Landscape features in single-objective continuous optimization: Have we hit a wall in algorithm selection generalization?

The process of identifying the most suitable optimization algorithm for a specific problem, referred to as algorithm selection (AS), entails training models that leverage problem landscape features to forecast algorithm performance. A significant challenge in this domain is ensuring that AS models can generalize effectively to novel, unseen problems. This study evaluates the generalizability of AS models based on different problem representations in the context of single-objective continuous optimization. In particular, it considers the most widely used Exploratory Landscape Analysis features, as well as recently proposed Topological Landscape Analysis features, and features based on deep learning, such as DeepELA, TransOptAS and Doe2Vec. Our results indicate that when presented with out-of-distribution evaluation data, none of the feature-based AS models outperform a simple baseline model, i.e., a Single Best Solver. • Benchmarking single-objective numerical optimization problem landscape features. • Investigating whether problem landscape features capture algorithm performance. • Analyzing problem landscape feature similarity and complementarity. • Evaluating Algorithm Selection generalizability with different feature groups.