Multi-objective combinatorial optimization (MOCO) problems are prevalent in various real-world applications. Most existing neural methods for MOCO problems rely solely on decomposition and utilize precise hypervolume to enhance diversity. However, these methods often approximate only limited regions of the Pareto front and spend excessive time on diversity enhancement because of ambiguous decomposition and time-consuming hypervolume calculation. To address these limitations, we design a Geometry-Aware Pareto set Learning algorithm named GAPL, which provides a novel geometric perspective for neural MOCO via a Pareto attention model based on hypervolume expectation maximization. In addition, we propose a hypervolume residual update strategy to enable the Pareto attention model to capture both local and non-local information of the Pareto set/front. We also design a novel inference approach to further improve quality of the solution set and speed up hypervolume calculation and local subset selection. Experimental results on three classic MOCO problems demonstrate that our GAPL outperforms state-of-the-art neural baselines via superior decomposition and efficient diversity enhancement.

通过基于超体积期望最大化的 Pareto 注意模型以及超体积残差更新策略，结合新颖的推理方法和局部子集选择方法，设计了一种名为 GAPL 的几何感知 Pareto 集学习算法，用于解决多目标组合优化问题，提高问题的分解能力和多样性增强。通过三个经典的多目标组合优化问题的实验结果表明，GAPL 算法在分解和多样性增强方面优于现有的神经基准模型。

面向几何感知的神经多目标组合优化 Pareto 集学习