The hybrid genetic algorithm with two local optimization strategies for traveling salesman problem

• The four vertices and three lines inequality is integrated with GA to improve its performance.
• The reversion of the local Hamiltonian paths with more than 2 vertices, which generates better solutions.
• The time complexity of the two local optimization strategies is O(n) and O(n3), respectively.

Traveling salesman problem (TSP) is proven to be NP-complete in most cases. The genetic algorithm (GA) is improved with two local optimization strategies for it. The first local optimization strategy is the four vertices and three lines inequality, which is applied to the local Hamiltonian paths to generate the shorter Hamiltonian circuits (HC). After the HCs are adjusted with the inequality, the second local optimization strategy is executed to reverse the local Hamiltonian paths with more than 2 vertices, which also generates the shorter HCs. It is necessary that the two optimization strategies coordinate with each other in the optimization process. The two optimization strategies are operated in two structural programs. The time complexity of the first and second local optimization strategies are O(n) and O(n3), respectively. The two optimization strategies are merged into the traditional GA. The computation results show that the hybrid genetic algorithm (HGA) can find the better approximate solutions than the GA does within an acceptable computation time.