We consider the non-convex quadratic maximization problem subjectto the l1 unit ball constraint. The nature of the l 1 normstructure makes this problem extremely hard to analyze, and as aconsequence, the same difficulties are encountered when trying tobuild suitable approximations for this problem by some tractableconvex counterpart formulations. We explore some properties ofthis problem, derive SDP-like relaxations and raise openquestions.

Let μ and ν be two probability measures on the real line and let c be a lower semicontinuous function on the plane. The mass transfer problem consists in determining a measure ξ whose marginals coincide with μ and ν, and whose total cost ∫∫ c(x,y)dξ(x,y) is minimum. In this paper we present three algorithms to solve numerically this Monge-Kantorovitch problem when the commodity being shipped is one-dimensional and not necessarily confined to a bounded interval . We illustrate these numerical methods and determine the convergence rate.

This article presents a basic scheme for deriving systematicallya filtering algorithm from the graph properties based representationof global constraints. This scheme is based on thebounds of the graph parameters used in the description ofa global constraint. The article provides bounds for the most commonused graph parameters.

We present a regularization method to approach a solution of the pessimistic formulation of ill-posed bilevel problems. This allows to overcome the difficulty arising from the non uniqueness of the lower level problems solutions and responses. We prove existence of approximated solutions, give convergence result using Hoffman-like assumptions. We end with objective value error estimates.

This paper analyzes adiscrete-time multi-server queue in which service capacity of eachserver is a minimum of one and a maximum of b customers. Theinterarrival- and service-times are assumed to be independent andgeometrically distributed. The queue is analyzed under theassumptions of early arrival system and late arrival system withdelayed access. Besides, obtaining state probabilities atarbitrary and outside observer's observation epochs, someperformance measures and waiting-time distribution in the queuehave also been discussed. Finally, it is shown that in limitingcase the results obtained in thispaper tend to the continuous-time counterpart.

This paper presents the approach that we developed to solve the ROADEF 2003 challenge problem. This work is part of a research program whose aim is to study the benefits and the computer-aided generation of hybrid solutions that mix constraint programming and meta-heuristics, such as large neighborhood search (LNS). This paper focuses on three contributions that were obtained during this project: an improved method for propagating Hamiltonian chain constraints, a fresh look at limited discrepancy search and the introduction of randomization and de-randomization within our combination algebra. This algebra is made of terms that represent optimization algorithms, following the approach of SALSA [1], which can be generated or tuned automatically using a learning meta-strategy [2]. In this paper, the hybrid combination that is investigated mixes constraint propagation, a special form of limited discrepancy search and large neighborhood search.

The NP-hard problem of car sequencing has received a lot of attention these last years. Whereas a directapproach based on integer programming or constraint programming is generally fruitless when the number of vehicles tosequence exceeds the hundred, several heuristics have shown their efficiency. In this paper, very large-scaleneighborhood improvement techniques based on integer programming and linear assignment are presented for solving carsequencing problems. The effectiveness of this approach is demonstrated through an experimental study made on seminalCSPlib's benchmarks.

We present a variant of the analytic center cutting plane algorithm proposedby Goffin et al. (1996) to approximately solve equilibrium problemsas proposed by Blum and Oettli (1994), which include as particular problemsthe variational inequalities problem, the Nash equilibria problem innon-cooperative games, the convex minimization problem, and the fixed pointproblem. Furthermore, we analyze the convergence and complexity of the modifiedalgorithm.

Fractionnal mathematical programs appear in numerous operations research, computer science and economic domains. We consider in this paper the problem of maximizing the sum of 0–1 hyperbolic ratios (SRH). In contrast to the single ratio problem, there has been little work inthe literature concerning this problem. We propose two mixed-integer linear programming formulations of SRH and develop two different strategies to solve them. The first one consists in using directly a general-purpose mixed-integer programming solver. The second one is based on a specialized branch and bound algorithm that reformulates more precisely the problem at every node of search tree. We also propose a heuristic method and we exploit the obtained solution in order to improve the first strategy. We present computational experiments that allow to compare the different approaches.

The purpose of this paper is to demonstrate that, for globally minimize one dimensional nonconvex problems withboth twice differentiable function and constraint, we can propose an efficientalgorithm based on Branch and Bound techniques. The method is firstdisplayed in the simple case with an interval constraint. The extension is displayedafterwards to the general case with an additional nonconvex twicedifferentiable constraint. A quadratic bounding function which is betterthan the well known linear underestimator is proposed while w-subdivision is added to support the branching procedure. Computational results on several andvarious types of functions show the efficiency of our algorithms and theirsuperiority with respect to the existing methods.

L'identification de structures propres à un problème est souvent une étapeclef pour la conception d'heuristiques de recherche comme pour la compréhension de lacomplexité du problème. De nombreuses approches en Recherche Opérationnelleemploient des stratégies de relaxation ou de décomposition dès lors quecertaines struc-tures idoines ont été identifiées. L'étape suivante est laconception d'algorithmes de résolution qui puissent intégrer à la volée,pendant la résolution, ce type d'information. Cet article propose d'utiliser unsolveur de contraintes à base d'explications pour collecter une informationpertinente sur les structures dynamiques et statiques inhérentes au problème.

