Enhanced Ant Colony Optimization with Four Vertices and Three Lines Inequality for Traveling Salesman Probelm

Traveling salesman problem (TSP) becomes hard when the number of cities and routes are large. The ant colony optimization method (ACO) is enhanced with the four vertices and three lines inequality to search the optimal Hamiltonian circuit (OHC). The four vertices and three lines inequality is the constraint of the local optimal Hamiltonian paths (LOHP) and all the LOHPs in the OHC conform to the inequality. The ACO is used to search the near OHCs. The local Hamiltonian paths in the near OHCs are altered into the better near OHCs based on the four vertices and three lines inequality. The enhanced ACO (EACO) is tested with TSP instances. The results show that the better near OHC are computed with the EACO than that with the ACO, and the computation cycles of convergence of EACO is smaller than that of the ACO under the same preconditions.