Gating Is Attention: A Plug-and-Play Preference-Gated Dual-Attention Module for Neural Multi-Objective Combinatorial Optimization

Neural multi-objective combinatorial optimization (MOCO) solves scalarized subproblems conditioned on preference vectors. Existing methods mainly use preferences for early representation fusion, weight-conditioned embedding, or route selection. However, they provide limited control over the attended features that directly guide decisions. We propose Preference-Gated Dual Attention (PGDA), a lightweight plug-and-play module that treats objective preferences as conditional controls over attention outputs. After standard attention, PGDA generates a gate from the context, the preference embedding, and the attention output. The gate then reweights the attended representation for preference-aware decision making. This modulation prioritizes preference-relevant features without altering instance representations. Experiments on multiple MOCO benchmarks show that PGDA provides consistent gains for single-model solvers and strong POCCO-based backbones. PGDA also achieves competitive solution quality with efficient inference, especially in cross-scale and large-scale generalization settings.