Towards Feature-Free Automated Algorithm Selection for Single-Objective Continuous Black-Box Optimization

We propose a novel method for automated algorithm selection in the domain of single-objective continuous black-box optimization. In contrast to existing methods, we use convolutional neural networks as the selection apparatus which bases its decision on a so-called ‘fitness map’. This fitness map is a 2D representation of a two dimensional search space where different gray scales indicate the quality of found solutions in certain areas. Our devised approach uses a modular CMA-ES framework which offers the option to create the conventional CMA-ES, CMA-ES with the alternate step-size adaptation and many other variants proposed over the years. In total, 4 608 different configurations are possible where most configurations are of complementary nature. In this proof-of-concept work, we consider a subset of 32 possible configurations. The developed method is evaluated against an excerpt of BBOB functions and its performance is compared against baselines that are commonly used in automated algorithm selection - the best standalone algorithm (configuration) and the best obtainable sequence of configurations. While the results indicate that the use of the fitness map is not superior on every benchmark problem, it indubitably shows its merit on more hard-to-solve problems. This offers a promising perspective for generalizing to other types of optimization problems and problem domains.