Traveling salesman problem using neural network techniques

We discuss two methods for solving the traveling salesman problem (TSP). First, ant system (Ant colony system (ACS)). Second, Neural Network (Hopfield Neural Network). In ACS, a set of cooperating agents called ants cooperate to find good solutions to TSPs. Ants cooperate using indirect form of communication mediated by pheromone they deposit on the edges of TSP graph while building solutions. A proposed algorithm and standard Algorithm that are applied to the traveling salesman problem (TSP) are derived. We study ACS by running experiments to understand its operation. Also we present a proposed Algorithm using continuous Hopfield neural network to solve TSP. To enable the N neurons in the TSP network to compute a solution to the problem, the network must be described by an energy function in which the lowest energy state (the most stable state of the network) corresponds to the best path. Results of programs (standard, proposed) are presented and compared.