A First Runtime Analysis of the NSGA-II on a Multimodal Problem
Résumé
Very recently, the first mathematical runtime analyses of the multiobjective evolutionary optimizer NSGA-II have been conducted. We continue this line of research with a first runtime analysis of this algorithm on a benchmark problem consisting of two multimodal objectives. We prove that if the population size N is at least four times the size of the Pareto front, then the NSGA-II with four different ways to select parents and bit-wise mutation optimizes the OneJump-ZeroJump benchmark with jump size 2 ≤ k ≤ n/4 in time O(N n k). When using fast mutation, a recently proposed heavy-tailed mutation operator, this guarantee improves by a factor of k Ω(k). Overall, this work shows that the NSGA-II copes with the local optima of the OneJumpZeroJump problem at least as well as the global SEMO algorithm.
Domaines
Informatique [cs]
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Doerr_Qu__A_First_Runtime_Analysis_of_the_NSGA-II_on_a_Multimodal__arxiv_v4__2023.pdf (252.85 Ko)
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