An Efficient Genetic Algorithm for Solving the Multi-Level Uncapacitated Facility Location Problem

In this paper a new evolutionary approach for solving the multi-level uncapacitated facility location problem (MLUFLP) is presented. Binary encoding scheme is used with appropriate objective function containing dynamic programming approach for finding sequence of located facilities on each level to satisfy clients' demands. The experiments were carried out on the modified standard single level facility location problem instances. Genetic algorithm (GA) reaches all known optimal solutions for smaller dimension instances, obtained by total enumeration and CPLEX solver. Moreover, all optimal/best known solutions were reached by genetic algorithm for a single-level variant of the problem

METAHEURISTICS FOR HUB LOCATION MODELS

In this research, we propose metaheuristics for solving two p-hub median problems.. The first p-hub median problem, which is NP-hard, is the uncapacitated single p-hub median problem (USApHMP). In this problem, metaheuristics such as genetic algorithms, simulated annealing and tabu search, are applied in different types of representations. Caching is also applied to speed up computational time of the algorithms. The results clearly demonstrate that tabu search with a permutation solution representation, augmented with caching is the highest performing method, both in terms of solution quality and computational time among these algorithms for the USApHMP. We also investigate the performance of hybrid metaheuristics, formed by path-relinking augmentation of the three base algorithms (genetic algorithms, simulated annealing and tabu search). The results indicate that hybridrization with path-relinking improvees the performance of base algorithms except tabu search since a good base metaheuristic does not require path-relinking. For the second p-hub median problem, the NP-hard uncapacitated multiple p-hub median problem (UMApHMP), we proposed Multiple TS. We identify multiple nodes using the convex hull and methods derived from the tabu search for the USApMHP. We find optimal allocations using the Single Reallocation Exchange procedure, developed for the USApHMP. The results show that implementing tabu search with a geometric interpretation allows nearly all optimal solutions to be found

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

RAMP para o Problema de Localização de Hubs com Afetação Múltipla e sem Restrições de Capacidade

Os Problemas de Localização de Instalações (Facility Location Problems – FLP) são problemas complexos que assumem um grande foco de estudo por parte da comunidade científica. Os FLP têm várias aplicações no mundo real e em diversas ´áreas, tais como, telecomunicações, redes de computadores, redes de transporte, rede elétrica, localização de hospitais, localização de aeroportos, entre muitos outros. O Problema de Localização de Hubs com Afetação múltipla e Sem Restrições de Capacidade (Uncapacitated Multiple Allocation Hub Location Problem – UMAHLP) faz parte do grupo de problemas de localização extensivamente estudados. Tratando-se de um problema de otimização combinatória NP-difícil, a utilização de métodos exatos na resolução de problemas práticos de grande dimensão pode ser seriamente comprometida pelos tempos computacionais necessários para a obtenção da solução ótima. Para ultrapassar esta dificuldade, um número significativo de algoritmos heurísticos têm sido propostos com o objetivo de encontrar soluções de boa qualidade em tempos tão reduzidos quanto possível. O sucesso da metaheurística Relaxation Adaptive Memory Programming (RAMP) aplicada ao Problema de Localização de Instalações sem Restrições de Capacidade (Uncapacitated Facility Location Problem – UFLP) apresenta esta abordagem como bastante promissora na aplicação a outros problemas de localização. O UMAHLP ´e um exemplo clássico destes problemas. Neste contexto, pretende-se com este estudo, explorar as vantagens da aplicação da abordagem RAMP ao UMAHLP. A abordagem RAMP baseia-se na exploração da relação primal-dual do problema, orientando a pesquisa com base em princípios de memória adaptativa. O m´etodo RAMP faz uso de vários níveis de sofisticação, definidos pelo grau de intensidade que são explorados os lados primal e dual do problema. Deve-se começar pela implementação da versão mais simples do método e só avançar para formas mais complexas, caso seja necessário, uma vez que o método RAMP é incremental. Para o UFLP foram implementados dois algoritmos, um com base na metaheurística Pesquisa por Dispersão (Scatter Search – SS) e outro tendo por base a versão mais sofisticada do método RAMP, designada de PD-RAMP, que explora intensivamente ambos os lados da relação primal-dual. O algoritmo PD-RAMP implementado engloba uma versão mais simples do algoritmo SS proposto, para explorar o espaço de soluções do lado primal, sendo o lado dual explorado pelo método Dual-Ascent. No UMAHLP foi aplicada uma versão mais simples do RAMP, intensificando a exploração do lado dual do Problema, através do método Dual-Ascent, enquanto que o lado primal é explorado, de uma forma mais simples, tendo por base o método de Pesquisa Tabu (Tabu Search – TS). A aplicação do método RAMP aos problemas UFLP e UMAHLP, revelou-se muito robusta e eficiente, demonstrando bons resultados para as instâncias de teste padrão existentes para cada um dos problemas. Em ambos os problemas tratados os algoritmos propostos conseguem encontrar a maior parte das melhores soluções conhecidas, obtendo excelentes resultados. Para o UMAHLP são encontradas duas soluções melhores do que as conhecidas. O método RAMP demonstrou, mais uma vez, ser uma metaheurística, que apesar de ser recente, já apresenta um elevado nível de sucesso na resolução de problemas complexos

