An extension of the Hopfield-Tank model for solution of the multiple traveling salesmen problem

The authors develop an efficient neural network algorithm for solving the multiple traveling salesman problem (MTSP). A novel transformation of the N-city, M-salesman MTSP to the standard TSP is introduced. The transformed problem is represented by an expanded version of the Hopfield-Tank neuromorphic city-position map with (N+M-1)-cities and a single fictitious salesman. The dynamic model associated with the problem is based on the basic differential multiplier method. The algorithm was successfully tested on many problems with up to 30 cities and 5 salesmen. In all cases the algorithm converged to valid solutions.<>