The Modular CMA-ES: A Framework for Modern Evolution Strategies

2026-10-07

AI Summary

This study addresses the limitation that existing improvement mechanisms for evolution strategies are typically investigated in isolation, with their interaction effects remaining underexplored. To this end, this work proposes a modular framework for Covariance Matrix Adaptation Evolution Strategy (CMA-ES). For the first time, core mechanisms such as sampling and adaptation are decoupled into interchangeable modules. By integrating automated algorithm configuration techniques, the framework enables systematic exploration of the algorithm design space and quantitative analysis of combinatorial effects. Experimental results validate the effectiveness and reproducibility of the proposed framework in terms of computational overhead, optimization performance, and customized benchmarking. Ultimately, this research establishes a novel paradigm for the modular design and automated tuning of evolutionary algorithms.

Abstract

Since their introduction, modern evolution strategies, such as the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), have become established as powerful methods for continuous black-box optimization. This success has led to a wide range of proposed modifications, each designed to improve performance or behavior in specific optimization scenarios. However, because these developments have largely been introduced and studied in isolation, their interactions remain comparatively underexplored. In this paper, we present the Modular CMA-ES (ModCMA), a configurable framework that integrates a wide range of mechanisms from modern evolution strategies within a single implementation. By decomposing CMA-ES into modules with interchangeable options for sampling, selection and recombination, step-size adaptation, matrix adaptation, and restarting, ModCMA enables systematic exploration of a large design space of modern evolution strategies and facilitates the construction, comparison, and automated configuration of new algorithm variants. We illustrate the benefits of this modular approach through two example studies. First, we compare several matrix-adaptation mechanisms in terms of their computational cost and optimization performance. Second, we use automated algorithm configuration to specialize ModCMA to individual benchmark problems and analyze the resulting configurations. Together, these examples demonstrate how the framework can be used both to study individual algorithmic design choices and to explore their combinations in a systematic and reproducible manner.

Problem

• Evolution Strategies
• CMA-ES
• Black-box Optimization
• Modular Framework
• Algorithm Configuration

Innovation

• Modular CMA-ES
• Evolution Strategies
• Automated Algorithm Configuration
• Black-box Optimization
• Matrix Adaptation