Collaborative Pareto Set Learning in Multiple Multi-Objective Optimization Problems

Pareto Set Learning (PSL) is an emerging research area in multi-objective optimization, focusing on training neural networks to learn the mapping from preference vectors to Pareto optimal solutions. However, existing PSL methods are limited to addressing a single Multi-objective Optimization Problem (MOP) at a time. When faced with multiple MOPs, this limitation not only leads to significant inefficiencies but also fails to exploit the potential synergies across varying MOPs. In this paper, we propose a Collaborative Pareto Set Learning (CoPSL) framework, which simultaneously learns the Pareto sets of multiple MOPs in a collaborative manner. CoPSL employs an architecture consisting of shared and MOP-specific layers, where shared layers aim to capture common relationships among MOPs collaboratively, and MOP-specific layers process these relationships to generate solution sets for each MOP. This collaborative approach enables CoPSL to efficiently learn the Pareto sets of multiple MOPs in a single run while leveraging the relationships among various MOPs. To further understand these relationships, we experimentally demonstrate that there exist shareable representations among MOPs. Leveraging these collaboratively shared representations can effectively improve the capability to approximate Pareto sets. Extensive experiments underscore the superior efficiency and robustness of CoPSL in approximating Pareto sets compared to state-of-the-art approaches on a variety of synthetic and real-world MOPs. Code is available at https://github.com/ckshang/CoPSL.