An algorithm for solving travelling salesman problem based on improved particle swarm optimisation and dynamic step Hopfield network

Abstract

The travelling salesman problem (TSP) is a typical combinatorial optimisation problem. With the increasing scale of cities, the optimal solution is difficult to be calculated. In this paper, an algorithm based on improved particle swarm optimisation (PSO) and a dynamic step Hopfield neural network is proposed. Simplifying the energy function improves calculation efficiency; as the Hopfield network with fixed step size converges slowly, dynamic step size is used instead. Meanwhile, the idea of PSO is introduced to address the problem that Hopfield tends to fall into local minima. According to the idea of exchange sequence, the PSO algorithm is redefined. On this basis, the random inertia weight is used to enhance the searching ability. Experiments show that the algorithm can converge faster, avoid invalid solutions better, jump out of possible local extremum points and obtain the global optimal solution with higher probability than the classical Hopfield network.