Adaptive Sampling of Pareto Frontiers with Binary Constraints Using Regression and Classification
This work addresses optimization problems with binary constraints for researchers and practitioners in fields like engineering or operations, but it is incremental as it builds on existing Bayesian optimization methods.
The authors tackled black-box multi-objective optimization with binary constraints by developing an adaptive algorithm based on Bayesian optimization, using regression and classification as surrogates and introducing an ellipsoid truncation method to speed up hypervolume calculations. They benchmarked it against an evolutionary algorithm on test problems, showing improved efficiency.
We present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints on the foundation of Bayes optimization. Our method is based on probabilistic regression and classification models, which act as a surrogate for the optimization goals and allow us to suggest multiple design points at once in each iteration. The proposed acquisition function is intuitively understandable and can be tuned to the demands of the problems at hand. We also present a novel ellipsoid truncation method to speed up the expected hypervolume calculation in a straightforward way for regression models with a normal probability density. We benchmark our approach with an evolutionary algorithm on multiple test problems.