Exploratory Landscape Analysis for Mixed-Variable Problems

Exploratory landscape analysis (ELA) and fitness landscape analysis in general have given valuable insight into problem hardness understanding as well as facilitating algorithm design and endeavors, such as automated algorithm selection (AAS) and configuration. These techniques have largely been limited to search spaces of a single domain. In this work, we provide the means to compute exploratory landscape features for mixed-variable problems where the decision space is a mixture of continuous, binary, integer, and categorical variables. This is achieved by introducing a preprocessing scheme which needs to be incorporated into the process of ELA feature generation. To highlight the merit of our approach for practical applications, we design and conduct an AAS study based on a hyperparameter optimization benchmark suite and our preprocessing scheme. Our trained algorithm selector is able to close the gap between the single best and the virtual best solver by 57.5% over all benchmark problems.