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

Author

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  • M. Rivier

    (Inria Saclay Île-de-France
    ArianeGroup)

  • P. M. Congedo

    (Inria Saclay Île-de-France)

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.

Suggested Citation

  • M. Rivier & P. M. Congedo, 2019. "Surrogate-assisted Bounding-Box approach for optimization problems with tunable objectives fidelity," Journal of Global Optimization, Springer, vol. 75(4), pages 1079-1109, December.
    • Handle: RePEc:spr:jglopt:v:75:y:2019:i:4:d:10.1007_s10898-019-00823-9
    DOI: 10.1007/s10898-019-00823-9
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    References listed on IDEAS

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    1. Antanas Žilinskas, 2010. "On similarities between two models of global optimization: statistical models and radial basis functions," Journal of Global Optimization, Springer, vol. 48(1), pages 173-182, September.
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    1. Rivier, M. & Congedo, P.M., 2022. "Surrogate-Assisted Bounding-Box approach applied to constrained multi-objective optimisation under uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 217(C).

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