Collaborative Pareto Set Learning in Multiple Multi-Objective
  Optimization Problems
Chikai Shang Rongguang Ye Jiaqi Jiang Fangqing Gu
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.