GaussianPSL: Soft partitioning for complex PSL problem

Many practical applications of multi-objective optimization (MOO), including engineering design, autonomous systems, and machine learning, often yield complex Pareto frontiers (e.g., discontinuous, degenerate, or non-convex), which pose challenges for traditional scalarization and Pareto Set Learning (PSL) methods that struggle to approximate them accurately. In this paper, we propose GaussianPSL, a novel framework that uses soft partitions of the Pareto decision/objective space to address the challenges posed by complex Pareto frontiers. Our method dynamically partitions the space, enabling simple MLP networks to learn localized features within each region and then aggregate this information for the final prediction. This partition-aware strategy enhances both exploration and convergence, reduces sensitivity to initialization, and improves robustness against local optima. Experimental results demonstrate that the proposed approach consistently outperforms standard PSL models in learning complex Pareto fronts while maintaining model simplicity. Overall, GaussianPSL offers a new direction for effective, scalable MOO in challenging frontier geometries.