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This work is related to the search of complexity measures for instances of combinatorial optimization problems. Particularly, we have carried out a study about the complexity of random instances of the Traveling Salesman Problem under the 2-exchange neighbor system. We have proposed two descriptors of complexity: the proportion of the size of the basin of attraction of the global optimum over the size of the search space and the proportion of the number of different local optima over the size of the search space. We have analyzed the evolution of these descriptors as the size of the problem grows. After that, and using our complexity measures, we find a phase transition phenomenon in the complexity of the instances.