A submodular representation for hub networkdesign problems with profits and single assignments

Hub network design problems (HNDPs) lie at the heart of network design planning in transportation and telecommunication systems. They constitute a challenging class of optimization problems that focus on the design of a hub network. In this work, we study a class of HNDPs, named hub network design problems with profits and single assignments, which forces each node to be assigned to exactly one hub facility. We propose three different combinatorial representations for maximizing the total profit defined as the difference between the perceived revenues from routing a set of commodities minus the setup cost for designing a hub network, considering the single allocation assumption. We investigate whether the objective function of each representation satisfies the submodular property or not. One representation satisfies submodularity, and we use it to present an approximation algorithm with polynomial running time. We obtain worst-case bounds on the approximations’ quality and analyze some special cases where these worst-case bounds are sharper

Iterative restricted space search : a solving approach based on hybridization

Face à la complexité qui caractérise les problèmes d'optimisation de grande taille l'exploration complète de l'espace des solutions devient rapidement un objectif inaccessible. En effet, à mesure que la taille des problèmes augmente, des méthodes de solution de plus en plus sophistiquées sont exigées afin d'assurer un certain niveau d 'efficacité. Ceci a amené une grande partie de la communauté scientifique vers le développement d'outils spécifiques pour la résolution de problèmes de grande taille tels que les méthodes hybrides. Cependant, malgré les efforts consentis dans le développement d'approches hybrides, la majorité des travaux se sont concentrés sur l'adaptation de deux ou plusieurs méthodes spécifiques, en compensant les points faibles des unes par les points forts des autres ou bien en les adaptant afin de collaborer ensemble. Au meilleur de notre connaissance, aucun travail à date n'à été effectué pour développer un cadre conceptuel pour la résolution efficace de problèmes d'optimisation de grande taille, qui soit à la fois flexible, basé sur l'échange d'information et indépendant des méthodes qui le composent. L'objectif de cette thèse est d'explorer cette avenue de recherche en proposant un cadre conceptuel pour les méthodes hybrides, intitulé la recherche itérative de l'espace restreint, ±Iterative Restricted Space Search (IRSS)>>, dont, la principale idée est la définition et l'exploration successives de régions restreintes de l'espace de solutions. Ces régions, qui contiennent de bonnes solutions et qui sont assez petites pour être complètement explorées, sont appelées espaces restreints "Restricted Spaces (RS)". Ainsi, l'IRSS est une approche de solution générique, basée sur l'interaction de deux phases algorithmiques ayant des objectifs complémentaires. La première phase consiste à identifier une région restreinte intéressante et la deuxième phase consiste à l'explorer. Le schéma hybride de l'approche de solution permet d'alterner entre les deux phases pour un nombre fixe d'itérations ou jusqu'à l'atteinte d'une certaine limite de temps. Les concepts clés associées au développement de ce cadre conceptuel et leur validation seront introduits et validés graduellement dans cette thèse. Ils sont présentés de manière à permettre au lecteur de comprendre les problèmes que nous avons rencontrés en cours de développement et comment les solutions ont été conçues et implémentées. À cette fin, la thèse a été divisée en quatre parties. La première est consacrée à la synthèse de l'état de l'art dans le domaine de recherche sur les méthodes hybrides. Elle présente les principales approches hybrides développées et leurs applications. Une brève description des approches utilisant le concept de restriction d'espace est aussi présentée dans cette partie. La deuxième partie présente les concepts clés de ce cadre conceptuel. Il s'agit du processus d'identification des régions restreintes et des deux phases de recherche. Ces concepts sont mis en oeuvre dans un schéma hybride heuristique et méthode exacte. L'approche a été appliquée à un problème d'ordonnancement avec deux niveaux de décision, relié au contexte des pâtes et papier: "Pulp Production Scheduling Problem". La troisième partie a permit d'approfondir les concepts développés et ajuster les limitations identifiées dans la deuxième partie, en proposant une recherche itérative appliquée pour l'exploration de RS de grande taille et une structure en arbre binaire pour l'exploration de plusieurs RS. Cette structure a l'avantage d'éviter l'exploration d 'un espace déjà exploré précédemment tout en assurant une diversification naturelle à la méthode. Cette extension de la méthode a été testée sur un problème de localisation et d'allocation en utilisant un schéma d'hybridation heuristique-exact de manière itérative. La quatrième partie généralise les concepts préalablement développés et conçoit un cadre général qui est flexible, indépendant des méthodes utilisées et basé sur un échange d'informations entre les phases. Ce cadre a l'avantage d'être général et pourrait être appliqué à une large gamme de problèmes

