We consider the lower-bounded facility location (LBFL) problem (, also known as load-balanced facility location), which is a generalization of uncapacitated facility location (UFL) problem where each open facility is required to serve a minimum number of clients. More formally, in the LBFL problem, we are given a set of clients Ɗ , a set of facilities Ƒ, a non-negative facility-opening cost f_i for each i ∈ Ƒ, a lower bound M, and a distance metric c(i,j) on the set Ɗ ∪ Ƒ, where c(i,j) denotes the cost of assigning client j to facility i. A feasible solution S specifies the set of open facilities F_S ⊆ Ƒ and the assignment of each client j to an open facility i(j) such that each open facility serves at least M clients. Our goal is to find feasible solution S that minimizes ∑_{i ∈ F_S} f_i + ∑_j c(i,j). The current best approximation ratio for LBFL is 550. We substantially advance the state-of-the-art for LBFL by devising an approximation algorithm for LBFL that achieves a significantly-improved approximation guarantee of 83.

We consider the lower-bounded facility location (LBFL) problem (, also known as load-balanced facility location), which is a generalization of uncapacitated facility location (UFL) problem where each open facility is required to serve a minimum number of clients. More formally, in the LBFL problem, we are given a set of clients Ɗ , a set of facilities Ƒ, a non-negative facility-opening cost f_i for each i ∈ Ƒ, a lower bound M, and a distance metric c(i,j) on the set Ɗ ∪ Ƒ, where c(i,j) denotes the cost of assigning client j to facility i. A feasible solution S specifies the set of open facilities F_S ⊆ Ƒ and the assignment of each client j to an open facility i(j) such that each open facility serves at least M clients. Our goal is to find feasible solution S that minimizes ∑_{i ∈ F_S} f_i + ∑_j c(i,j). The current best approximation ratio for LBFL is 550. We substantially advance the state-of-the-art for LBFL by devising an approximation algorithm for LBFL that achieves a significantly-improved approximation guarantee of 83.

The study of Stochastic Local Search (SLS) algorithms is becoming more pivotal these days, due to their vast number of applications in decision making. Prior to the implementation of algorithmic knowledge for decision making, many decisions were made based on manual calculation, on the fly, or even based on guts feeling. Nowadays, such an approach is more rarely seen, especially when the decisions that need to be made are high-risk, cost intensive, or time-consuming. The increasingly often used SLS algorithms are one of the options available to assist the decision making process these days.The work discussed in this thesis concerns the study of SLS algorithms for solving the Quadratic Assignment Problem (QAP), a prominent combinatorial optimization problem, which until today is very hard to solve. Our interest is to study the behavior and performance of SLS algorithms for solving QAP instances of different characteristics, such as size, sparsity, and structure. In this study, we have also proposed new variants of SLS algorithms, inspired by existing, well-performing SLS algorithms for solving the QAP. The new variants of SLS algorithms are then further extended for solving the bi-objective QAP (bQAP).One main focus in this study is to see how the performance of algorithms scales with instance size. We have considered instances that are much larger than the ones usually used in the studies of algorithms for solving the QAP. By understanding how the algorithms perform when the instance size changes, we might be able to solve other problems effectively by considering the similarity in their characteristics to the ones of the QAP, or by seeing common trends in the relative performance of the various available SLS methods. For single objective QAP instances we found that the structure and size of instances do have a significant impact on the performance of SLS algorithms. For example, comparisons between Tabu Search (TS) and Simulated Annealing (SA) on instances with randomly generated matrices show that the overall performance of TS is better than SA, irrespective the size of instances considered. The results on a class of structured instances however show that TS performs well on small-sized instances, while on the larger ones, SA shows better results. In another experiment, Hierarchical Iterated Local Search (HILS) has shown very good results compared to several Iterated Local Search (ILS) variants. This experiment was done on a class of structured instances of size from 100 to 500. An extensive experiment on a class of structured instances of size 30 to 300 using tuned parameter settings shows that population based algorithms perform very well on most of the instance classes considered. SA however, shows very good performance especially on large-sized instances with low sparsity level. For the bQAP, the correlation between the flow matrices does have a strong effect that determines the performance of algorithms for solving them. Hybrid Simulated Annealing (HSA) clearly outperforms Hybrid Iterative Improvement (HII). When compared to Multi Objective Ant Colony Optimization (MOACO) and Strength Pareto Evolutionary Algorithm 2 (SPEA2), HSA shows very good performance, where HSA outperforms MOACO and SPEA2, especially on instances of large size, thus, offering a better scaling behavior. Based the results obtained in this study, it is possible to come up with a general idea on the suitability of SLS algorithms for solving instances with a certain characteristic. Given an unknown QAP instance, one can guess the most suitable algorithm for solving it depending on the type, size, and sparsity of the instance, while for a bQAP instance the most suitable algorithm can be guessed based on its size and correlation between the flow matrices. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

