The recent advancement in real-world critical infrastructure networks has led to an exponential growth in the use of automated devices which in turn has created new security challenges. In this paper, we study the robust and adaptive maximum flow problem in an uncertain environment where the network parameters (e.g., capacities) are known and deterministic, but the network structure (e.g., edges) is vulnerable to adversarial attacks or failures. We propose a robust and sustainable network flow model to effectively and proactively counter plausible attacking behaviors of an adversary operating under a budget constraint. Specifically, we introduce a novel scenario generation approach based on an iterative two-player game between a defender and an adversary. We assume that the adversary always takes a best myopic response (out of some feasible attacks) against the current flow scenario prepared by the defender. On the other hand, we assume that the defender considers all the attacking behaviors revealed by the adversary in previous iterations in order to generate a new conservative flow strategy that is robust (maximin) against all those attacks. This iterative game continues until the objectives of the adversary and the administrator both converge. We show that the robust network flow problem to be solved by the defender is NP-hard and that the complexity of the adversary's decision problem grows exponentially with the network size and the adversary's budget value. We propose two principled heuristic approaches for solving the adversary's problem at the scale of a large urban network. Extensive computational results on multiple synthetic and real-world data sets demonstrate that the solution provided by the defender's problem significantly increases the amount of flow pushed through the network and reduces the expected lost flow over four state-of-the-art benchmark approaches.

中文翻译：

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用于计算稳健和自适应网络流的迭代安全博弈

现实世界关键基础设施网络的最新进展导致自动化设备的使用呈指数增长，这反过来又带来了新的安全挑战。在本文中，我们研究了网络参数（例如，容量）已知且具有确定性，但网络结构（例如，边缘）容易受到对抗性攻击或故障的影响的不确定环境中的鲁棒性和自适应性最大流问题。我们提出了一个强大且可持续的网络流模型，以有效和主动地对抗在预算约束下运营的对手的合理攻击行为。具体来说，我们引入了一种新颖的场景生成方法，该方法基于防御者和对手之间的迭代两人游戏。我们假设对手总是对防御者准备的当前流动场景采取最佳近视反应（在一些可行的攻击中）。另一方面，我们假设防御者考虑了对手在先前迭代中揭示的所有攻击行为，以生成一个新的保守流策略，该策略对所有这些攻击都具有鲁棒性（最大值）。这种迭代游戏一直持续到对手和管理员的目标都收敛为止。我们表明，防御者要解决的鲁棒网络流问题是 NP-hard 问题，并且对手决策问题的复杂性随着网络规模和对手的预算值呈指数增长。我们提出了两种有原则的启发式方法，用于在大型城市网络的规模上解决对手的问题。