and delivery problem

further results on the probabilistic traveling salesman problem abstract in 1985 jaillet introduced the probabilistic traveling salesman problem ptsp a variant of the classical tsp in which only a subset of the nodes may be present in any given instance of the problem the goal is to find an a priori tour of minimal expected length with the strategy of visiting the present nodes in a particular instance in the same order as they appear in the a priori tour in this paper we reexamine the ptsp using a variety of theoretical and computational approaches we sharpen the best known bounds for the ptsp derive several asymptotic relations and compare from various veiwpoints the ptsp with the re optimization strategy i e finding an optimal tour in every problem instance when a euclidean metric is used and the nodes are uniformly distributed in the unit square a heuristic for the ptsp is shown to be very close to the re optimization strategy we examine some ptsp heuristics with provable worst case performance and address the question of finding constant guarantee heuristics implementations of various heuristics some based on sorting and some on local optimality permit us to discuss the qualitative and quantitative properties of computational problems with up to 5000 nodes

risky traveling salesman problem abstract in this paper we introduce a methodology for optimizing the expected cost of routing a single vehicle which has a probability of breaking down or failing to complete some of its tasks more specifically a calculus is devised for finding the optimal order in which each site should be visited

characterizations of normal hyponormal and ep operators abstract in this paper normal and hyponormal operators with closed ranges as well as ep operators are characterized in arbitrary hilbert spaces all characterizations involve generalized inverses thus recent results of s cheng and y tian s cheng y tian two sets of new characterizations for normal and ep matrices linear algebra appl 375 2003 181 195 are extended to infinite dimensional settings

a dilation theory for polynomially bounded operators abstract in this paper we construct a special sort of dilation for an arbitrary polynomially bounded operator this enables us to show that the problem whether every polynomially bounded operator is similar to a contraction can be reduced to a subclass of it

exact algorithms for the chance constrained vehicle routing problem we study the chance constrained vehicle routing problem ccvrp a version of the vehicle routing problem vrp with stochastic demands where a limit is imposed on the probability that each vehicle s capacity is exceeded a distinguishing feature of our proposed methodologies is that they allow correlation between random demands whereas nearly all existing exact methods for the vrp with stochastic demands require independent demands we first study an edge based formulation for the ccvrp in particular addressing the challenge of how to determine a lower bound on the number of vehicles required to serve a subset of customers we then investigate the use of a branch and cut and price bcp algorithm while bcp algorithms have been considered the state of the art in solving the deterministic vrp few attempts have been made to extend this framework to the vrp with stochastic demands in contrast to the deterministic vrp we find that the pricing problem for the ccvrp problem is strongly mathcal np hard even when the routes being priced are allowed to have cycles we therefore propose a further relaxation of the routes that enables pricing via dynamic programming we also demonstrate how our proposed methodologies can be adapted to solve a distributionally robust ccvrp problem numerical results indicate that the proposed methods can solve instances of ccvrp having up to 55 vertices

a dynamic traveling salesman problem with stochastic arc costs we propose a dynamic traveling salesman problem tsp with stochastic arc costs motivated by applications such as dynamic vehicle routing in which the cost of a decision is known only probabilistically beforehand but is revealed dynamically before the decision is executed we formulate this as a dynamic program dp and compare it to static counterparts to demonstrate the advantage of the dynamic paradigm over an a priori approach we then apply approximate linear programming alp to overcome the dp s curse of dimensionality obtain a semi infinite linear programming lower bound and discuss its tractability we also analyze a rollout version of the price directed policy implied by our alp and derive worst case guarantees for its performance our computational study demonstrates the quality of a heuristically modified rollout policy using a computationally effective a posteriori bound

a tabu search algorithm for maximum parsimony phylogeny inference abstract phylogeny reconstruction is too complex a combinatorial problem for an exhaustive search because the number of possible solutions increases exponentially with the number of taxa involved in this paper we adopt the parsimony principle and design a tabu search algorithm for finding a most parsimonious phylogeny tree a special array structure is employed to represent the topology of trees and to generate the neighboring trees we test the proposed tabu search algorithm on randomly selected data sets obtained from nuclear ribosomal dna sequence data the experiments show that our algorithm explores fewer trees to reach the optimal one than the commonly used program dnapenny branch and bound based while it generates much more accurate results than the default options of the program dnapars heuristic search based the percentage of search space needed to find the best solution for our algorithm decreased rapidly as the number of taxa increased for a 20 taxon phylogeny problem it needs on average to examine only 3 92 10 15 of the sample space

