Bi-objective branch-and-cut algorithms applied to the binary knapsack problem: surrogate upper bound sets, dynamic branching strategies, generation and exploitation of cover inequalities

Abstract : In this work, we are interested in solving multi-objective combinatorial optimization problems. These problems have received a large interest in the past decades. In order to solve exactly and efficiently these problems, which are particularly difficult, the designed algorithms are often specific to a given problem. In this thesis, we focus on the branch-and-bound method and propose an extension by a branch-and-cut method, in bi-objective context. Knapsack problems are the case study of this work. Three main axis are considered: the definition of new upper bound sets, the elaboration of a dynamic branching strategy and the generation of valid inequalities. The defined upper bound sets are based on the surrogate relaxation, using several multipliers. Based on the analysis of the different multipliers, algorithms are designed to compute efficiently these surrogate upper bound sets. The dynamic branching strategy arises from the comparison of different static branching strategies from the literature. It uses reinforcement learning methods. Finally, cover inequalities are generated and introduced, all along the solving process, in order to improve it. Those different contributions are experimentally validated and the obtained branch-and-cut algorithm presents encouraging results.
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Submitted on : Friday, December 11, 2015 - 3:51:35 PM
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Audrey Cerqueus. Bi-objective branch-and-cut algorithms applied to the binary knapsack problem: surrogate upper bound sets, dynamic branching strategies, generation and exploitation of cover inequalities. Computer Science [cs]. université de Nantes, 2015. English. ⟨tel-01242210⟩

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