A Hybrid Method to Search the Optimal Hamiltonian Circuit

Abstract

The objective of the well-known travelling salesman problem (TSP) is to search the optimal Hamiltonian circuit (OHC) in a tourist map. Finding the OHC becomes hard once the number of the cities and routes in the tourist map are large. The four vertices and three lines inequality was introduced as the constraints of the local optimal Hamiltonian paths (LOHPs) included in the OHC. The chaotic depth-priority algorithm was designed by adding the computation process with the chaotic operator to verify the rationality of the LOHPs generated with the depth-priority algorithm under the inequality constraints. A lot of non-LOHPs are abandoned in the search process and the search space of the OHC is reduced greatly. The method was verified with an example and it can be applied to the network optimization, path planning, task scheduling, assembly sequence planning etc.