The problem of targeting and engaging individual missiles (targets) with an arsenal of interceptors (weapons) is known as the weapon target assignment problem. Many optimal solution techniques are applied to solve problem variants having linear approximations of the objective function, and their final solutions rarely yield optimal solutions to the original problem. Herein, we propose a nonlinear branch and bound algorithm to solve the untransformed problem. We also develop two heuristics respectively based on a branch and bound algorithm and the optimal solution to the quiz problem, and we compare them to a well-embraced heuristic from the literature. We test the three heuristics to solve a set of 15 problem sizes and 20 instances for each size, comparing their performance with respect to solution quality and required computational effort. The heuristic based upon the optimal solution to the quiz problem finds solutions within \(6\%\) of optimal for small problems and provides statistically similar results as one of the best heuristics found in the literature for larger problems, while solving these problems in ten thousandths of the time.

中文翻译：

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静态武器目标分配问题的实时启发式算法

用一系列拦截器（武器）瞄准并与单个导弹（目标）交战的问题被称为武器目标分配问题。应用了许多最佳解决方案技术来解决具有目标函数线性近似的问题变体，并且它们的最终解决方案很少能为原始问题提供最佳解决方案。在此，我们提出了一种非线性分支定界算法来解决未变换的问题。我们还分别基于分支定界算法和测验问题的最佳解决方案开发了两种启发式算法，并将它们与文献中精心设计的启发式算法进行了比较。我们测试了三种启发式方法，以解决15种问题的大小以及每种大小的20个实例，并比较了它们在解决方案质量和所需计算量方面的性能。\（6 \％\）对于小问题的最优解，并提供统计上相似的结果，作为文献中针对大问题的最佳启发式方法之一，而在十分之一的时间内解决了这些问题。