Result diversification by multi-objective evolutionary algorithms with theoretical guarantees

Qian, Chao; Liu, Dan-Xuan; Zhou, Zhi‐Hua

doi:10.1016/j.artint.2022.103737

Cited by 10 publications

(1 citation statement)

References 36 publications

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“…The first runtime analyses of MOEAs date back to the early 2000s (Laumanns et al 2002;Giel 2003;Thierens 2003) and regarded the artificial SEMO and GSEMO algorithms, which are still the most regarded algorithms in MOEA theory (see, e.g., Bian, Qian, and Tang (2018); Qian et al (2019); Qian, Liu, and Zhou (2022) for some recent works). Some time later, the first analyses of the more realistic SIBEA (Brockhoff, Friedrich, and Neumann 2008;Nguyen, Sutton, and Neumann 2015;Doerr, Gao, and Neumann 2016) and the MOEA/D (Li et al 2016;Huang et al 2019;Huang and Zhou 2020;Huang et al 2021) followed.…”

Section: Previous Workmentioning

confidence: 99%

From Understanding the Population Dynamics of the NSGA-II to the First Proven Lower Bounds

Doerr

2023

AAAI

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Due to the more complicated population dynamics of the NSGA-II, none of the existing runtime guarantees for this algorithm is accompanied by a non-trivial lower bound. Via a first mathematical understanding of the population dynamics of the NSGA-II, that is, by estimating the expected number of individuals having a certain objective value, we prove that the NSGA-II with suitable population size needs Omega(Nn log n) function evaluations to find the Pareto front of the OneMinMax problem and Omega(Nn^k) evaluations on the OneJumpZeroJump problem with jump size k. These bounds are asymptotically tight (that is, they match previously shown upper bounds) and show that the NSGA-II here does not even in terms of the parallel runtime (number of iterations) profit from larger population sizes. For the OneJumpZeroJump problem and when the same sorting is used for the computation of the crowding distance contributions of the two objectives, we even obtain a runtime estimate that is tight including the leading constant.

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