Pareto Set Learning for Expensive Multi-Objective Optimization

• URL: http://arxiv.org/abs/2210.08495v1
• Date: Sun, 16 Oct 2022 09:41:54 GMT
• Title: Pareto Set Learning for Expensive Multi-Objective Optimization
• Authors: Xi Lin, Zhiyuan Yang, Xiaoyuan Zhang, Qingfu Zhang
• Abstract summary: Expensive multi-objective optimization problems can be found in many real-world applications. This paper develops a novel learning-based method to approximate the whole Pareto set for MOBO.
• Score: 5.419608513284392
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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