Pareto Set Learning for Expensive Multi-Objective Optimization
This addresses the need for flexible decision-making in applications with expensive evaluations, such as engineering or scientific experiments, by providing a continuous approximation of Pareto sets, though it is incremental as it builds on existing decomposition-based methods.
The paper tackles the problem of approximating the entire Pareto set for expensive multi-objective optimization, where objective evaluations are costly, by developing a learning-based method that generalizes decomposition algorithms from finite populations to models, resulting in effective performance on synthetic and real-world problems.
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.