| spelling |
Maurício Cardoso de Souzahttp://lattes.cnpq.br/2834522198832797Philippe Maheyhttp://lattes.cnpq.br/8308891394810420Mourad BaïouNelson Maculan FilhoDenis CornazJean-Philippe GayonHande YamanFrancisco Barahonahttp://lattes.cnpq.br/7861160392673953Rui Sá Shibasaki2020-12-15T16:57:36Z2020-12-15T16:57:36Z2020-09-22http://hdl.handle.net/1843/345110000-0002-5561-4937Typically present in logistics and telecommunications domains, the Fixed- Charge Multicommodity Capacitated Network Design Problem remains challenging, especially when large-scale contexts are involved. In this particular case, the ability to produce good quality solutions in a reasonable amount of time leans on the availability of efficient algorithms. In that sense, the present thesis proposed Lagrangian approaches that are able to provide relatively sharp bounds for large-scale instances of the problem. The efficiency of the methods depends on the algorithm applied to solve Lagrangian duals, so we choose between two of the most efficient solvers in the literature: the Volume Algorithm and the Bundle Method, providing a comparison between them. The results showed that the Volume Algorithm is more efficient in the present context, being the one kept for further research. A first Lagrangian heuristic was devised to produce good quality feasible solutions for the problem, obtaining far better results than Cplex, for the largest instances. Concerning lower bounds, a Relax-and-Cut algorithm was implemented embedding sensitivity analysis and constraint scaling, which improved results. The increases in lower bounds attained 11%, but on average they remained under 1%. The Relax-and-Cut algorithm was then included in a Branch-and-Cut scheme, to solve linear programs in each node of the search tree. Moreover, a Feasibility Pump heuristic using the Volume Algorithm as a solver for linear programs was implemented to accelerate the search for good feasible solutions in large-scale cases. The obtained results showed that the proposed scheme is competitive with the best algorithms in the literature, and provides the best results in large-scale contexts. Moreover, a heuristic version of the Branch-and-Cut algorithm based on the Lagrangian Feasibility Pump was tested, providing the best results in general, when compared to efficient heuristics in the literature.Tipicamente presente nas áreas de logística e telecomunicações, o problema de síntese de redes multi-fluxo de custo fixo e capacitada permanece desafiador, especialmente quando contextos de grande escala estão envolvidos. Nesse caso, a capacidade de produzir soluções de boa qualidade em um tempo computacional praticável depende da disponibilidade de algoritmos eficientes. Nesse sentido, a presente tese propõem abordagens lagrangianas capazes de fornecer limites relativamente próximos ao ótimo para instâncias de grande escala. A eficiência dos métodos depende do algoritmo aplicado para resolver duais Lagrangianos, portanto escolhemos entre dois dos solvers mais eficientes da literatura: o Algoritmo de Volume e o Método Bundle, proporcionando uma comparação entre eles. Os resultados mostraram que o Algoritmo de Volume é mais eficiente no contexto considerado, sendo o escolhido para o desenvolvimento do projeto de pesquisa. Uma primeira heurística Lagrangiana foi desenvolvida para produzir soluções viáveis de boa qualidade para o problema, obtendo resultados muito melhores do que Cplex, para as maiores instâncias. Em relação aos limites inferiores, um algoritmo Relax-and-Cut foi implementado incorporando análise de sensibilidade e uma normalização das restrições, o que melhorou os resultados. Os aumentos nos limites inferiores atingiram 11%, mas em média permaneceram abaixo de 1%. O algoritmo Relax-and-Cut foi então incluído em um esquema Branch-and-Cut, para resolver programas lineares em cada nó da árvore de busca. Além disso, uma heurística de Feasibility Pump lagrangiana foi implementada para acelerar a busca por boas soluções viáveis. Os resultados obtidos mostraram que o esquema proposto é competitivo com os melhores algoritmos da literatura, e fornece os melhores resultados em contextos de larga escala. Além disso, foi testada uma versão heurística do algoritmo Branch-and-Cut baseado no Feasibility Pump lagrangiano, proporcionando os melhores resultados em geral quando comparada às heurísticas mais eficientes da literatura.FAPEMIG - Fundação de Amparo à Pesquisa do Estado de Minas GeraisengUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em Engenharia de ProduçãoUFMGBrasilENG - DEPARTAMENTO DE ENGENHARIA PRODUÇÃOhttp://creativecommons.org/licenses/by-nc-nd/3.0/pt/info:eu-repo/semantics/openAccessEngenharia de produçãoAlgoritmosHeurísticaMulticommodity network designLagrangian relaxationVolume algorithmBundle methodRelax-and-CutBranch- and-CutLagrangian decomposition methods for large-scale fixed-charge capacitated multicommodity network design problemMétodos de decomposição lagrangiana para problema de síntese de redes multi-fluxo de custo fixoinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALLagrangian Decomposition Methods for Large-Scale Fixed-Charge Capacitated Multicommodity Network Design Problem.pdfLagrangian Decomposition Methods for Large-Scale Fixed-Charge Capacitated Multicommodity Network Design Problem.pdfapplication/pdf1915660https://repositorio.ufmg.br/bitstream/1843/34511/1/Lagrangian%20Decomposition%20Methods%20for%20Large-Scale%20Fixed-Charge%20Capacitated%20Multicommodity%20Network%20Design%20Problem.pdf0dfebc87457a0c38753ad817031440c3MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufmg.br/bitstream/1843/34511/2/license_rdfcfd6801dba008cb6adbd9838b81582abMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-82119https://repositorio.ufmg.br/bitstream/1843/34511/3/license.txt34badce4be7e31e3adb4575ae96af679MD531843/345112020-12-15 13:57:36.526oai:repositorio.ufmg.br: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Repositório InstitucionalPUBhttps://repositorio.ufmg.br/oaiopendoar:2020-12-15T16:57:36Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
|