Evolutionary Algorithms with Self-adjusting Asymmetric Mutation

TL;DR

This paper introduces a self-adjusting asymmetric mutation operator for (1+1) evolutionary algorithms that adapts based on success rates, leading to improved performance on specific binary optimization problems.

Contribution

It extends previous asymmetric mutation methods by enabling the operator to adapt dynamically, improving efficiency on OneMax-like functions.

Findings

Self-adjusting asymmetric mutation improves runtime on OneMax$_a$ functions.

Adaptive operator outperforms fixed asymmetry in experiments.

The approach effectively learns optimal asymmetry levels during search.

Abstract

Evolutionary Algorithms (EAs) and other randomized search heuristics are often considered as unbiased algorithms that are invariant with respect to different transformations of the underlying search space. However, if a certain amount of domain knowledge is available the use of biased search operators in EAs becomes viable. We consider a simple (1+1) EA for binary search spaces and analyze an asymmetric mutation operator that can treat zero- and one-bits differently. This operator extends previous work by Jansen and Sudholt (ECJ 18(1), 2010) by allowing the operator asymmetry to vary according to the success rate of the algorithm. Using a self-adjusting scheme that learns an appropriate degree of asymmetry, we show improved runtime results on the class of functions OneMax$_a$ describing the number of matching bits with a fixed target $a\in\{0,1\}^n$.