Towards Generic and Efficient Architectures for Graph Neural Combinatorial Optimization

Constructive neural solvers have become a leading paradigm for combinatorial optimization (CO). However, building an architectural framework that is both generic enough across diverse problems without per-problem component redesign and efficient enough for step-wise inference remains an open challenge. To reduce this gap, we propose GECO, a generic and efficient architecture for edge-aware graph neural CO. To reduce computational cost, GECO introduces ScoreMixer-in-Attention (SMA), which follows a head-coupled attention-logit modeling principle: it treats the pre-softmax multi-head logits as a compact node–edge compatibility representation and refines it through a light-weight sub-network, avoiding expensive high-dimensional pairwise feature transformations. To enable generic instantiation, GECO further introduces a learnable warm-up attention layer that initializes node embeddings by aggregating edge information in a task-agnostic manner, together with an instance-preserving normalization framework that provides a principled feature-scaling normalization recipe for CO problems. Experiments on five representative routing and scheduling tasks show that GECO achieves strong solution quality while substantially reducing computational cost compared with state-of-the-art edge-aware architectures. Overall, GECO offers a concrete step toward systematically instantiable architectures for efficient edge-aware graph-based CO.