Classical Control Strength and Exact/Certified Anchors in Neural TSP Evaluation

Across four separately controlled Euclidean TSP blocks spanning $n\in \{20,50\}$ and uniform/clustered spatial generators, fixed-start nearest-neighbor construction lies roughly 17–25% above the exact or certified optimization anchor, whereas the specified audited local-search controls lie roughly 1.2–3.6% above it. The clustered protocol and primary endpoint were fixed before the 50,000-step training runs, with the held-out evaluation sets sampled only afterward. The clustered replication reproduces this separation at both sizes. This replicated separation shows how comparator strength changes the scale on which comparisons between learned and classical methods are interpreted; interpretation also depends on the selected checkpoint, inference multiplicity, and the form of the optimization anchor. We use common-instance evaluation, independently recomputed float64 objectives, exact float64 Held–Karp anchors at TSP20, and certified float64 optimum intervals from exact scaled-integer Concorde solves at TSP50. Across both tested distributions, the selected local POMO model has the smaller gap at $n=20$, whereas audited 2-opt has the smaller gap at $n=50$. Because the blocks use separately trained models and different inference/search protocols, this observation is descriptive and does not support a causal scaling claim or a ranking of method families.