Primal-dual variable neighborhood search for the simple plant-location problem

Copyright @ 2007 INFORMSThe variable neighborhood search metaheuristic is applied to the primal simple plant-location problem and to a reduced dual obtained by exploiting the complementary slackness conditions. This leads to (i) heuristic resolution of (metric) instances with uniform fixed costs, up to n = 15,000 users, and m = n potential locations for facilities with an error not exceeding 0.04%; (ii) exact solution of such instances with up to m = n = 7,000; and (iii) exact solutions of instances with variable fixed costs and up to m = n = 15, 000.This work is supported by NSERC Grant 105574-02; NSERC Grant OGP205041; and partly by the Serbian Ministry of Science, Project 1583

A Tabu Search Heuristic Procedure for the Capacitated Facility Location Problem

A tabu search heuristic procedure for the capacitated facility location problem is developed, implemented and computationally tested. The heuristic procedure uses both short term and long term memories to perform the main search process as well as the diversification and intensification functions. Visited solutions are stored in a primogenitary linked quad tree as a long term memory. The recent iteration at which a facility changed its status is stored for each facility site as a short memory. Lower bounds on the decreases of total cost are used to measure the attractiveness of switching the status of facilities and are used to select a move in the main search process. A specialized transportation algorithm is developed and employed to exploit the problem structure in solving transportation problems. The performance of the heuristic procedure is tested through computational experiments using test problems from the literature and new test problems randomly generated. It found optimal solutions for a most all test problems used. As compared to the Lagrangean and the surrogate/Lagrangean heuristic methods, the tabu search heuristic procedure found much better solutions using much less CPU time.Capacitated facility location, Tabu search, Metaheuristics

Matheuristics: using mathematics for heuristic design

Matheuristics are heuristic algorithms based on mathematical tools such as the ones provided by mathematical programming, that are structurally general enough to be applied to different problems with little adaptations to their abstract structure. The result can be metaheuristic hybrids having components derived from the mathematical model of the problems of interest, but the mathematical techniques themselves can define general heuristic solution frameworks. In this paper, we focus our attention on mathematical programming and its contributions to developing effective heuristics. We briefly describe the mathematical tools available and then some matheuristic approaches, reporting some representative examples from the literature. We also take the opportunity to provide some ideas for possible future development

Solution Methods for the \u3cem\u3ep\u3c/em\u3e-Median Problem: An Annotated Bibliography

The p-median problem is a graph theory problem that was originally designed for, and has been extensively applied to, facility location. In this bibliography, we summarize the literature on solution methods for the uncapacitated and capacitated p-median problem on a graph or network

A model and methodologies for the location problem with logistical components

This paper significantly extends traditional facility location models by introducing several logistical cost components such as holding, ordering, and transportation costs in a multi-commodity, multi-location framework. Since location and logistical costs are highly inter-related, the paper provides an integrated model, and seeks to minimize total physical distribution costs by simultaneously determining optimal locations, flows, shipment compositions, and shipment cycle times. Two sophisticated heuristic methodologies, based on Lagrangian relaxation and simulated annealing, respectively, are provided and compared in an extensive computational experiment

Matheuristics:survey and synthesis

In integer programming and combinatorial optimisation, people use the term matheuristics to refer to methods that are heuristic in nature, but draw on concepts from the literature on exact methods. We survey the literature on this topic, with a particular emphasis on matheuristics that yield both primal and dual bounds (i.e., upper and lower bounds in the case of a minimisation problem). We also make some comments about possible future developments

Facility Location Problems: Models, Techniques, and Applications in Waste Management

This paper presents a brief description of some existing models of facility location problems (FLPs) in solid waste management. The study provides salient information on commonly used distance functions in location models along with their corresponding mathematical formulation. Some of the optimization techniques that have been applied to location problems are also presented along with an appropriate pseudocode algorithm for their implementation. Concerning the models and solution techniques, the survey concludes by summarizing some recent studies on the applications of FLPs to waste collection and disposal. It is expected that this paper will contribute in no small measure to an integrated solid waste management system with specific emphasis on issues associated with waste collection, thereby boosting the drive for e�ective and e�cient waste collection systems. The content will also provide early career researchers with some necessary starting information required to formulate and solve problems relating to FLP

Resolution Search et problèmes d'optimisation discrète

Les problèmes d optimisation discrète sont pour beaucoup difficiles à résoudre, depar leur nature combinatoire. Citons par exemple les problèmes de programmationlinéaire en nombres entiers. Une approche couramment employée pour les résoudreexactement est l approche de Séparation et Évaluation Progressive. Une approchedifférente appelée Resolution Search a été proposée par Chvátal en 1997 pourrésoudre exactement des problèmes d optimisation à variables 0-1, mais elle restemal connue et n a été que peu appliquée depuis.Cette thèse tente de remédier à cela, avec un succès partiel. Une première contributionconsiste en la généralisation de Resolution Search à tout problème d optimisationdiscrète, tout en introduisant de nouveaux concepts et définitions. Ensuite,afin de confirmer l intérêt de cette approche, nous avons essayé de l appliquer enpratique pour résoudre efficacement des problèmes bien connus. Bien que notrerecherche n ait pas abouti sur ce point, elle nous a amené à de nouvelles méthodespour résoudre exactement les problèmes d affectation généralisée et de localisationsimple. Après avoir présenté ces méthodes, la thèse conclut avec un bilan et desperspectives sur l application pratique de Resolution Search.The combinatorial nature of discrete optimization problems often makes them difficultto solve. Consider for instance integer linear programming problems, which arecommonly solved using a Branch-and-Bound approach. An alternative approach,Resolution Search, was proposed by Chvátal in 1997 for solving 0-1 optimizationproblems, but remains little known to this day and as such has seen few practicalapplications.This thesis attempts to remedy this state of affairs, with partial success. Itsfirst contribution consists in the generalization of Resolution Search to any discreteoptimization problem, while introducing new definitions and concepts. Next, wetried to validate this approach by attempting to solve well-known problems efficientlywith it. Although our research did not succeed in this respect, it lead usto new methods for solving the generalized assignment and uncapacitated facilitylocation problems. After presenting these methods, this thesis concludes with asummary of our attempts at practical application of Resolution Search, along withfurther perspectives on this matter.AVIGNON-Bib. numérique (840079901) / SudocSudocFranceF