Ant Colony Optimisation – A Proposed Solution Framework for the Capacitated Facility Location Problem

This thesis is a critical investigation into the development, application and evaluation of ant colony optimisation metaheuristics, with a view to solving a class of capacitated facility location problems. The study is comprised of three phases. The first sets the scene and motivation for research, which includes; key concepts of ant colony optimisation, a review of published academic materials and a research philosophy which provides a justification for a deductive empirical mode of study. This phase reveals that published results for existing facility location metaheuristics are often ambiguous or incomplete and there is no clear evidence of a dominant method. This clearly represents a gap in the current knowledge base and provides a rationale for a study that will contribute to existing knowledge, by determining if ant colony optimisation is a suitable solution technique for solving capacitated facility location problems. The second phase is concerned with the research, development and application of a variety of ant colony optimisation algorithms. Solution methods presented include combinations of approximate and exact techniques. The study identifies a previously untried ant hybrid scheme, which incorporates an exact method within it, as the most promising of techniques that were tested. Also a novel local search initialisation which relies on memory is presented. These hybridisations successfully solve all of the capacitated facility location test problems available in the OR-Library. The third phase of this study conducts an extensive series of run-time analyses, to determine the prowess of the derived ant colony optimisation algorithms against a contemporary cross-entropy technique. This type of analysis for measuring metaheuristic performance for the capacitated facility location problem is not evident within published materials. Analyses of empirical run-time distributions reveal that ant colony optimisation is superior to its contemporary opponent. All three phases of this thesis provide their own individual contributions to existing knowledge bases: the production of a series of run-time distributions will be a valuable resource for future researchers; results demonstrate that hybridisation of metaheuristics with exact solution methods is an area not to be ignored; the hybrid methods employed in this study ten years ago would have been impractical or infeasible; ant colony optimisation is shown to be a very flexible metaheuristic that can easily be adapted to solving mixed integer problems using hybridisation techniques

An iterated local search algorithm for the facility location problem

Desenvolupar un Iterated Local Search amb tècniques d'aleatorització esbiaixada per solucionar el Uncapacitated Facility Location Problem

Χωροθέτηση και ενοικίαση κοινόχρηστων πόρων. Πειραματική αξιολόγηση αλγορίθμων

Στην εργασία αυτή μελετάται το πρόβλημα της χωροθέτησης (facility location) και ενοικίασης (facility leasing) κοινόχρηστων πόρων και συγκεκριμένα η εκδοχή του προβλήματος που απαιτεί ανοχή σε σφάλματα των κοινόχρηστων πόρων μέσω πλεονασμού (fault tolerant facility location). Εξετάζεται πειραματικά η δυσκολία του προβλήματος της χωροθέτησης καθώς και της ενοικίασης. Επίσης υλοποιούνται και αξιολογούνται δύο ευρέως αποδεκτοί αλγόριθμοι και εξετάζεται αναλυτικά η προσέγγιση τους στις βέλτιστες τιμές και η διακύμανση της με διάφορους παράγοντες. Με βάση τα αποτελέσματα προτείνονται δύο νέοι αλγόριθμοι με καλύτερη συμπεριφορά.In this work, we deal with facility location problems and especially with fault tolerant facility location and offline facility leasing. We perform an experimental study of the difficulty of these two problems. Also two well known algorithms are implemented and evaluated and their approximation to the optimal solution is being studied as it fluctuates when changing various factors. Based on the results we propose two new algorithms which perform even better