On Non-elitist Evolutionary Algorithms Optimizing Fitness Functions with a Plateau

Eremeev, Anton V.

doi:10.1007/978-3-030-49988-4_23

Cited by 4 publications

(2 citation statements)

References 15 publications

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“…This includes, for example, (1) the hidden subset problem [25][26][27][28], where the fitness only depends on a small fraction of all variables, and it is not known which variables are relevant and which ones only lead to neutral changes, (2) majority functions returning the majority bit value [29,30], (3) the moving Hamming ball benchmark [31] from dynamic optimisation where a Hamming ball around a moving target must be tracked and the fitness areas within and outside of the Hamming ball are both flat, and (4) the Plateau k function [32,33], a variant of OneMax in which the best k fitness levels are turned into a neutral region, except for the optimum at 1. However, except for [32,33] the above results either concern populations of size 1 or do not give detailed insights into the diversity of the population. The aforementioned work on Jump [22] does give insights into the population diversity as part of the analysis, however these insights are limited to the specific set of search points with n − k ones.…”

Section: Introductionmentioning

confidence: 99%

Analysing Equilibrium States for Population Diversity

Lengler,

Opris,

Sudholt

2024

Algorithmica

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Population diversity is crucial in evolutionary algorithms as it helps with global exploration and facilitates the use of crossover. Despite many runtime analyses showing advantages of population diversity, we have no clear picture of how diversity evolves over time. We study how the population diversity of $$(\mu +1)$$ ( μ + 1 ) algorithms, measured by the sum of pairwise Hamming distances, evolves in a fitness-neutral environment. We give an exact formula for the drift of population diversity and show that it is driven towards an equilibrium state. Moreover, we bound the expected time for getting close to the equilibrium state. We find that these dynamics, including the location of the equilibrium, are unaffected by surprisingly many algorithmic choices. All unbiased mutation operators with the same expected number of bit flips have the same effect on the expected diversity. Many crossover operators have no effect at all, including all binary unbiased, respectful operators. We review crossover operators from the literature and identify crossovers that are neutral towards the evolution of diversity and crossovers that are not.

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Section: Introductionmentioning

confidence: 99%

Analysing Equilibrium States for Population Diversity

Lengler,

Opris,

Sudholt

2024

Algorithmica

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“…С обширным перечнем известных результатов и их обсуждением можно ознакомиться в обзорах [54,55]. Среди российских ученых стоит отметить В. Редько [56,57], Е. Семенкина [58,59], С. Родзина [60,61], А. Еремеева [62][63][64][65].…”

Section: Introductionunclassified

The “One-Fifth Rule” with Rollbacks for Self-Adjustment of the Population Size in the (1 + (λ, λ)) Genetic Algorithm

Bassin

Buzdalov

Shalyto

2021

Aut. Control Comp. Sci.

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Self-adjustment of parameters can signi cantly improve the performance of evolutionary algorithms. A notable example is the (1 + ( , )) genetic algorithm, where adaptation of the population size helps to achieve the linear running time on the OneMax problem. However, on problems which interfere with the assumptions behind the self-adjustment procedure, its usage can lead to the performance degradation. In particular, this is the case with the "one-h rule" on problems with weak tness-distance correlation. We propose a modi cation of the "one-h rule" in order to have less negative impact on the performance in the cases where the original rule is destructive. Our modi cation, while still yielding a provable linear runtime on OneMax, shows be er results on linear function with random weights, as well as on random satis able MAX-3SAT problems.

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Fourier Analysis Meets Runtime Analysis: Precise Runtimes on Plateaus

Doerr,

Kelley

2024

Algorithmica

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On Non-elitist Evolutionary Algorithms Optimizing Fitness Functions with a Plateau

Cited by 4 publications

References 15 publications

Analysing Equilibrium States for Population Diversity

Analysing Equilibrium States for Population Diversity

The “One-Fifth Rule” with Rollbacks for Self-Adjustment of the Population Size in the (1 + (λ, λ)) Genetic Algorithm

Fourier Analysis Meets Runtime Analysis: Precise Runtimes on Plateaus

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