Solving TSP Problem Using Hopfield Neural Network

This article explores the implementation of Hopfield neural networks for solving the Traveling Salesman Problem. Specifically, we focus on finding optimal routes connecting six major cities: Beijing, Tianjin, Shijiazhuang, Taiyuan, Hohhot, and Shanghai. The implementation involves configuring the energy function to represent TSP constraints, where city visitation sequences are encoded through neuron activation patterns. Key implementation aspects include designing the weight matrix to enforce valid tours (each city visited exactly once) and minimizing total distance through iterative updates using the differential equation: dU/dt = -U/τ + ΣWijVj + Ii. The algorithm employs sigmoid activation functions and convergence checks to ensure valid solutions. We discuss challenges like local minima prevention through simulated annealing techniques and parameter tuning for convergence stability. Through code examples and matrix operations explanation, readers will understand how to map TSP constraints to neural network parameters and implement energy minimization for route optimization.