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Méthodes pour la résolution efficace de très grands problèmes combinatoires stochastiques : application à un problème industriel d'EDF

Abstract : The purpose of this Ph.D. thesis is to study optimization techniques for large-scale stochastic combinatorial problems. We apply those techniques to the problem of scheduling EDF nuclear power plant maintenance outages, which is of significant importance due to the major part of the nuclear energy in the French electricity system. We build on a two-stages extended formulation, the first level of which fixes nuclear outage dates and production profiles for nuclear plants, while the second evaluates the cost to meet the demand. This formulation enables the solving of deterministic industrial instances to optimality, by using a MIP solver. However, the computational time increases significantly with the number of scenarios. Hence, we resort to a procedure combining column generation of a Dantzig-Wolfe decomposition with Benders’ cut generation, to account for the linear relaxation of stochastic instances. We then obtain integer solutions of good quality via a heuristic, up to fifty scenarios. We further assume that outage durations are uncertain and that unexpected shutdowns of plants may occur. We investigate robust optimization methods in this context while ignoring possible recourse on power plants outage dates. We report on several approaches, which use bi-objective or probabilistic methods, to ensure the satisfaction of constraints which might be relaxed in the operating process. For other constraints, we apply a budget uncertainty-based approach to limit future re-organizations of the scheduling. Adding probabilistic information leads to better control of the price of the robustness.
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Rodolphe Griset. Méthodes pour la résolution efficace de très grands problèmes combinatoires stochastiques : application à un problème industriel d'EDF. Optimisation et contrôle [math.OC]. Université de Bordeaux, 2018. Français. ⟨NNT : 2018BORD0219⟩. ⟨tel-01994127⟩

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