Uncertainty quantification on pareto fronts and high-dimensional strategies in bayesian optimization, with applications in multi-objective automotive design

Abstract : This dissertation deals with optimizing expensive or time-consuming black-box functionsto obtain the set of all optimal compromise solutions, i.e. the Pareto front. In automotivedesign, the evaluation budget is severely limited by numerical simulation times of the considered physical phenomena. In this context, it is common to resort to “metamodels” (models of models) of the numerical simulators, especially using Gaussian processes. They enable adding sequentially new observations while balancing local search and exploration. Complementing existing multi-objective Expected Improvement criteria, we propose to estimate the position of the whole Pareto front along with a quantification of the associated uncertainty, from conditional simulations of Gaussian processes. A second contribution addresses this problem from a different angle, using copulas to model the multi-variate cumulative distribution function. To cope with a possibly high number of variables, we adopt the REMBO algorithm. From a randomly selected direction, defined by a matrix, it allows a fast optimization when only a few number of variables are actually influential, but unknown. Several improvements are proposed, such as a dedicated covariance kernel, a selection procedure for the low dimensional domain and of the random directions, as well as an extension to the multi-objective setup. Finally, an industrial application in car crash-worthiness demonstrates significant benefits in terms of performance and number of simulations required. It has also been used to test the R package GPareto developed during this thesis.
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Mickaël Binois. Uncertainty quantification on pareto fronts and high-dimensional strategies in bayesian optimization, with applications in multi-objective automotive design. General Mathematics [math.GM]. Ecole Nationale Supérieure des Mines de Saint-Etienne, 2015. English. ⟨NNT : 2015EMSE0805⟩. ⟨tel-01310521⟩

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