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Crossover operator plays a crucial role in the efficiency of genetic algorithm (GA). Several crossover operators have been proposed for solving the travelling salesman problem (TSP) in the literature. These operators have paid less attention to the characteristics of the traveling salesman problem, and majority of these operators can only generate feasible solutions. In this paper, a crossover operator is presented that has the capability of generating solutions based on a logical reasoning. In other words, the solution space is explored by the proposed method purposefully. Numerical results based on 26 benchmark instances demonstrate the efficiency of the proposed method compared with the previous meta-heuristic methods.