用软分区方法提升复杂帕累托前沿的优化学习效果
GaussianPSL: Soft partitioning for complex PSL problem
- 通过动态软分区划分决策/目标空间，分区域学习局部特征
- 在多个复杂前沿上优于传统PSL模型，收敛更稳定
- 适合处理非凸、不连续等困难前沿的多目标优化问题
多目标优化（MOO）在工程设计、自主系统和机器学习等实际应用中常产生复杂帕累托前沿（如不连续、退化或非凸），传统标量化与帕累托集学习（PSL）方法难以准确逼近。本文提出GaussianPSL，一种新框架，通过在帕累托决策/目标空间进行软分区，解决复杂前沿带来的挑战。该方法动态划分空间，使简单的MLP网络能在每个区域学习局部特征，并聚合信息进行最终预测。这种分区感知策略提升了探索能力与收敛性，降低对初始化的敏感度，增强对局部最优的鲁棒性。实验表明，该方法在学习复杂帕累托前沿方面持续优于标准PSL模型，同时保持模型简洁。GaussianPSL为复杂前沿几何下的高效可扩展多目标优化提供了新方向。
原文摘要 · Abstract (English)
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.
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