Asymptotical Analysis of the $(1+(λ,λ))$ GA Escape Time from Local Optima on Jump Functions

• URL: http://arxiv.org/abs/2607.14278v1
• Date: Wed, 15 Jul 2026 18:37:48 GMT
• Title: Asymptotical Analysis of the $(1+(λ,λ))$ GA Escape Time from Local Optima on Jump Functions
• Abstract summary: The paper develops the approach to the runtime analysis of evolutionary algorithms on the basis of limit theorems from probability theory.<n>The main result of this work is a tightened upper bound on the escape time from the work of Antipov, Doerr and Karavaev (2022). Besides that, the obtained bound applies to a wider range of algorithm parameters.
• Score: 0.5156484100374058
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The paper develops the approach to the runtime analysis of evolutionary algorithms on the basis of limit theorems from probability theory. We consider the family of Jump$_k$ benchmark functions, defined on the search space of binary strings of length $n$, parametrized by the integer $k$, which have multiple local optima at the Hamming distance $k$ from a unique global optimum. In this work, we consider the genetic algorithm $(1+(λ,λ)) GA$ from (Doerr, Doerr and Ebel, 2015) with tunable parameters of the mutation rate $p$, crossover bias $c$, and two intermediate population sizes $λ_M$ and $λ_C$, and study the time it escapes from the plateau in the case of Jump$_k$ fitness function when $np$ tends to infinity. The main result of this work is a tightened upper bound on the escape time from the work of Antipov, Doerr and Karavaev (2022). Besides that, the obtained bound applies to a wider range of algorithm parameters.

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