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Solving repeated optimization problems by Machine Learning

Abstract : This thesis aims at using machine learning techniques in the context of Mixed Integer LinearProgramming instances generated by stochastic data. Rather than solve these instances independentlyusing the Branch and Bound algorithm (B&B), we propose to leverage the similarities between instancesby learning inner strategies of this algorithm, such as node selection and branching.The main approach developed in this work is to use reinforcement learning to discover by trials-and-errorsstrategies which minimize the B&B tree size. To properly adapt to the B&B environment, we definea new kind of tree-based transitions, and elaborate on different cost models in the correspondingMarkov Decision Processes. We prove the optimality of the unitary cost model under both classical andtree-based transitions, either for branching or node selection. However, we experimentally show that itmay be beneficial to bias the cost so as to improve the learning stability. Regarding node selection, weformally exhibit an optimal strategy which can be more efficiently learnt directly by supervised learning.In addition, we propose to exploit the structure of the studied problems. To this end, we propose adecomposition-coordination methodology, a branching heuristic based on a graph representation of aB&B node and finally an approach for learning to disrupt the objective function.
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Submitted on : Monday, May 23, 2022 - 10:51:16 AM
Last modification on : Wednesday, May 25, 2022 - 3:21:03 AM


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  • HAL Id : tel-03675471, version 1



Marc Etheve. Solving repeated optimization problems by Machine Learning. Technology for Human Learning. HESAM Université, 2021. English. ⟨NNT : 2021HESAC040⟩. ⟨tel-03675471⟩



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