On the Interaction of Adaptive Population Control with Cumulative Step-Size Adaptation

TL;DR

This paper investigates how adaptive population control strategies interact with cumulative step-size adaptation in evolution strategies, analyzing their theoretical scaling properties and empirical performance on benchmark functions.

Contribution

It provides a theoretical analysis of scaling properties and compares three PCS strategies within CSA-ES, identifying effective parameter sets for various test functions.

Findings

Scaling properties derived for large populations on the sphere.

Performance of PCS strategies depends on CSA adaptation properties.

Identified well-performing parameter sets for different test functions.

Abstract

Three state-of-the-art adaptive population control strategies (PCS) are theoretically and empirically investigated for a multi-recombinative, cumulative step-size adaptation Evolution Strategy $(\mu/\mu_I, \lambda)$-CSA-ES. First, scaling properties for the generation number and mutation strength rescaling are derived on the sphere in the limit of large population sizes. Then, the adaptation properties of three standard CSA-variants are studied as a function of the population size and dimensionality, and compared to the predicted scaling results. Thereafter, three PCS are implemented along the CSA-ES and studied on a test bed of sphere, random, and Rastrigin functions. The CSA-adaptation properties significantly influence the performance of the PCS, which is shown in more detail. Given the test bed, well-performing parameter sets (in terms of scaling, efficiency, and success rate) for both the CSA- and PCS-subroutines are identified.