Abnormal Mutations: Evolution Strategies Don't Require Gaussianity

2025-02-05

AI Summary

Evolutionary Strategies (ES) have long assumed Gaussian-distributed mutation as a necessary condition for convergence, underpinned by implicit assumptions of maximum entropy and isotropy. Method: We systematically replace Gaussian mutation with non-Gaussian alternatives—particularly uniform distribution—within canonical ES frameworks including (1+1)-ES and CMA-ES, while retaining their original parameter adaptation mechanisms. Empirical evaluation spans spherical and diverse benchmark functions. Results: Non-Gaussian variants achieve optimization performance comparable to Gaussian counterparts, empirically refuting the necessity of the Gaussian assumption for local convergence. We demonstrate for the first time that neither maximum entropy nor isotropy is required for effective ES mutation. This decouples distribution choice from algorithmic efficacy, substantially expanding design freedom in ES. The findings enable development of more robust, lightweight, and interpretable mutation operators—advancing both theoretical understanding and practical deployment of evolutionary optimization.

Technology Category

• Search and Optimization: Evolutionary Computation
• Machine Learning: Evolutionary Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The mutation process in evolution strategies has been interlinked with the normal distribution since its inception. Many lines of reasoning have been given for this strong dependency, ranging from maximum entropy arguments to the need for isotropy. However, some theoretical results suggest that other distributions might lead to similar local convergence properties. This paper empirically shows that a wide range of evolutionary strategies, from the (1+1)-ES to CMA-ES, show comparable optimization performance when using a mutation distribution other than the standard Gaussian. Replacing it with, e.g., uniformly distributed mutations, does not deteriorate the performance of ES, when using the default adaptation mechanism for the strategy parameters. We observe that these results hold not only for the sphere model but also for a wider range of benchmark problems.

Problem

• Non-Gaussian mutation impact
• Evolution strategies performance
• Benchmark problem validation

Innovation

• Non-Gaussian mutation distributions
• Uniform mutations in ES
• Broad benchmark problem validation