A traveling salesman objective function that works

An Ising-like objective function has been used by J. Hopfield (1985) and others for finding the optimal tour in a traveling salesman problem using a neural network. This function contains four terms: one which reflects the length of the tour and three more penalty terms which attempt to maintain a feasible solution. These terms are combined into a weighted sum using four coefficients determined by the user. The quality of the final solution is very sensitive to these weighting factors, and good values for them are difficult to find when even a moderate number of cities are considered. A novel objective function is developed here that requires one weighting factor the value of which is easily determined. The use of this function in combination with an algorithm combining characteristics of neural networks and simulated annealing allows good, valid solutions to be found.<>