We introduce a new barrier function to solve a class ofSemidefinite Optimization Problems (SOP) with bounded variables.That class is motivated by some (SOP) as the minimization of thesum of the first few eigenvalues of symmetric matrices and graphpartitioning problems. We study the primal-dual central pathdefined by the new barrier and we show that this path is analytic,bounded and that all cluster points are optimal solutions of theprimal-dual pair of problems. Then, using some ideas fromsemi-analytic geometry we prove its full convergence. Finally, weintroduce a new proximal point algorithm for that class ofproblems and prove its convergence.

We present a Branch-and-Cut algorithm where the volume algorithm is applied instead of the traditionally used dual simplex algorithm to the linear programming relaxations in the root node of the search tree. This means that we use fast approximate solutions to these linear programs instead of exact but slower solutions. We present computational results with the Steiner tree and Max-Cut problems. We show evidence that one can solve these problems much faster with the volume algorithm based Branch-and-Cut code than with a dual simplex based one. We discuss when the volume based approach might be more efficient than the simplex based approach.

In the course of globalization, many enterprises change theirstrategies and are coupled in partnerships with suppliers,subcontractors and customers. This coupling forms supply chainscomprising several geographically distributed productionfacilities. Production planning in a supply chain is a complicatedand difficult task, as it has to be optimal both for the localmanufacturing units and for the whole supply chain network. Inthis paper two analytical models are used to solve the productionplanning problem in supply chain involving several enterprises.Generally in practice, for competitive and/or practical reasons,frequently each enterprise prefers to optimize its production planwith little care about the other members of the supply chain. Thiscase is presented through a simple model of decentralizedoptimization. The aim of this study is to analyze and compare thetwo types of optimization: centralized and decentralized. Theinitial question is: what are the profit and the optimal policy ofglobal (centralized) optimization in contrast to local(decentralized)? We characterize this gain by comparing theoptimal profits obtained in both cases.

In on-line computation, the instance of the problem dealt is notentirely known from the beginning of the solution process, but itis revealed step-by-step. In this paper we deal with on-lineindependent set. On-line models studied until now for this problemsuppose that the input graph is initially empty and revealedeither vertex-by-vertex, or cluster-by-cluster. Here we present anew on-line model quite different to the ones already studied. Itassumes that a superset of the final graph is initially present(in our case the complete graph on the order n of the finalgraph) and edges are progressively removed until the achievementof the final graph. Next, we revisit the model introduced in[Demange, Paradon and Paschos, Lect. Notes Comput. Sci.1963 (2000)326–334] and study relaxations assuming that somepaying backtracking is allowed.

A bound for the greedy heuristic applied to the K-facility location problem can be calculated,using values gathered during the calculation of the heuristic. The bound strengthens awell-known bound for the heuristic. Computational experiments show that this bound can bebeneficial when the number of facilities is small or close to the total number of potential sites. In addition, it is consistent with previous results about the influence of the data characteristicsupon the optimal value.

Periodic Vehicle Routing Problem: classification and heuristic for tactical planning.The Periodic Vehicle Routing Problem (PVRP) consists in assigning customer visits to vehicle routes in some periods of a time horizon so as to satisfy some service level requirements that can take theform of frequency of visit, constraint on time lag between visits, or pre-defined visit patterns. We present different variants of this problem and propose a classification. Then, we consider a model for tactical planning for which we propose a heuristic: we optimise theplanning of customer visits to achieve both workload balancing andregionalisation of the routes. The objective of regionalisation reflects a desire to specializeroutes to restricted geographical area. The standard minimisation of distancetravelled is left for the underlying operational decision making model.Our heuristic achieves practical solutions for an industrialinstance with 16658 visits to schedule over a horizon of 20 days.

Markov Decision Processes (MDPs) are a classical framework forstochastic sequential decision problems, based on an enumerated statespace representation. More compact and structured representations havebeen proposed: factorization techniques use state variablesrepresentations, while decomposition techniques are based on apartition of the state space into sub-regions and take advantage ofthe resulting structure of the state transition graph. We use a familyof probabilistic exploration-like planning problems in order to studythe influence of the modeling structure on the MDP solution. We firstdiscuss the advantages and drawbacks of a graph based representationof the state space, then present our comparisons of two decompositiontechniques, and propose to use a global approach combining both statespace factorization and decomposition techniques. On the explorationproblem instance, it is proposed to take advantage of the naturaltopological structure of the navigation space, which is partitionedinto regions. A number of local policies are optimized within eachregion, that become the macro-actions of the global abstract MDPresulting from the decomposition. The regions are the correspondingmacro-states in the abstract MDP. The global abstract MDP is obtainedin a factored form, combining all the initial MDP state variables andone macro-state “region” variable standing for the different possiblemacro-states corresponding to the regions. Further research ispresently conducted on efficient solution algorithms implementing thesame hybrid approach for tackling large size MDPs.