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A First Runtime Analysis of the NSGA-II on a Multimodal Problem (2204.13750v5)

Published 28 Apr 2022 in cs.NE, cs.AI, cs.DS, and math.OC

Abstract: Very recently, the first mathematical runtime analyses of the multi-objective 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 OneJumpZeroJump benchmark with jump size~$2 \le k \le n/4$ in time $O(N nk)$. When using fast mutation, a recently proposed heavy-tailed mutation operator, this guarantee improves by a factor of $k{\Omega(k)}$. 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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Authors (2)
  1. Benjamin Doerr (131 papers)
  2. Zhongdi Qu (5 papers)
Citations (55)

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