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Handling of constraints in multiobjective blackbox optimization

Jean Bigeon, Sébastien Le Digabel and Ludovic Salomon

Article (2024)

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Abstract

This work proposes the integration of two new constraint-handling approaches into the blackbox constrained multiobjective optimization algorithm DMulti-MADS, an extension of the Mesh Adaptive Direct Search (MADS) algorithm for single-objective constrained optimization. The constraints are aggregated into a single constraint violation function which is used either in a two-phase approach, where the search for a feasible point is prioritized if not available before improving the current solution set, or in a progressive barrier approach, where any trial point whose constraint violation function values are above a threshold are rejected. This threshold is progressively decreased along the iterations. As in the single-objective case, it is proved that these two variants generate feasible and/or infeasible sequences which converge either in the feasible case to a set of local Pareto optimal points or in the infeasible case to Clarke stationary points according to the constraint violation function. Computational experiments show that these two approaches are competitive with other state-of-the-art algorithms.

Uncontrolled Keywords

multiple objective programming; multiobjective optimization; derivative-free optimization; blackbox optimization; constrained optimization

Subjects: 2950 Applied mathematics > 2950 Applied mathematics
Department: Department of Mathematics and Industrial Engineering
Research Center: GERAD - Research Group in Decision Analysis
PolyPublie URL: https://publications.polymtl.ca/58801/
Journal Title: Computational Optimization and Applications
Publisher: Springer Nature
DOI: 10.1007/s10589-024-00588-2
Official URL: https://doi.org/10.1007/s10589-024-00588-2
Date Deposited: 21 Aug 2024 00:09
Last Modified: 25 Sep 2024 16:51
Cite in APA 7: Bigeon, J., Le Digabel, S., & Salomon, L. (2024). Handling of constraints in multiobjective blackbox optimization. Computational Optimization and Applications, 45 pages. https://doi.org/10.1007/s10589-024-00588-2

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