Solving 50-City TSP Problem Using Hopfield Neural Network

In this document, we demonstrate how to solve the Traveling Salesman Problem (TSP) using a Hopfield neural network, specifically targeting the 50-city TSP instance. This approach is particularly suitable for beginners due to its straightforward implementation logic. The solution employs energy minimization principles where city visit sequences are represented through neuron activation patterns. Key implementation aspects include: designing a proper energy function that incorporates distance optimization constraints, configuring neuron connections to enforce valid TSP routes (each city visited exactly once), and implementing convergence checks through iterative updates. The algorithm utilizes matrix operations for efficient weight updates, with critical functions handling distance matrix calculations and state evolution monitoring. By leveraging the Hopfield network's associative memory properties, we can identify near-optimal travel routes that minimize total distance while ensuring all cities are visited. This method significantly improves computational efficiency and reduces time complexity compared to brute-force approaches, making it particularly valuable for introductory optimization studies. The implementation includes detailed comments explaining parameter tuning for stability and convergence optimization.