一种求解WTA问题的二次松弛方法

为了求解联合作战中的武器目标分配问题（WTA），在简要介绍WTA模型的基础上，根据WTA模型特征，利用松驰理论和方法，先将模型松弛为混合整数线性规划问题，然后利用Lagrange松弛，将模型分解为2个子问题：线性规划子问题和整数规划子问题，利用全单模矩阵特性求解整数规划子问题，并根据2个子问题的关系调整参数范围。理论证明该方法可以快速有效地给出改善的WTA问题的可行解。数值实验结果表明该方法对不同规模的WTA问题都有较好效果，适合不同战场环境下联合作战对WTA问题求解的实时性要求。

Method of 2 phase relaxation for solving WTA problem

Weapon target assignment(WTA) problem is important in joint operation and is NP complete. WTA problem was introduced briefly. Then based on relaxation theories and methods, WTA problem was relaxed into a mixed integer linear programming.Lagrange relaxation was introduced and the WTA problem decomposed into two sub problems, linear programming and mixed integer linear programming. The integer linear programming was solved based on totally unimodular matrix, and the parameters' scale modified according to the relationship among them. The proposed method is feasible and effective. Computational results also verify that it is effective not only for small scale but also for large scale of WTA problem.