Abstract: Based on the analysis of Inver-over operator，two improved Inver-over operators—1st-Inver-over operator and 2nd-Inver-over operator are proposed.Two-stage Evolutionary Algorithm based on improved Inver-over operator（Two-stage Inver-over EA） for TSP is implemented.In the prior period of the Two-stage Inver-over EA，in order to guarantee the convergence rate of the population，the algorithm only uses 1st-Inver-over operator.In the later period of the Two-stage Inver-over EA，in order to coordinate the convergence rate and the diversity of the population，the algorithm self-adaptively uses 1st-Inver-over operator and 2nd-Inver-over operator on the basis of the diversity of the population.The experiments results on TSPLIB（Traveling Salesman Problem Library） show that the Two-stage Inver-over EA is improved a lot on the convergence rate and efficiency compared with the classic GT algorithm.

摘要： 对Inver-over算子进行了改进，提出了1st-Inver-over算子和2nd-Inver-over算子，实现了求解TSP问题的基于改进Inver-over算子的二阶段演化算法（Two-stage Inver-over EA）。在算法前期，只采用1st-Inver-over算子来保证算法的收敛速度；在算法后期，根据种群的多样性自适应地选取1st-Inver-over算子和2nd-Inver-over算子来协调算法的收敛速度和种群的多样性。在TSPLIB（Traveling Salesman Problem Library）中的典型实例上的实验结果表明，Two-stage Inver-over EA比经典的GT算法具有更好的收敛性和搜索效率。