Surrogate-assisted Bounding-Box approach for optimization problems with tunable objectives fidelity

M. Rivier () and P. M. Congedo ()
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M. Rivier: Inria Saclay Île-de-France
P. M. Congedo: Inria Saclay Île-de-France

Journal of Global Optimization, 2019, vol. 75, issue 4, No 8, 1079-1109

Abstract: Abstract In this work, we present a novel framework to perform multi-objective optimization when considering expensive objective functions computed with tunable fidelity. This case is typical in many engineering optimization problems, for example with simulators relying on Monte Carlo or on iterative solvers. The objectives can only be estimated, with an accuracy depending on the computational resources allocated by the user. We propose here a heuristic for allocating the resources efficiently to recover an accurate Pareto front at low computational cost. The approach is independent from the choice of the optimizer and overall very flexible for the user. The framework is based on the concept of Bounding-Box, where the estimation error can be regarded with the abstraction of an interval (in one-dimensional problems) or a product of intervals (in multi-dimensional problems) around the estimated value, naturally allowing the computation of an approximated Pareto front. This approach is then supplemented by the construction of a surrogate model on the estimated objective values. We first study the convergence of the approximated Pareto front toward the true continuous one under some hypotheses. Secondly, a numerical algorithm is proposed and tested on several numerical test-cases.

Keywords: Multi-objective optimization; Uncertainty-based optimization; Error Bounding-Boxes; Tunable fidelity; Surrogate-assisting strategy (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-019-00823-9

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