Using Structural Bias to Analyse the Behaviour of Modular CMA-ES

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 CMAES 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.