A Method to Reduce the Search Space of TSP

Abstract

A method to convert a frequency graph into a frequency sub-graph is proposed to reduce the search space of traveling salesman problem (TSP). The frequency graph is computed with a set of local optimal Hamiltonian paths (LOHPs). The numbers on the edges are their frequencies emulated from the set of LOHPs. It includes the law of conversion between the LOHPs and the global optimal solution. The frequency threshold is derived to delete the edges with frequencies below it and a sparse frequency sub-graph is obtained. A smaller number of edges exist in the frequency sub-graph and the search space of TSP is reduced. A branch and bound algorithm is designed to search the optimal solution Based on the frequency sub-graph. The computation results show that the optimal solutions are found within an acceptable computation time.