Research on one kind of multiple traveling salesmen problem requires minimizing the maximum length of the cycles traveled by all the salesmen. A new local search operator is designed, this operator not only optimizes one cycle, but also reorganizes and optimizes two cycles, its optimization ability is better than the existing local search operators under the equivalent calculation cost. Based on this operator, an iterative strategy named "search-select-mutate- search" is proposed, according to this strategy, the Competitive Search Algorithm (CSA) is designed. The experiments on the open data sets showed that CSA performs better than recent literatures.