A case study: Performance enhancement of nonlinear combinational optimization problem by neural networks

Artificial Neural Networks have been widely used for obtaining solutions for combinational optimization problems. Traveling Salesman problem is a well known nonlinear combinational optimization problem. In Traveling Salesman problem, a fixed number of cities is given. An optimal tour of all these cities is required such that each city is visited only once and the total tour distance to be covered has to be minimized. Hopfield Networks have been applied for generating an optimal solution. However there are certain factors which result in instability and local optimization of Hopfield Networks. In such cases the solutions obtained may not be optimal and feasible. In this thesis, the application of the K-Means algorithm is combined with the Hopfield Networks to generate more stable and optimum solutions to traveling salesperson problem.