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The Decision-Making (DM) problem is investigated for Cooperative Multiple Target Attack in air combat. It is to search for a proper attack assignment of M friendly fighters, with multiple target attack capability, to N hostile fighters called targets to achieve an optimal missile-target attack effect. Thus, Missile-Target Assignment (MTA) is regarded as the main part of the DM problem and has to be solved firstly. Then, the DM solution is derived from the optimal MTA solution. To the MTA problem, a Heuristic Adaptive Genetic Algorithm (HAGA) is proposed to search for its optimal solution. The HAGA utilizes specific heuristic knowledge to improve the search capability of the Adaptive Genetic Algorithm (AGA). Simulation results show that the HAGA is effective and has much better performance than the AGA.