Adaptive Sampling of Pareto Frontiers with Binary Constraints Using Regression and Classification

TL;DR

This paper introduces an adaptive Bayesian optimization method using regression and classification models to efficiently explore Pareto frontiers in multi-objective problems with binary constraints, improving speed and flexibility.

Contribution

It proposes a new surrogate-based optimization algorithm with an intuitive acquisition function and a novel ellipsoid truncation for faster hypervolume computation.

Findings

Outperforms evolutionary algorithms on benchmark problems

Offers a tunable acquisition function for diverse problem demands

Speeds up hypervolume calculation with ellipsoid truncation

Abstract

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.