Tensor-Network Formulation of the Traveling Salesman Problem and Variants
For researchers interested in combinatorial optimization, this is an incremental theoretical framework that reformulates TSP in tensor-network language but lacks empirical evidence of practical advantage.
This work presents a tensor-network formulation of the Traveling Salesman Problem and its variants, using Boltzmann-weighted layers and constraint filters. On small illustrative experiments, the method is contextualized against exact and heuristic references but does not demonstrate general superiority over specialized classical solvers.
This work presents a tensor-network formulation of the Traveling Salesman Problem (TSP) and several of its variants. The approach represents candidate tours with tensor-network layers, weights them by Boltzmann factors, and enforces constraints through explicit counting filters. This formalism also yields an explicit tensor-network marginal formula whose zero-temperature, exact-arithmetic limit identifies an optimal feasible tour through a sequential marginal rule. At finite $τ$ and finite precision, the implemented extraction is a heuristic whose behavior depends on numerical contrast, calibration, and near-degeneracies. We adapt the construction to several generalizations of the TSP and apply it to the Job Reassignment Problem, as a representative industrial integration. The experiments are deliberately small and illustrative; they contextualize the method against exact and heuristic references but do not establish general computational superiority over specialized classical solvers.