Using structural bias to analyse the behaviour of modular CMA-ES
Diederick Vermetten, Fabio Caraffini, Bas van Stein, Anna V. Kononova · Proceedings of the Genetic and Evolutionary Computation Conference Companion · 2022
The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is a commonly used iterative optimisation heuristic for optimising black-box functions. CMA-ES comes in many flavours with different configuration settings. In this work, we investigate whether CMA-ES suffers from structural bias and which modules and parameters affect the strength and type of structural bias. Structural bias occurs when an algorithm or a component of the algorithm biases the search towards a specific direction in the search space irrespective of the objective function. In addition to this investigation, we propose a method to assess the relationship between structural bias and the performance of configurations with different types of bias on the BBOB suite of benchmark functions. Surprisingly for such a popular algorithm, 90.3% of the 1 620 CMA-ES configurations were found to have Structural Bias. Some interesting patterns between module settings and bias types are presented and further insights are discussed.