Publicação
A comparative analysis of formulations for the Hamiltonian p-Median Problem
| Resumo: | In this dissertation we study the Hamiltonian p-Median Problem, a combinatorial optimization problem in which, given an undirected graph G = (V, E) and a cost for each edge, the objective is to find the cheapest way to partition the set of nodes into p subsets with each subset being connected by a single cycle. This is a problem which may therefore be seen as a generalization of the Travelling Salesman Problem (TSP). When working with MILP models for the TSP, sets of constraints to prevent feasible solutions with more than one cycle are added to an assignment formulation. Similarly, when working with such models for the HpMP, sets of constraints to prevent feasible solutions with more than p cycles can also be added to an assignment formulation, and these are often very similar to sets of constraints already used in models for the TSP, albeit with some modifications. However, these sets are not sufficient to guarantee every feasible solution has exactly p cycles, since it may have fewer than p cycles. To this end, additional sets of constraints for preventing solutions with less than p cycles may be introduced, and these will be the focal point of this work. The work begins with a brief introduction to the problem and some literature review. After that, several compact formulations for this problem are presented. The presentation of these models will be split into three parts. In the first part, a model upon which all other models are built is presented. The second part focuses on a model used to prevent solutions with more than p cycles, while the third part focuses on two models used to prevent solutions with less than p cycles (in which nodes are assigned to depots or cycles), accompanied by some valid inequalities. Finally, some of the models presented in this work are tested and the results and possibilities for future work are discussed. |
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| Autores principais: | Canas, Francisco Miguel Paulo |
| Assunto: | Otimização combinatória Problema do Caixeiro Viajante Problema da p-Mediana Problema da p-Mediana Hamiltoniana Formulações Compactas Tese de mestrado - 2022 |
| Ano: | 2022 |
| País: | Portugal |
| Tipo de documento: | dissertação de mestrado |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| Resumo: | In this dissertation we study the Hamiltonian p-Median Problem, a combinatorial optimization problem in which, given an undirected graph G = (V, E) and a cost for each edge, the objective is to find the cheapest way to partition the set of nodes into p subsets with each subset being connected by a single cycle. This is a problem which may therefore be seen as a generalization of the Travelling Salesman Problem (TSP). When working with MILP models for the TSP, sets of constraints to prevent feasible solutions with more than one cycle are added to an assignment formulation. Similarly, when working with such models for the HpMP, sets of constraints to prevent feasible solutions with more than p cycles can also be added to an assignment formulation, and these are often very similar to sets of constraints already used in models for the TSP, albeit with some modifications. However, these sets are not sufficient to guarantee every feasible solution has exactly p cycles, since it may have fewer than p cycles. To this end, additional sets of constraints for preventing solutions with less than p cycles may be introduced, and these will be the focal point of this work. The work begins with a brief introduction to the problem and some literature review. After that, several compact formulations for this problem are presented. The presentation of these models will be split into three parts. In the first part, a model upon which all other models are built is presented. The second part focuses on a model used to prevent solutions with more than p cycles, while the third part focuses on two models used to prevent solutions with less than p cycles (in which nodes are assigned to depots or cycles), accompanied by some valid inequalities. Finally, some of the models presented in this work are tested and the results and possibilities for future work are discussed. |
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