The sensor-weapon–target assignment (S-WTA) problem is a crucial decision issue in C4ISR. The cooperative engagement capability (CEC) of sensors and weapons depends on the S-WTA schemes, which can greatly affect the operational effectiveness. In this paper, a mathematical model based on the synthetical framework of the S-WTA problem is established, combining the dependent and independent cooperative engagement modes of sensors and weapons. As this problem is a complex combinatorial optimization problem, a novel genetic algorithm is proposed to improve the solution of this formulated S-WTA model. Based on the prior knowledge of this problem, a problem-specific population initialization method and two novel repair operators are introduced. The performances of the proposed algorithm have been validated on the known benchmarks. Extensive experimental studies compared with three state-of-the-art approaches demonstrate that the proposed algorithm can generate better assignment schemes for the most of the benchmarks.