Hybrid neural–heuristic TSP solver with attention-guided refinement for real-time AMR coordination

Autonomous mobile robot (AMR) fleets in warehouses must solve hundreds of Traveling Salesman Problem (TSP) instances per second within strict latency budgets. Classical heuristics such as Lin–Kernighan achieve near-optimal tour quality but violate the 50–100 ms deadlines imposed by 10–20 Hz control loops; neural combinatorial optimization methods offer fast inference but exhibit 10%–25% optimality gaps that are economically unacceptable in production logistics. This paper introduces a hybrid neural–heuristic TSP solver that couples a Transformer-based encoder–decoder for constructive tour generation with an attention-guided 2-opt refinement stage. The attention matrix from the final encoder layer provides learned geometric priors that reduce the number of 2-opt candidates evaluated from the exhaustive O (N2) set to an O(N)-sized filtered subset per iteration. An adaptive curriculum learning strategy is accompanied by a convergence analysis under standard smoothness and bounded-gradient assumptions, and we derive assumption-dependent bounds relating attention Precision@K to attainable post-refinement solution quality. The solver is validated on 600 synthetic Euclidean instances (N=20–200), 847 real warehouse mission trajectories collected over six months from an industrial logistics partner, and a six-month production deployment with a 15-robot AMR fleet. It achieves 3.2–8.7% optimality gaps relative to Concorde optimal, 6.3–18.5 × speedups over Lin–Kernighan, and deterministic sub-80 ms latency for N≤100 on embedded hardware, with sub-130 ms probabilistic compliance for N≤150. Field deployment yields 22% throughput improvement, 18% energy reduction, and no recorded failures over 18,400 robot-hours, establishing hybrid neural–heuristic solvers as a practical and theoretically principled paradigm for real-time combinatorial optimization in cyber–physical systems.