Generalized Heavy-tailed Mutation for Evolutionary Algorithms

• URL: http://arxiv.org/abs/2604.00502v1
• Date: Wed, 01 Apr 2026 05:33:12 GMT
• Title: Generalized Heavy-tailed Mutation for Evolutionary Algorithms
• Abstract summary: The heavy-tailed mutation operator is proposed by Doerr, Le, Makhmara, and Nguyen for evolutionary algorithms.<n>We generalize the power-law assumption using a regularly varying constraint on the distribution function of mutation rate.<n>A new version of the heavy-tailed mutation operator is proposed, satisfying the generalized conditions.
• Score: 0.45880283710344055
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: The heavy-tailed mutation operator, proposed by Doerr, Le, Makhmara, and Nguyen (2017) for evolutionary algorithms, is based on the power-law assumption of mutation rate distribution. Here we generalize the power-law assumption using a regularly varying constraint on the distribution function of mutation rate. In this setting, we generalize the upper bounds on the expected optimization time of the $(1+(λ,λ))$ genetic algorithm obtained by Antipov, Buzdalov and Doerr (2022) for the OneMax function class parametrized by the problem dimension $n$. In particular, it is shown that, on this function class, the sufficient conditions of Antipov, Buzdalov and Doerr (2022) on the heavy-tailed mutation, ensuring the $O(n)$ optimization time in expectation, may be generalized as well. This optimization time is known to be asymptotically smaller than what can be achieved by the $(1+(λ,λ))$ genetic algorithm with any static mutation rate. A new version of the heavy-tailed mutation operator is proposed, satisfying the generalized conditions, and promising results of computational experiments are presented.

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