  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 results in
significant inefficiencies and hinders the ability to exploit potential
synergies across varying MOPs. In this paper, we propose a Collaborative Pareto
Set Learning (CoPSL) framework, which learns the Pareto sets of multiple MOPs
simultaneously in a collaborative manner. CoPSL particularly employs an
architecture consisting of shared and MOP-specific layers. The shared layers
are designed to capture commonalities among MOPs collaboratively, while the
MOP-specific layers tailor these general insights to generate solution sets for
individual MOPs. This collaborative approach enables CoPSL to efficiently learn
the Pareto sets of multiple MOPs in a single execution while leveraging the
potential relationships among various MOPs. To further understand these
relationships, we experimentally demonstrate that shareable representations
exist among MOPs. Leveraging these shared representations effectively improves
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.
