Population Diversity Leads to Short Running Times of Lexicase Selection

Helmuth, Thomas; Lengler, Johannes; Cava, William La

doi:10.1007/978-3-031-14721-0_34

Cited by 4 publications

(2 citation statements)

References 21 publications

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“…Several studies confirmed the benefits of such explicit diversity-preserving mechanisms on various test functions [6][7][8][9][10][11][12]. For some operators, like lexicase selection, it is even known that diversity decreases the runtime of this operator [13].…”

Section: Introductionmentioning

confidence: 82%

“…Moreover, we have S(P t ) max ≤ μ 2 n, since two individuals have Hamming distance at most n and so the diversity is at most 2 μ 2 n. For (13), we have 1/δ = μ 2 n 2n+4(μ−1)χ , which implies 1/δ ∈ (μ • min{μ, n/χ }). Now (13) follows immediately by plugging this into the bounds from Theorem 12. For (14), note that max /α = n/χ .…”

Section: Equilibria and Time Boundsmentioning

confidence: 92%

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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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