Traveling Salesperson Problem

The Traveling Salesperson Problem (TSP) asks for the shortest closed route through a set of cities, a difficult problem with practical links to logistics, manufacturing, and circuit design. Classical approaches include exact branch-and-cut and integer programming, alongside heuristics such as Lin–Kernighan search, genetic algorithms, ant colony optimization, and 2-opt local search. Neural methods use graph neural networks, reinforcement learning, diffusion models, and geometric symmetry to construct or improve tours, often tested on synthetic Euclidean instances and TSPLIB benchmarks. A central challenge is balancing solution quality, runtime, and scalability to very large instances while preserving reliable generalization and, where possible, guarantees of validity or optimality.