Полиномиальный рандомизированный алгоритм для задачи «Асимметричный коммивояжер»

The asymmetric travelling salesman problem without metric restrictions is considered. The randomized algorithm is proposed. It has a certain approximation guarantee and possesses a certain property regarding the probabilities of the tours built. The computational complexity of the algorithm is polynomial and affordable. Рассматривается задача «Асимметричный коммивояжер», в которой нужно найти обход вершин с минимальной суммарной стоимостью дуг в полном ориентированном графе. На задачу не накладывается неравенство треугольника. Для решения данной задачи построен рандомизированный алгоритм, у которого есть определенная гарантированная степень приближения. Вычислительная сложность алгоритма позволяет использовать данный алгоритм для компьютерных программ

An overview of neighbourhood search metaheuristics

This paper gives details of the steps needed to undertake neighbourhood search for a combinatorial optimization problem. The main variations are briefly described and pointers for future research briefly discussed. Throughout there is extensive referencing to some of the most important publications in the are

Effective Local and Guided Variable Neighbourhood Search Methods for the Asymmetric Travelling Salesman Problem

In this paper we present effective new local and variable neighbourhood search heuristics for the asymmetric Travelling Salesman Problem. Our local search approach, HyperOpt, is inspired by a heuristic developed for a sequencing problem arising in the manufacture of printed circuit boards. In our approach we embed an exact algorithm into a local search heuristic in order to exhaustively search promising regions of the solution space. We propose a hybrid of HyperOpt and 3-opt which allows us to benefit from the advantages of both approaches and gain better tours overall. Using this hybrid within the Variable Neighbourhood Search (VNS) metaheuristic framework, as suggested by Hansen and Mladenovic, allows us to overcome local optima and create tours of very high quality. We introduce the notion of a "guided shake" within VNS and show that this yields a heuristic which is more effective than the random shakes proposed by Hansen and Mladenovic. The heuristics presented form a continuum from very fast ones which produce reasonable results to much slower ones which produce excellent results. All of the heuristics have proven capable of handling the sort of constraints which arise for real life problems, such as those in electronics assembly

Méthodologie de conception de matériaux architecturés : application au packaging de l’électronique embarquée

The design process involving both the architectures and the materialsrepresents an hard task mainly because of the high number of possible configurations.This issue requires the development of new approaches and new tools. In this study, a newstrategy for the design of architectured materials is proposed. An architectured material,or multimaterial, can be defined by its architecture, its components and their volumefractions, and the nature of the interface between them. The design of a multimaterial isbased on the analysis of numerous quantitative and qualitative parameters. In this study,a multimaterial design method allowing a simultaneous selection of architectures andmaterials was developed. This work deals with the association of a database of elementaryarchitectures and a database of materials. The search of solutions is based on an hybridmethod using genetic algorithm and constraint programming algorithm. This hybridmethod allowed the definition of solutions, with optimal geometrical parameters in answerto the specifications requirements. This study was carried out within the MUJU project(Mutimaterial mUltiphysics JUnction) framework supported by the National ResearchAgency. The developed method was applied to the design of heat sink in embeddedelectronic packaging for aeronautic. Currently made of metallic alloy, the packaging mustsimultaneously satisfy thermal, mechanical and electrical constraint. The achievedsolutions allowed a weight saving lies in the range 20 to 40% while keeping the sameperformance.Le processus de conception d’un multimatériau impliquant à la foisl'architecture et les matériaux représente une tâche difficile en raison du nombre élevé deconfigurations possibles. Ce processus oblige les concepteurs d'une part à développer desapproches nouvelles, mais aussi à développer de nouveaux outils. Ainsi ce travail proposeune nouvelle méthode pour la conception de matériaux architecturés. Un matériauarchitecturé, ou multimatériau, peut être défini par son architecture, ses matériauxconstitutifs associés à leurs fractions volumiques et la nature de leurs interfaces. Laconception d'un multimatériau est basée sur le choix de nombreux paramètres aussi bienquantitatifs que qualitatifs. Dans ce travail, la méthode de conception proposée permetune sélection simultanée des architectures et des matériaux. Celle-ci est axée autour del'association d'une base de données d’architectures élémentaires et d’une base de donnéesde matériaux. La recherche de solutions est basée sur une méthode hybride utilisant unalgorithme génétique et un algorithme de programmation sous contraintes. La méthodehybride permet la définition de solutions intégrant des paramètres géométriques optimisésen réponse aux astreintes du cahier des charges. Ce travail a été réalisé au sein du projetMUJU (Mutimaterial mUltiphysics JUnction) financé par l'Agence Nationale de laRecherche. Le travail développé a ainsi été appliqué à la conception de packaging del’électronique embarquée. Actuellement fabriqué en alliage métallique, ce packaging utilisédans l'aéronautique doit satisfaire à la fois des contraintes thermiques, mécaniques etélectriques. Les solutions obtenues ont permis un gain de masse de 20 à 40% tout enassurant des performances équivalentes

New local search in the space of infeasible solutions framework for the routing of vehicles

Combinatorial optimisation problems (COPs) have been at the origin of the design of many optimal and heuristic solution frameworks such as branch-and-bound algorithms, branch-and-cut algorithms, classical local search methods, metaheuristics, and hyperheuristics. This thesis proposes a refined generic and parametrised infeasible local search (GPILS) algorithm for solving COPs and customises it to solve the traveling salesman problem (TSP), for illustration purposes. In addition, a rule-based heuristic is proposed to initialise infeasible local search, referred to as the parameterised infeasible heuristic (PIH), which allows the analyst to have some control over the features of the infeasible solution he/she might want to start the infeasible search with. A recursive infeasible neighbourhood search (RINS) as well as a generic patching procedure to search the infeasible space are also proposed. These procedures are designed in a generic manner, so they can be adapted to any choice of parameters of the GPILS, where the set of parameters, in fact for simplicity, refers to set of parameters, components, criteria and rules. Furthermore, a hyperheuristic framework is proposed for optimizing the parameters of GPILS referred to as HH-GPILS. Experiments have been run for both sequential (i.e. simulated annealing, variable neighbourhood search, and tabu search) and parallel hyperheuristics (i.e., genetic algorithms / GAs) to empirically assess the performance of the proposed HH-GPILS in solving TSP using instances from the TSPLIB. Empirical results suggest that HH-GPILS delivers an outstanding performance. Finally, an offline learning mechanism is proposed as a seeding technique to improve the performance and speed of the proposed parallel HH-GPILS. The proposed offline learning mechanism makes use of a knowledge-base to keep track of the best performing chromosomes and their scores. Empirical results suggest that this learning mechanism is a promising technique to initialise the GA’s population