a tabu search heuristic for the generalized assignment problem abstract this paper considers the generalized assignment problem gap it is a well known np hard combinatorial optimization problem that is interesting in itself and also appears as a subproblem in other problems of practical importance a tabu search heuristic for the gap is proposed the algorithm uses recent and medium term memory to dynamically adjust the weight of the penalty incurred for violating feasibility the most distinctive features of the proposed algorithm are its simplicity and its flexibility these two characteristics result in an algorithm that compared to other well known heuristic procedures provides good quality solutions in competitive computational times computational experiments have been performed in order to evaluate the behavior of the proposed algorithm

real time vehicle rerouting problems with time windows this paper introduces and studies real time vehicle rerouting problems with time windows applicable to delivery and or pickup services that undergo service disruptions due to vehicle breakdowns in such problems one or more vehicles need to be rerouted in real time to perform uninitiated services with the objective to minimize a weighted sum of operating service cancellation and route disruption costs a lagrangian relaxation based heuristic is developed which includes an insertion based algorithm to obtain a feasible solution for the primal problem a dynamic programming based algorithm solves heuristically the shortest path problems with resource constraints that result from the lagrangian relaxation computational experiments show that the developed lagrangian heuristic performs very well

routing optimization under uncertainty we consider a class of routing optimization problems under uncertainty in which all decisions are made before the uncertainty is realized the objective is to obtain optimal routing solutions that would as much as possible adhere to a set of specified requirements after the uncertainty is realized these problems include finding an optimal routing solution to meet the soft time window requirements at a subset of nodes when the travel time is uncertain and sending multiple capacitated vehicles to different nodes to meet the customers uncertain demands we introduce a precise mathematical framework for defining and solving such routing problems in particular we propose a new decision criterion called the requirements violation rv index which quantifies the risk associated with the violation of requirements taking into account both the frequency of violations and their magnitudes whenever they occur the criterion can handle instances when probability distributions are known and ambiguity when dis

a priori solution of a travelling salesman problem in which a random subset of the customers are visited consider a problem of routing through a set of n points on any given instance of the problem only a subset consisting of k out of n points 0 k n has to be visited with the number k random with known probability distribution we wish to find a priori a tour through all n points on any given instance the k points present will then be visited in the same order as they appear in the a priori tour the problem of finding such a tour of minimum length in the expected value sense is defined as a probabilistic traveling salesman problem ptsp what distinguishes one ptsp from another is the probability distribution or more generally the probability law that specifies the number k and the identity of the points that need to be visited on any given instance of the problem after motivating the problem by applications we first derive closed form expressions for computing efficiently the expected length of any given tour under very general probabilistic assumptions we then provide in a unified way

satisficing measure approach for vehicle routing problem with time windows under uncertainty the complexity of evaluating chance constraints makes chance constrained programming problem difficult to solve one way to handle this complexity is by devising satisficing measures for the relevant uncertainties this paper focuses on solving the stochastic vehicle routing problem with time windows vrptw by satisficing measure approach sma that mitigates the dissatisfaction experienced by the customers satisficing measures are first proposed for the vrptw with stochastic demand on various distributions to demonstrate the dependency of customers satisfaction towards lack of inventory based on the vehicle s capacity similar satisficing measures are extended to vrptw with stochastic travel times we integrate the proposed satisficing measures into an existing tabu search heuristics to solve a set of generalized solomon instances in a short amount of computation time compared with best known results the sma saves the effort to design recourse actions applicable to many popular probability distributions and produces very competitive results c 2015 elsevier b v and association of european operational research societies euro within the international federation of operational research societies ifors all rights reserved

solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation abstract this paper considers the routing of vehicles with limited capacity from a central depot to a set of geographically dispersed customers where actual demand is revealed only when the vehicle arrives at the customer the solution to this vehicle routing problem with stochastic demand vrpsd involves the optimization of complete routing schedules with minimum travel distance driver remuneration and number of vehicles subject to a number of constraints such as time windows and vehicle capacity to solve such a multiobjective and multi modal combinatorial optimization problem this paper presents a multiobjective evolutionary algorithm that incorporates two vrpsd specific heuristics for local exploitation and a route simulation method to evaluate the fitness of solutions a new way of assessing the quality of solutions to the vrpsd on top of comparing their expected costs is also proposed it is shown that the algorithm is capable of finding useful tradeoff solutions for the vrpsd and the solutions are robust to the stochastic nature of the problem the developed algorithm is further validated on a few vrpsd instances adapted from solomon s vehicle routing problem with time windows vrptw benchmark problems

extremal growth of powers of operators satisfying resolvent conditions of kreiss ritt type let e be a compact subset of the unit circle we determine the extremal rate of growth of tn n 1 for banach space operators t satisfying the resolvent condition t i 1 const dist e 1 this includes as extreme cases the kreiss condition e t and the ritt condition e 1 for intermediate sets e the cardinality the measure and the hausdorff dimension of e all play a role in determining the growth of tn as a by product we also obtain lower bounds for the taylor coefficients of functions f holomorphic on the unit disk and satisfying f z 1dist z e z 1

