A Hybrid Particle Swarm Optimization Method for Traveling Salesman Problem.

Traveling salesman problem TSP is one well-known NP-Complete problem. The objective is to search the optimal Hamiltonian circuit OHC in a tourist map. The particle swarm optimization PSO integrated with the four vertices and three lines inequality is introduced to detect the OHC or approximate OHC. The four vertices and three lines inequality is taken as local heuristics to find the local optimal paths composed of four vertices and three lines. Each of this kind of paths in the OHC or approximate OHC conforms to the inequality. The particle swarm optimization is used to search an initial approximation. The four vertices and three lines inequality is applied to convert all the paths in the approximation into the optimal paths. Then a better approximation is obtained. The method is tested with several Euclidean TSP instances. The results show that the much better approximations are searched with the hybrid PSO. The convergence rate is also faster than the traditional PSO under the same preconditions.