Reinforcement Learning for Solving Colored Traveling Salesman Problems: An Entropy-Insensitive Attention Approach

The utilization of neural network models for solving combinatorial optimization problems (COPs) has gained significant attention in recent years and has demonstrated encouraging outcomes in addressing analogous problems such as the traveling salesman problem (TSP). The multiple TSP (MTSP) has sparked the interest of researchers as a special kind of COPs. The colored TSP (CTSP) is a variation of the MTSP, which utilizes colors to distinguish the accessibility of cities to salesmen. This article proposes a gated entropy-insensitive attention model (GEIAM) to solve CTSP. In specific, the original problem is first modeled as a sequence and preprocessed by the problem feature extraction network of the model, and then solved by the autoregressive solution constructor subsequently. The policy (parameters of the neural network model) is trained via reinforcement learning (RL). The proposed approach is compared with several commercial solvers as well as heuristics and demonstrates superior solving speed with comparable solution quality.