Pareto Set Learning for Expensive Multi-Objective Optimization

TL;DR

This paper introduces a novel learning-based approach to approximate the entire Pareto set in expensive multi-objective optimization, enabling flexible decision-making and efficient exploration of trade-offs.

Contribution

It develops the first model to approximate the whole Pareto set in expensive multi-objective Bayesian optimization, extending MOEA/D to models and supporting batch evaluation.

Findings

Effective approximation of the Pareto set demonstrated on synthetic problems.

Supports flexible decision-making by exploring any trade-off area.

Outperforms existing methods in real-world applications.

Abstract

Expensive multi-objective optimization problems can be found in many real-world applications, where their objective function evaluations involve expensive computations or physical experiments. It is desirable to obtain an approximate Pareto front with a limited evaluation budget. Multi-objective Bayesian optimization (MOBO) has been widely used for finding a finite set of Pareto optimal solutions. However, it is well-known that the whole Pareto set is on a continuous manifold and can contain infinite solutions. The structural properties of the Pareto set are not well exploited in existing MOBO methods, and the finite-set approximation may not contain the most preferred solution(s) for decision-makers. This paper develops a novel learning-based method to approximate the whole Pareto set for MOBO, which generalizes the decomposition-based multi-objective optimization algorithm (MOEA/D) from finite populations to models. We design a simple and powerful acquisition search method based on the learned Pareto set, which naturally supports batch evaluation. In addition, with our proposed model, decision-makers can readily explore any trade-off area in the approximate Pareto set for flexible decision-making. This work represents the first attempt to model the Pareto set for expensive multi-objective optimization. Experimental results on different synthetic and real-world problems demonstrate the effectiveness of our proposed method.