Surrogate-Assisted Bounding-Box Approach Applied to Constrained Multi-Objective Optimisation Under Uncertainty

Mickael Rivier 1 Pietro Marco Congedo 1
1 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : This paper is devoted to tackling constrained multi-objective optimisation under uncertainty problems. A Surrogate-Assisted Bounding-Box approach (SABBa) is formulated here to deal with robustness and reliability measures, which can be computed with tunable and refinable fidelity. A Bounding-Box is defined as a multi-dimensional product of intervals centred on the estimated objectives and constraints that contains the true underlying values. The fidelity of these estimations can be tuned throughout the optimisation so as to reach high accuracy only on promising designs, which allows quick convergence toward the optimal area. In SABBa, this approach is supplemented with a Surrogate-Assisting (SA) strategy, which is very useful to reduce the overall computational cost. The adaptive refinement within the Bounding-Box approach is based on the computation of a Pareto Optimal Probability (POP) for each box. We first assess the proposed method on several analytical uncertainty-based optimisation test-cases with respect to an \textit{a priori} metamodel approach in terms of a probabilistic modified Hausdorff distance to the true Pareto optimal set. The method is then applied to two engineering applications: the design of two-bar truss in structural mechanics and the design of a thermal protection system for atmospheric reentry.
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Mickael Rivier, Pietro Marco Congedo. Surrogate-Assisted Bounding-Box Approach Applied to Constrained Multi-Objective Optimisation Under Uncertainty. [Research Report] RR-9214, Inria Saclay Ile de France. 2018, pp.1-37. ⟨hal-01897399v2⟩

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