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Although many significant achievements have been made on using ant colony optimization (ACO) algorithm to solve traveling salesman problem (TSP) and similar large-scale computational problems, the long convergent time required in the large-scale optimization still remains a computing bottle neck of ACO algorithm. In this paper, we present a rapidly convergent ant colony optimization (rcACO) algorithm to solve the TSP. In this algorithm, adaptive pheromone update is carried out according to the distance ants have moved, meanwhile, the inversion operator is used to enhance local search, etc. Our huge numerical experimental results demonstrate that the convergence speed of rcACO is tens to hundreds times faster than the recently improved ACO algorithms, meanwhile the global optimal solution can be achieved.