Leveraging Structural Constraints for Diffusion-based Neural TSP Solvers

2026-06-08

AI Summary

This work addresses the high computational cost and structural mismatch of existing neural TSP solvers that rely on gradient-based optimization during inference, which struggles to respect the discrete nature of tour solutions. The authors propose Projected Consistency Inference (PCI), a novel approach that explicitly incorporates structural constraints into the inference process of diffusion models. PCI operates by applying a structure-aware projection followed by a lightweight 2-opt local search directly on the output of a consistency model, yielding valid Hamiltonian cycles without requiring retraining or fine-tuning. Evaluated on TSP instances with 500 and 1,000 cities, PCI achieves average optimality gaps of 0.17% and 0.31%, respectively—outperforming FT2T—while accelerating inference by 30–40%, reducing memory consumption, and surpassing classical heuristics such as LKH3.

Abstract

Neural combinatorial optimization has recently achieved strong results on the Euclidean Traveling Salesman Problem (TSP) using generative models such as diffusion and consistency models. State-ofthe-art approaches like FT2T combine fast consistency-based prediction with gradient-based inference time refinement. However, gradient search often incurs significant computational overhead and may not align with the discrete structure of feasible solutions. We introduce Projected Consistency Inference (PCI), a plug-and-play, retraining-free alternative that replaces gradient refinement with structure-aware projections: PCI decodes valid Hamiltonian tours from the consistency model output and applies a lightweight local search (e.g., 2-opt). PCI achieves an average optimality gap (OG) of 0.17% on TSP with 500 cities, and 0.31% on TSP with 1000 cities, outperforming FT2T best settings (OG 0.22% and 0.36%, respectively) while reducing the inference time up to 30 to 40%. PCI also exhibits lower variance and memory usage, and can surpass classical heuristics such as LKH3 in rapid solution generation. Our results demonstrate that structure-aware inference time operations provide a practical and principled path for neural TSP solvers, complementing training time objectives.

Problem

• Traveling Salesman Problem
• Neural Combinatorial Optimization
• Diffusion Models
• Gradient-based Refinement
• Discrete Structure

Innovation

• Projected Consistency Inference
• Neural Combinatorial Optimization
• Structure-aware Projection
• Diffusion Models
• Traveling Salesman Problem