On computational complexity of the constructive-optimizer neural network for the traveling salesman problem

Abstract

Abstract The authors formerly proposed the constructive-optimizer neural network (CONN) for the traveling salesman problem (TSP) to provide the best compromise between the solution quality and convergence speed. However, the computational complexity of CONN were cautiously reported as o(n3). In this paper, by using a probabilistic analysis approach, we prove that the real computational complexity of CONN is of O(n2logn). Three sets of benchmark TSPs from TSPLIB were used to evaluate the performance of CONN. We demonstrated that a polynomial of order n2logn provided the best fit to the CPU time of CONN versus the number of TSP cities. Also, CONN was further compared with a large number of state-of-the-art neural networks in terms of both solution quality and CPU time. We demonstrated that for ordinary TSPs, CONN may provide the best tradeoff between the CPU time and solution quality while for very large-scale TSPs, the memetic self-organizing map may be preferred.