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Conference Papers Year : 2023

Multiobjective optimization with a quadratic surrogate-assisted CMA-ES

Abstract

We present a surrogate-assisted multiobjective optimization algorithm. The aggregation of the objectives relies on the Uncrowded Hypervolume Improvement (UHVI) which is partly replaced by a linear-quadratic surrogate that is integrated into the CMA-ES algorithm. Surrogating the UHVI poses two challenges. First, the UHVI is a dynamic function, changing with the empirical Pareto set. Second, it is a composite function, defined differently for dominated and nondominated points. The presented algorithm is thought to be used with expensive functions of moderate dimension (up to about 50) with a quadratic surrogate which is updated based on its ranking ability. We report numerical experiments which include tests on the COCO benchmark. The algorithm shows in particular linear convergence on the double sphere function with a convergence rate that is 6-20 times faster than without surrogate assistance.
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hal-04078483 , version 1 (23-04-2023)

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Mohamed Gharafi, Nikolaus Hansen, Dimo Brockhoff, Rodolphe Le Riche. Multiobjective optimization with a quadratic surrogate-assisted CMA-ES. GECCO 2023 - Genetic and Evolutionary Computation Conference, GECCO, Jul 2023, Lisbon, Portugal. ⟨10.1145/3583131.3590492⟩. ⟨hal-04078483⟩
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