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This thesis presents two new routing problems, both with objective functions focused on relative positioning of teams during the routing horizon. The relative positioning results in temporal and spatial dependencies among routes and is quantified with a nonlinear dispersion metric, designed to evaluate the instantaneous distances among teams over a time interval. This metric allows the design of objective functions to approximate teams during routes execution, when minimized, or disperse them, when maximized. Both approximation and dispersion are important routing characteristics in some practical applications, and two new optimization problems are proposed with these opposite objectives. The first one is a variation of the Multiple Traveling Salesman Problem, and its goal is to find a set of tours where the salesmen travel close to each other, minimizing dispersion. A Local Search Genetic Algorithm is proposed to solve the problem. It includes specialized genetic operators and neighborhoods. A new set of benchmark instances is proposed, adapted for the new problem from literature instances. Computational results show that the proposed approach provides solutions with the desired characteristics of minimal dispersion. The second problem is a bi-objective arc routing problem in which routes must be constructed in order to maximize collected profit and dispersion of teams. The maximization of the dispersion metric fosters the scattering of the teams during routing procedure. Usually, profit and dispersion objectives are conflicting, and by using a bi-objective approach the decision maker is able to choose a trade-off between collecting profits and scattering teams. Two solution methods are proposed, a Multi-objective Genetic Algorithm and a Multi-objective Genetic Local Search Algorithm, both specialized in order to exploit the characteristics of the problem. It is demonstrated, by means of computational experiments on a new set of benchmark instances, that the proposed approach provides approximation sets with the desired characteristics. / Esta tese apresenta dois novos problemas de roteamento, ambos com funções objetivo voltadas para o posicionamento relativo das equipes durante o horizonte de roteamento. O posicionamento relativo resulta em uma dependência temporal e espacial entre rotas e é quantificado com uma métrica de dispersão não-linear, projetada para avaliar as distâncias instantâneas entre as equipes ao longo de um intervalo de tempo. Esta métrica permite a concepção de funções objetivo para aproximar as equipes durante a execução das rotas, quando minimizada, ou para dispersá-las, quando maximizada. Tanto a aproximação quanto a dispersão são características importantes de roteamento em algumas aplicações práticas, e dois novos problemas de otimização são propostos com esses objetivos opostos. O primeiro é uma variação do Problema de Múltiplos Caixeiros Viajantes, e seu objetivo é encontrar um conjunto de rotas em que os caixeiros viajam próximos uns dos outros, minimizando a dispersão. Um Algoritmo Genético com Busca Local é proposto para resolver o problema. Ele inclui operadores genéticos e vizinhanças especializados. Um novo conjunto de instâncias é proposto, adaptado para o novo problema de instâncias da literatura. Resultados computacionais mostram que a abordagem proposta proporciona soluções com as características desejadas de dispersão mínima. O segundo problema é um problema de roteamento de arcos biobjetivo em que as rotas devem ser construídas de modo a maximizar o lucro recolhido e o distanciamento entre as equipes. A maximização da métrica promove a dispersão das equipes durante a execução das rotas. Normalmente, os objetivos de lucro e dispersão são conflitantes, e com uma abordagem biobjetivo o tomador de decisão é capaz de avaliar a troca entre a coleta de lucros e a dispersão de equipes. Dois métodos de solução são propostos, um Algoritmo Genético Multiobjetivo e um Algoritmo Genético Multiobjetivo com Busca Local, ambos especializados para explorar as características do problema. É demonstrado, por meio de experimentos computacionais sobre um novo conjunto de instâncias, que a abordagem proposta fornece conjuntos de aproximação com as características desejadas.