polyhedral study of the capacitated vehicle routing problem the capacitated vehicle routing problem cvrp considered in this paper occurs when goods must be delivered from a central depot to clients with known demands usingk vehicles of fixed capacity each client must be assigned to exactly one of the vehicles the set of clients assigned to each vehicle must satisfy the capacity constraint the goal is to minimize the total distance traveled when the capacity of the vehicles is large enough this problem reduces to the famous traveling salesman problem tsp a variant of the problem in which each client is visited by at least one vehicle called the graphical vehicle routing problem gvrp is also considered in this paper and used as a relaxation of cvrp our approach for cvrp and gvrp is to extend the polyhedral results known for tsp for example the subtour elimination constraints can be generalized to facets of both cvrp and gvrp interesting classes of facets arise as a generalization of the comb inequalities depending on whether the depot is in a handle a tooth both or neither we report on the optimal solution of two problem instances by a cutting plane algorithm that only uses inequalities from the above classes

modeling vehicle routing with uncertain demands as a stochastic program properties of the corresponding solution abstract in this paper we address the issue of different mathematical models for the stochastic vehicle routing problem svrp this problem is inherently much more difficult than the generic deterministic vehicle routing problem vrp for which optimal procedures can solve only small problems presently we cannot even begin optimal solution procedures for the svrp for any problem size exceeding 3 nodes thus we need to examine modeling approaches to this problem in order to exploit the structure and solution properties we present a multistate stochastic model for the svrp we prove that this model has an interesting minimal graph representation in which a svrp solution corresponds to a hamiltonian cycle we also present a markov decision model for the problem concluding with a discussion of solution prospects and directions

on the computational complexity of the probabilistic traveling salesman problem with deadlines abstract the probabilistic traveling salesman problem with deadlines ptspd is a stochastic vehicle routing problem considering time dependencies in terms of deadlines the evaluation of the ptspd objective function is believed to be a computationally demanding task and all efforts to find a polynomial time approach have failed so far on the other hand no hardness results regarding the evaluation of the ptspd objective function are known we fill this gap and show that the evaluation of the ptspd objective function is indeed a computationally demanding task even for euclidean instances this task is p hard we then derive additional hardness results for different computational tasks related to the ptspd among other results we show that the decision variant and the optimization variant of the ptspd are both p hard following this we focus on polynomial time approximations of the ptspd objective function we prove the existence of an fpras under certain conditions and examine the approximation guarantees obtained by the existing approaches finally we give a strong inapproximability result regarding the objective function of a slightly more general problem the dependent ptspd

some modular varieties of low dimension ii the paper extends results obtained by frieder hermann and eberhard freitag about a six dimensional modular variety related to the orthogonal group of signature 2 6 the ring of modular forms of this variety turns out to be a weighted polynomial ring in 7 variables

resolvent tests for similarity to a normal operator the main result of this paper is the resolvent similarity criterion which says that linear growth of the resolvent towards the spectrum is sufficient for a hilbert space contraction with finite rank defect operators and spectrum not covering the unit disc to be similar to a normal operator similar results are proved for operators having a spectral set bounded by a dini smooth jordan curve in particular a dissipative operator with finite rank imaginary part is similar to a normal operator if and only if its resolvent grows linearly towards the spectrum relevant results on the insufficiency of linear resolvent growth not accompanied by smallness of defect operators are presented also it is proved that there is no restriction on the spectrum other than finiteness which together with linear resolvent growth implies similarity to a normal operator the construction of corresponding examples depends on a characterization of well known ahlfors curves as curves of linear length growth with respect to linear fractional transformations

resolvent criteria for similarity to a normal operator with spectrum on a curve abstract we give some new criteria for a hilbert space operator with spectrum on a smooth curve to be similar to a normal operator in terms of pointwise and integral estimates of the resolvent these results generalize criteria of stampfli van casteren and naboko and answers several questions posed by stampfli in 48 the main tools are from our recent results 12 on dilation to the boundary of the spectrum along with the dynkin functional calculus for smooth functions which is based on pseudoanalytic continuation

the mixed capacitated general routing problem under uncertainty abstract we study the general routing problem defined on a mixed graph and with stochastic demands the problem under investigation is aimed at finding the minimum cost set of routes to satisfy a set of clients whose demand is not deterministically known since each vehicle has a limited capacity the demand uncertainty occurring at some clients affects the satisfaction of the capacity constraints that hence become stochastic the contribution of this paper is twofold firstly we present a chance constrained integer programming formulation of the problem for which a deterministic equivalent is derived the introduction of uncertainty into the problem poses severe computational challenges addressed by the design of a branch and cut algorithm for the exact solution of limited size instances and of a heuristic solution approach exploring promising parts of the search space the effectiveness of the solution approaches is shown on a probabilistically constrained version of the benchmark instances proposed in the literature for the mixed capacitated general routing problem

