Sensitivity analysis in neural net solutions

Neural networks have been shown to have promise for solving certain types of optimization problems. A particular example is the classic NP-complete problem of the traveling salesman (TSP) in which a minimum distance tour of n cities is to be found. J.J. Hopfield and D.W. Tank (1985) presented a simulation of a neural network that was able to produce good, if not optimal, tours. However, little information was given concerning the validity and quality of the network solutions in general. In the present study, a more detailed analysis of the TSP network is given. In particular, a sensitivity analysis is performed with respect to the bias-input and intercity-distance contributions to the network energy function. The results indicate that a statistical approach is needed to specify the performance of the network. Additionally, the behavior of the network is studied across a range in numbers of cities (10 through 30). An analysis of TSPs for 10, 15, 20, 25 and 30 cities indicated that the practical maximum number of cities that can be analyzed with the permutation-matrix network configuration is about 50 cities.<>