Preference-Modulated Structural Attention for Multi-Objective Combinatorial Optimization

Recent decomposition-based approaches have achieved significant success in Multi-Objective Combinatorial Optimization (MOCO). However, existing methods typically rely exclusively on node-centric representations, failing to capture the complementary representations provided by edge features for problem instances, resulting in a persistent optimality gap. To address this, we propose a preference-modulated structural attention mechanism to enhance problem representation by synergizing node and edge features. It includes:

(1) Utilizing preference-modulated edge features as explicit structural biases during attention calculation, enabling model to perceive sub-problem structures conditioned on specific preferences, and (2) an edge feature aggregation strategy that dynamically incorporates node-specific context into edge representations to enhance the perception of preference-aware structures. Experiments on classic MOCOP benchmarks demonstrate the superiority of our approach in terms of both performance and generalization capabilities.