考虑攻防博弈的基础设施选址问题研究

The destruction of critical infrastructures could have a debilitating impact on the economy, security, public health, or safety of a nation. Thus, this proposed research will integrate protection against intentional attacks into the problem of facility location, in order to mitigate the impact of one of the most important risks, intentional attacks. Current approaches dealing with the protection of existed facilities, usually consider the game between defender and attacker as a leader-follower game, assuming that an attacker can obtain all information regarding protection strategies before making decisions. In this proposed research, to make the problem more realistic, we assume that no player can obtain any information regarding their adversary's strategies and thus consider the game as a simultaneous game. A new algorithm to identify the mixed-strategy Nash equilibrium of the proposed game will also be developed. Studies on the problem of considering protection against intentional attacks in the stage of making decisions on facility locations are still scarce. Moreover, when multiple objectives are involved, existing researches usually transform the problem into single-objective optimization problems via weighted-sum approach. In order to better assist the decision-making on facility locations, we will propose a multi-objective optimization approach to simultaneously consider multiple objectives including minimizing the transportation cost before and after intentional attacks happen. Multi-objective evolutionary algorithm will be developed to deal with the complexity of the proposed problem. The application of the proposed approach can help the decision maker better understand the trade-off between multiple objectives, based on which Pareto optimal facility location decision can be made. This would guarantee the ability of facilities serving the economic development and social well-being of modern societies even when intentional attacks happen.

基础设施的损坏将严重影响现代社会的经济发展和人们的生活。为有效应对其面临的蓄意攻击风险，本课题拟研究考虑攻防博弈的基础设施选址问题。在研究已设立设施面临的攻防博弈时，现有的方法通常假设攻击者可以获取关于保护策略的完备信息，而采用领导者-跟随者博弈模型。本研究拟采用同时博弈模型，以考虑保护者采取保密策略，使攻击者行动前无法获取关于保护策略的信息的情景，并给出寻找混合策略纳什均衡的方法。对于拟设立设施，在选址决策阶段考虑攻防博弈的研究还很不足。而且，在涉及多个目标时，现有的研究大多通过加权和等方法将问题转化为单目标优化问题。为了更好地服务于选址决策，本研究将给出多目标优化模型，同时考虑包括故障发生前后的运输成本在内的多个目标，并给出求解算法。本课题的应用将能够使决策者更深入地理解各目标之间的关系，制定考虑攻防博弈的帕累托最优设施选址方案，使其即使在蓄意攻击发生时，依然能够有效地提供服务。

邮局、医院、消防站等设施对现代社会的经济发展和人民的幸福具有举足轻重的作用，因而被视为基础设施。然而，这些基础设施正遭受越发频繁的蓄意攻击的威胁。为了有效保障基础设施的安全，本项目研究了综合考虑攻防博弈的基础设施选址问题。在研究攻防博弈时，信息公开策略是需要考虑的一个重要因素。现有的研究通常假定保护者采取公开策略，即将关于保护策略的所有信息全部公开。与已有文献不同，本项目重点研究了保护者将关于保护策略的信息保密时的攻防博弈，并比较了其相对于公开策略的优势。.我们首先在设施选址方案给定（即，假定设施位置已确定）的条件下，建立了保护者与攻击者之间的同时博弈模型，以研究保护者采取保密策略的效果。为了应对该同时博弈模型求解的复杂性，我们首先提出了最优攻击策略和最优保护策略寻找的方法。接着，我们基于对已有算法的改进设计了能够高效求解所提出的同时博弈模型的混合策略纳什均衡解的算法。.在此基础上，我们创新性地建立了多目标优化模型用于求解能够同时最小化设施建设成本、故障发生前的总运输成本以及蓄意攻击可能带来的期望损失三个目标的帕累托最优设施选址方案。其中，蓄意攻击可能带来的期望损失由同时博弈模型的混合策略纳什均衡解所决定。本研究应用了多目标演化算法，MO-PSDA，以应对所提出的涉及同时博弈的多目标优化问题的复杂性并求解其帕累托最优解。采用本研究所提出的多目标优化方法，可以通过一次求解便获得一系列帕累托最优解。这样，决策者就能够通过分析多个帕累托最优解，充分理解各目标之间的关系，从而更好地平衡各目标，做出符合自己风险偏好的决策。同时，可以在系统设计阶段就考虑到未来可能发生的蓄意攻击及能够采取的保护策略，从而能够设计出具有蓄意攻击承受能力的设施系统。