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

Distance-constrained vehicle routing problem: exact and approximate solution (mathematical programming)

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The asymmetric distance-constrained vehicle routing problem (ADVRP) looks at finding vehicle tours to connect all customers with a depot, such that the total distance is minimised; each customer is visited once by one vehicle; every tour starts and ends at a depot; and the travelled distance by each vehicle is less than or equal to the given maximum value. We present three basic results in this thesis. In the first one, we present a general flow-based formulation to ADVRP. It is suitable for symmetric and asymmetric instances. It has been compared with the adapted Bus School Routing formulation and appears to solve the ADVRP faster. Comparisons are performed on random test instances with up to 200 customers. We reach a conclusion that our general formulation outperforms the adapted one. Moreover, it finds the optimal solution for small test instances quickly. For large instances, there is a high probability that an optimal solution can be found or at least improve upon the value of the best feasible solution found so far, compared to the other formulation which stops because of the time condition. This formulation is more general than Kara formulation since it does not require the distance matrix to satisfy the triangle inequality. The second result improves and modifies an old branch-and-bound method suggested by Laporte et al. in 1987. It is based on reformulating a distance-constrained vehicle routing problem into a travelling salesman problem and uses the assignment problem as a lower bounding procedure. In addition, its algorithm uses the best-first strategy and new branching rules. Since this method was fast but memory consuming, it would stop before optimality is proven. Therefore, we introduce randomness in choosing the node of the search tree in case we have more than one choice (usually we choose the smallest objective function). If an optimal solution is not found, then restart is required due to memory issues, so we restart our procedure. In that way, we get a multistart branch and bound method. Computational experiments show that we are able to exactly solve large test instances with up to 1000 customers. As far as we know, those instances are much larger than instances considered for other VRP models and exact solution approaches from recent literature. So, despite its simplicity, this proposed algorithm is capable of solving the largest instances ever solved in literature. Moreover, this approach is general and may be used in solving other types of vehicle routing problems. In the third result, we use VNS as a heuristic to find the best feasible solution for groups of instances. We wanted to determine how far the difference is between the best feasible solution obtained by VNS and the value of optimal solution in order to use the output of VNS as an initial feasible solution (upper bound procedure) to improve our multistart method. Unfortunately, based on the search strategy (best first search), using a heuristic to find an initial feasible solution is not useful. The reason for this is because the branch and bound is able to find the first feasible solution quickly. In other words, in our method using a good initial feasible solution as an upper bound will not increase the speed of the search. However, this would be different for the depth first search. However, we found a big gap between VNS feasible solution and an optimal solution, so VNS can not be used alone unless for large test instances when other exact methods are not able to find any feasible solution because of memory or stopping conditions

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

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

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

Model and solution methods for some hub location problems

In this thesis we study some hub location problems in the context of transportation networks. These are combinatorial optimization problems appearing in situations where there is a need of transporting some traffic, like items, people, and information, from many origins to many destinations. Instead of sending these flows using a direct shipment between all pairs of nodes in the network, a subset of these nodes is selected to use as hubs, with the aim of consolidating and distribute the flows. Thus, hubs induce a subnetwork that sends the traffic more efficiently and at a cheaper cost, allowing economies of scale when large amounts of traffic between nodes on this subnet are transported. We study different variants of hub location problems that try to model several real world situations and characteristics. In all of them, we aim to minimize the cost of sending traffic through the transportation network.In this thesis we study some hub location problems in the context of transportation networks. These are combinatorial optimization problems appearing in situations where there is a need of transporting some traffic, like items, people, and information, from many origins to many destinations. Instead of sending these flows using a direct shipment between all pairs of nodes in the network, a subset of these nodes is selected to use as hubs, with the aim of consolidating and distribute the flows. Thus, hubs induce a subnetwork that sends the traffic more efficiently and at a cheaper cost, allowing economies of scale when large amounts of traffic between nodes on this subnet are transported. We study different variants of hub location problems that try to model several real world situations and characteristics. In all of them, we aim to minimize the cost of sending traffic through the transportation network

Solving the time capacitated arc routing problem under fuzzy and stochastic travel and service times

[EN] Stochastic, as well as fuzzy uncertainty, can be found in most real-world systems. Considering both types of uncertainties simultaneously makes optimization problems incredibly challenging. In this paper we propose a fuzzy simheuristic to solve the Time Capacitated Arc Routing Problem (TCARP) when the nature of the travel time can either be deterministic, stochastic or fuzzy. The main goal is to find a solution (vehicle routes) that minimizes the total time spent in servicing the required arcs. However, due to uncertainty, other characteristics of the solution are also considered. In particular, we illustrate how reliability concepts can enrich the probabilistic information given to decision-makers. In order to solve the aforementioned optimization problem, we extend the concept of simheuristic framework so it can also include fuzzy elements. Hence, both stochastic and fuzzy uncertainty are simultaneously incorporated into the CARP. In order to test our approach, classical CARP instances have been adapted and extended so that customers' demands become either stochastic or fuzzy. The experimental results show the effectiveness of the proposed approach when compared with more traditional ones. In particular, our fuzzy simheuristic is capable of generating new best-known solutions for the stochastic versions of some instances belonging to the tegl, tcarp, val, and rural benchmarks.Spanish Ministry of Science, Grant/Award Number: PID2019-111100RB-C21/AEI/10.13039/501100011033; Barcelona Council and the "la Caixa" Foundation under the framework of the Barcelona Science Plan 2020-2023, Grant/Award Number: 21S09355-001; Generalitat Valenciana,Grant/Award Number: PROMETEO/2021/065Martín, XA.; Panadero, J.; Peidro Payá, D.; Pérez Bernabeu, E.; Juan-Pérez, ÁA. (2023). Solving the time capacitated arc routing problem under fuzzy and stochastic travel and service times. Networks. 82(4):318-335. https://doi.org/10.1002/net.2215931833582

Solving the time capacitated arc routing problem under fuzzy and stochastic travel and service times

Stochastic, as well as fuzzy uncertainty, can be found in most real-world systems. Considering both types of uncertainties simultaneously makes optimization problems incredibly challenging. In this paper we propose a fuzzy simheuristic to solve the Time Capacitated Arc Routing Problem (TCARP) when the nature of the travel time can either be deterministic, stochastic or fuzzy. The main goal is to find a solution (vehicle routes) that minimizes the total time spent in servicing the required arcs. However, due to uncertainty, other characteristics of the solution are also considered. In particular, we illustrate how reliability concepts can enrich the probabilistic information given to decision-makers. In order to solve the aforementioned optimization problem, we extend the concept of simheuristic framework so it can also include fuzzy elements. Hence, both stochastic and fuzzy uncertainty are simultaneously incorporated into the CARP. In order to test our approach, classical CARP instances have been adapted and extended so that customers' demands become either stochastic or fuzzy. The experimental results show the effectiveness of the proposed approach when compared with more traditional ones. In particular, our fuzzy simheuristic is capable of generating new best-known solutions for the stochastic versions of some instances belonging to the tegl, tcarp, val, and rural benchmarks.This work has been partially supported by the Spanish Ministry of Science (PID2019-111100RB-C21/AEI/10.13039/01100011033), as well as by the Barcelona Council and the “laCaixa” Foundation under the framework of the Barcelona Science Plan 2020-2023 (grant21S09355-01) and Generalitat Valenciana (PROMETEO/2021/065).Peer ReviewedPostprint (published version