张量网络生成器增强优化在旅行推销员问题中的应用

This study presents an application of the tensor network generator-enhanced optimization (TN-GEO) framework to tackle the traveling salesman problem (TSP), a fundamental combinatorial optimization challenge. The approach employs a tensor network Born machine based on automatically differentiable matrix product states (MPS) as the generative model, utilizing the Born rule to define probability distributions over candidate solutions. Unlike binary encoding methods, which require $N^2$ variables and penalty terms to enforce valid tour constraints, a permutation-based formulation with integer variables is adopted. Autoregressive sampling with masking is used to ensure that every generated sample is a valid tour by construction. Additionally, new optimization strategies are introduced to enhance solution efficiency and quality.