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A new hybrid method iterative extended changing crossover operators which can efficiently obtain the optimum solution of the traveling salesman problem through flexibly alternating ant colony optimization (ACO) which simulates process of learning swarm intelligence in ants' feeding behavior and edge assembly crossover (EAX) which has been recently noticed as an available method for efficient selection of optimum solution with preserving diversity of chromosomes at any time, is studied. It automatically controls the generation on which it exchanges ACO for EAX by observing diversity and convergence of chromosomes generated by ACO with both lengths and their variance. It uses ACO in early stage of generations to create variable local optimum solutions and it uses EAX in later stage of generations efficiently to generate global optimum solutions using chromosomes generated by ACO. If it cannot find the optimum solution in this trial it makes ACO regenerate new chromosomes to merge with the last best solution searched through EAX in order to maintain diversity of chromosomes, before it makes EAX reproduce better solutions with the merged chromosomes. This trial is repeatedly executed until EAX can find the best solution. In this paper its validity is experimentally verified by using medium-sized TSP data.