Hybridizing Target- and SHAP-encoded Features for Algorithm Selection in Mixed-variable Black-box Optimization

TL;DR

This paper explores hybrid feature encoding methods combining target- and SHAP-encoded features for algorithm selection in mixed-variable black-box optimization, demonstrating that hybridization improves performance over individual encodings.

Contribution

The study introduces a hybrid approach combining target- and SHAP-encoded features for algorithm selection in mixed-variable problems, showing improved results through complementary encoding strategies.

Findings

Hybrid feature sets outperform individual encodings.

Combining target- and SHAP-encoded features improves algorithm selection.

Meta-selection methods effectively leverage the complementarity of features.

Abstract

Exploratory landscape analysis (ELA) is a well-established tool to characterize optimization problems via numerical features. ELA is used for problem comprehension, algorithm design, and applications such as automated algorithm selection and configuration. Until recently, however, ELA was limited to search spaces with either continuous or discrete variables, neglecting problems with mixed variable types. This gap was addressed in a recent study that uses an approach based on target-encoding to compute exploratory landscape features for mixedvariable problems. In this work, we investigate an alternative encoding scheme based on SHAP values. While these features do not lead to better results in the algorithm selection setting considered in previous work, the two different encoding mechanisms exhibit complementary performance. Combining both feature sets into a hybrid approach outperforms each encoding mechanism individually. Finally, we experiment with two different ways of meta-selecting between the two feature sets. Both approaches are capable of taking advantage of the performance complementarity of the models trained on target-encoded and SHAP-encoded feature sets, respectively.