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

TL;DR

This paper tackles automated algorithm selection for mixed-variable black-box optimization by comparing SHAP-based exploratory landscape analysis (ELA) features to target-encoded features and by hybridizing them. It trains two algorithm selectors on ELA features derived from each encoding and shows that the encodings offer complementary strengths. A pair of hybrid strategies—a meta-model chooser and a prediction-confidence rule—substantially improve selection performance beyond either encoding alone, though the gap to a theoretical best solver remains. The work advances ELA for MVP and points to future directions for deeper encoding integration and broader MVP domains.

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.

Figures (3)

• Figure 1: General procedure of ELA feature generation. Based on the initial design several feature sets can be computed. The feature set 'meta model' fits the several linear and quadratic models and uses model coefficients as well as the adjusted $R^2$ as features.
• Figure 2: Performance of both algorithm selectors. The $x$-axis shows the relERT values of the SH model whereas the $y$-axis shows the relERT values of the TE model. Points on the grey line exhibit (nearly) identical relERT values for both models. Points above the grey line represent instances where the SH model produces a better performance. Points below the grey line represent the other case.
• Figure 3: Illustration of our two suggested approaches to capitalize on the complementary of the two AAS strategies. The meta model classifier utilizes ELA features derived from SHAP values and TE for each problem instance. With a binary target variable representing either the TE or SH model based on better prediction performance, the classifier selects the appropriate algorithm selector. Subsequently, the chosen selector utilizes ELA features specific to its encoding type and selects an algorithm from the portfolio. Alternatively, the prediction confidence approach relies on comparing prediction probabilities from independent AAS models, with the higher probability indicating greater confidence in the prediction.