a priori optimization of the probabilistic traveling salesman problem the probabilistic traveling salesman problem ptsp is defined on a graph g v e where v is the vertex set and e is the edge set each vertex vi has a probability pi of being present with each edge vi vj is associated a distance or cost cij in a first stage an a priori hamiltonian tour on g is designed the list of present vertices is then revealed in a second stage the a priori tour is followed by skipping the absent vertices the ptsp consists of determining a first stage solution that minimizes the expected cost of the second stage tour the problem is formulated as an integer linear stochastic program and solved by means of a branch and cut approach which relaxes some of the constraints and uses lower bounding functionals on the objective function problems involving up to 50 vertices are solved to optimality

using intermediate infeasible solutions to approach vehicle routing problems with precedence and loading constraints logistics and transportation issues have been receiving increasing attention during the last decades and their requirements have gradually changed making it necessary to take into account new situations and conditions the double traveling salesman problem with multiple stacks dtspms is a pickup and delivery problem in which some additional precedence and loading constraints are imposed on the vehicle to be used in this paper we approach the problem using intermediate infeasible solutions to diversify the search process and we develop some fixing procedures and infeasibility measures to deal with this kind of solutions and take advantage of their potential

the graded ring of quaternionic modular forms of degree 2 in the 1960 s igusa i described the graded ring of siegel modular forms of degree 2 in the sequel a few more concrete examples of graded rings of modular forms with respect to paramodular groups or hermitian modular groups were given e g by freitag f aoki and ibukiyama ai or dern and krieg dk

bounds and heuristics for capacitated routing problems in a capacitated routing problem the objective is to minimize the total distance travelled by vehicles of limited capacity to serve a set of customers that are located in the euclidean plane we develop asymptotically optimal bounds and heuristics for this problem under the assumption that the capacity of a vehicle is expressed in terms of an upper bound on the number of customers that it can serve the analysis culminates in an algorithm that for a given capacity and given will find a solution with relative error at most in time polynomial in the number of customers

a tabu search heuristic for the vehicle routing problem the purpose of this paper is to describe taburoute a new tabu search heuristic for the vehicle routing problem with capacity and route length restrictions the algorithm considers a sequence of adjacent solutions obtained by repeatedly removing a vertex from its current route and reinserting it into another route this is done by means of a generalized insertion procedure previously developed by the authors during the course of the algorithm infeasible solutions are allowed numerical tests on a set of benchmark problems indicate that tabu search out performs the best existing heuristics and taburoute often produces the best known solutions

heuristic and lower bound for a stochastic location routing problem in this article a stochastic location routing problem is defined and cast as a two stage model in a first stage the set of plants and a family of routes are determined in a second stage a recourse action is applied to adapt these routes to the actual set of customers to visit once they are known a two phase heuristic is developed an initial feasible solution is built by solving a sequence of subproblems and an improvement phase is then applied a lower bound based on bounding separately different parts of the cost of any feasible solution is also developed computational results are reported

a tabu search heuristic for the vehicle routing problem with stochastic demands and customers this paper considers a version of the stochastic vehicle routing problem where customers are present at locations with some probabilities and have random demands a tabu search heuristic is developed for this problem comparisons with known optimal solutions on problems whose sizes vary from 6 to 46 customers indicate that the heuristic produces an optimal solution in 89 45 of cases with an average deviation of 0 38 from optimality

a vehicle routing problem with stochastic demand we consider a natural probabilistic variation of the classical vehicle routing problem vrp in which demands are stochastic given only a probabilistic description of the demand we need to design routes for the vrp motivated by applications in strategic planning and distribution systems rather than resolving the problem when the demand becomes known we propose to construct an a priori sequence among all customers of minimal expected total length we analyze the problem using a variety of theoretical approaches we find closed form expressions and algorithms to compute the expected length of an a priori sequence under general probabilistic assumptions based on these expressions we find upper and lower bounds for the probabilistic vrp and the vrp re optimization strategy in which we find the optimal route at every instance we propose heuristics and analyze their worst case performance as well as their average behavior using techniques from probabilistic analysis our results suggest that our approac

tests for complete k spectral sets abstract let be a family of functions analytic in some neighborhood of a complex domain and let t be a hilbert space operator whose spectrum is contained in our typical result shows that under some extra conditions if the closed unit disc is complete k spectral for t for every then is complete k spectral for t for some constant k in particular we prove that under a geometric transversality condition the intersection of finitely many k spectral sets for t is again k spectral for some k k these theorems generalize and complement results by mascioni stessin stampfli badea beckermann crouzeix and others we also extend to non convex domains a result by putinar and sandberg on the existence of a skew dilation of t to a normal operator with spectrum in as a key tool we use the results from our previous paper 11 on traces of analytic uniform algebras