A Genetic Algorithm with the Mixed Heuristics for Traveling Salesman Problem

Traveling salesman problem (TSP) is one of well-known discrete optimization problems. The genetic algorithm is improved with the mixed heuristics to resolve TSP. The first heuristics is the four vertices and three lines inequality, which is applied to the 4-vertex paths to generate the shorter Hamiltonian cycles (HC). The second local heuristics is executed to reverse the i-vertex paths with more than two vertices, which also generates the shorter HCs. It is necessary that the two heuristics coordinate with each other in the optimization process. The time complexity of the first and second heuristics are O(n) and O(n(3)), respectively. The two heuristics are merged into the original genetic algorithm. The computation results show that the improved genetic algorithm with the mixed heuristics can find better solutions than the original GA does under the same conditions.