Predicting Algorithm Performance in Constrained Multiobjective Optimization: A Tough Nut to Crack

Predicting algorithm performance is crucial for selecting the best performing algorithm for a given optimization problem. While some research on this topic has been done for single-objective optimization, it is still largely unexplored for constrained multiobjective optimization. In this work, we study two methodologies as candidates for predicting algorithm performance on 2D constrained multiobjective optimization problems. The first one consists of using state-of-the-art exploratory landscape analysis (ELA) features, designed specifically for constrained multiobjective optimization, as input to classical machine learning methods, and applying the resulting models to predict the performance classes. As an alternative methodology, we analyze an end-to-end deep neural network trained to predict algorithm performance from a suitable problem representation, without relying on ELA features. The experimental results obtained on benchmark problems with three multiobjective optimizers show that neither of the two methodologies is capable of substantially outperforming a dummy classifier. This suggests that, with the current benchmark problems and ELA features, predicting algorithm performance in constrained multiobjective optimization remains a challenge.