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Article Dans Une Revue IEEE Transactions on Evolutionary Computation Année : 2023

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.
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Dates et versions

hal-04078224 , version 1 (22-04-2023)

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Benjamin Doerr, Zhongdi Qu. A First Runtime Analysis of the NSGA-II on a Multimodal Problem. IEEE Transactions on Evolutionary Computation, 2023, 27 (5), pp.1288-1297. ⟨10.1109/TEVC.2023.3250552⟩. ⟨hal-04078224⟩
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