LINC: Decoupling Local Consequence Scoring from Hidden Matching in Constructive Neural Routing

Abstract

Constructive neural routing solvers usually score the next action by matching a decoder context to candidate embeddings, leaving deterministic one-step consequences such as travel, waiting, slack, and capacity changes implicit. We propose LINC, a decoder-side candidate decision architecture that computes these consequences explicitly. LINC uses them according to their decision role: candidate-level consequences are scored by a state-conditioned shared linear comparator, while feasible-set summaries modulate the decoder context. This preserves standard global matching while reducing the burden on the hidden state to reconstruct transition arithmetic. The Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) serves as the main constrained-routing testbed, and the same interface extends to the Capacitated Vehicle Routing Problem (CVRP) and Traveling Salesman Problem (TSP). Across external benchmarks and no-retraining scale-transfer settings, LINC consistently improves strong neural baselines, with the advantage becoming more pronounced as test size moves further beyond the training scale, especially on constrained routing problems.