We consider a bilevel model of estimating the costs of the attacking party (the Attacker) for a successful attack of a given set of objects protected by the other party (the Defender). The Attacker and the Defender have multiple means to, correspondingly, attack and protect the objects, and the Attacker’s costs depend on the Defender’s means of protection. The model under consideration is based on the Stackelberg game, where the Attacker aims to successfully attack the objects with the least costs, while the Defender maximizes the Attacker’s losses committing some limited budget. Formally, the “Attacker—Defender” model can be written as a bilevel mixed-integer program. The particularity of the problem is that the feasibility of the upper-level solution depends on all lower-level optimal solutions. To compute an optimal solution of the bilevel problem under study, we suggest some algorithm that splits the feasible region of the problem into subsets and reducing the problem to a sequence of bilevel subproblems. Specificity of feasible regions of these subproblems allows us to reduce them to common mixed-integer programming problems of two types.

中文翻译：

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选择攻击手段构成的双层“攻击者-防御者”模型

我们考虑一种双层模型，该模型可以估算出成功攻击另一方（防御者）给定对象集的攻击方（攻击者）的成本。攻击者和防御者具有相应的攻击和保护对象的多种手段，并且攻击者的费用取决于防御者的保护手段。所考虑的模型基于Stackelberg游戏，其中攻击者旨在以最低的成本成功攻击对象，而后卫则将有限的预算用于最大化攻击者的损失。正式地，“攻击者-防御者”模型可以编写为双层混合整数程序。问题的特殊性在于上层解决方案的可行性取决于所有下层最佳解决方案。为了计算正在研究的双层问题的最优解，我们建议一种算法，将问题的可行区域划分为子集，并将问题简化为一系列双层子问题。这些子问题的可行区域的特异性使我们可以将它们简化为两种常见的混合整数编程问题。