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Lagrangian Decomposition Methods for Large-Scale Fixed-Charge Capacitated Multicommodity Network Design Problem

Abstract : Typically 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 soutions 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 depend 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 largests instances. Concerning lower bounds, a Relax-and-Cut algorithm was implemented embbeding 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 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.
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https://tel.archives-ouvertes.fr/tel-03076909
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Submitted on : Wednesday, December 16, 2020 - 3:16:09 PM
Last modification on : Thursday, December 17, 2020 - 3:37:57 AM

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Rui Sa Shibasaki. Lagrangian Decomposition Methods for Large-Scale Fixed-Charge Capacitated Multicommodity Network Design Problem. Networking and Internet Architecture [cs.NI]. Université Clermont Auvergne; Universidade federal de Minas Gerais, 2020. English. ⟨NNT : 2020CLFAC024⟩. ⟨tel-03076909⟩

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