Une approche Bayésienne pour l'optimisation multi-objectif sous contraintes

Abstract : In this thesis, we address the problem of the derivative-free multi-objective optimization of real-valued functions subject to multiple inequality constraints. In particular, we consider a setting where the objectives and constraints of the problem are evaluated simultaneously using a potentially time-consuming computer program. To solve this problem, we propose a Bayesian optimization algorithm called BMOO. This algorithm implements a new expected improvement sampling criterion crafted to apply to potentially heavily constrained problems and to many-objective problems. This criterion stems from the use of the hypervolume of the dominated region as a loss function, where the dominated region is defined using an extended domination rule that applies jointly on the objectives and constraints. Several criteria from the Bayesian optimization literature are recovered as special cases. The criterion takes the form of an integral over the space of objectives and constraints for which no closed form expression exists in the general case. Besides, it has to be optimized at every iteration of the algorithm. To solve these difficulties, specific sequential Monte-Carlo algorithms are also proposed. The effectiveness of BMOO is shown on academic test problems and on four real-life design optimization problems.
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https://tel.archives-ouvertes.fr/tel-01629453
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Submitted on : Monday, November 6, 2017 - 2:45:08 PM
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Paul Feliot. Une approche Bayésienne pour l'optimisation multi-objectif sous contraintes. Autre. Université Paris-Saclay, 2017. Français. ⟨NNT : 2017SACLC045⟩. ⟨tel-01629453⟩

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