This paper studies the problem of defending (1D and 2D) boundaries against a large number of continuous attacks with a heterogeneous group of defenders. The defender team has perfect information of the attack events within some time (finite or infinite) horizon, with the goal of intercepting as many attacks as possible. An attack is considered successfully intercepted if a defender is present at the boundary location when and where the attack happens. Through proposing a network-flow and integer programming-based method for computing optimal solutions, and an exhaustive defender pairing heuristic method for computing near-optimal solutions, we are able to significantly reduce the computation burden in solving the problem in comparison to the previous state of the art. Extensive simulation experiments confirm the effectiveness of the algorithms. Leveraging our efficient methods, we also characterize the solution structures, revealing the relationships between the attack interception rate and the various problem parameters, e.g., the heterogeneity of the defenders, attack rate, boundary topology, and the look-ahead horizon.

翻译：本文研究利用异质防御者群体防御（一维和二维）边界免受大量连续攻击的问题。防御团队在某个（有限或无限）时间范围内拥有攻击事件的完全信息，目标是尽可能拦截更多的攻击。若在攻击发生的时间和地点有防御者位于边界位置，则认为攻击被成功拦截。通过提出一种基于网络流和整数规划的方法计算最优解，以及一种穷举防御者配对启发式方法计算近优解，我们相比现有最先进技术显著降低了求解该问题的计算负担。大量仿真实验证实了这些算法的有效性。借助我们的高效方法，我们还刻画了解的结构，揭示了攻击拦截率与各类问题参数（如防御者异质性、攻击速率、边界拓扑结构及前瞻时间范围）之间的关系。