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.

In everyday life, we often face decisions where multiple goals clash. For instance, when a delivery company plans routes, it wants to minimize both driving distance and travel time. Current AI methods for these complex planning problems usually focus entirely on the destinations (the "nodes"), while ignoring the unique characteristics of the roads connecting them, such as specific traffic conditions or distances between two points. This oversight often leads to sub-optimal routes. To bridge this gap, we introduce a smart decision-making mechanism for AI. Instead of looking at locations in isolation, our method seamlessly blends information about both the places and the roads connecting them. Crucially, it adapts to the user's current priority—whether they care more about saving time or saving fuel—and dynamically tailors how the AI evaluates the roads based on that preference. Tests on classic routing and scheduling tasks prove that our approach not only generates higher-quality balancing solutions almost instantly, but also adapts remarkably well to entirely new, unfamiliar environments.