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This paper is concerned with the task assignment problem for a team of mobile robots in adversarial environments. Based on the geometric topology of the targets, two key factors are defined: the impact factor and the suffering factor, and a stochastic assignment model based on these factors is built, through which the robots can exhibit temporal cooperation. To reduce the computational complexity, genetic algorithm is employed to optimize the relative weights of the impact factor and the suffering factor, and after that, the Improved Hungarian algorithm is used to solve the assignment problem. Simulation results demonstrate the effectiveness of the proposed method.