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Tri-level mixed-binary linear programming: Solution approaches and application in defending critical infrastructure
European Journal of Operational Research ( IF 6.4 ) Pub Date : 2021-07-24 , DOI: 10.1016/j.ejor.2021.07.034
Ramy Fakhry 1 , Elkafi Hassini 1 , Mohamed Ezzeldin 2 , Wael El-Dakhakhni 2
Affiliation  

Decentralized decision-making is becoming more ubiquitous in different organizations that often follow a hierarchical structure. To model these problems, multi-level programming has been suggested as a suitable methodology for modeling the interaction between the different levels of decisions. However, multi-level programming, even for the case of bi-levels, is known to be strongly NP-hard. To address this computational challenge, we develop three different heuristic-based approaches for solving a specific class of tri-level programming problems, in which the leader has direct control over the follower’s decisions to a certain extent, with a common objective function shared at all levels. As expected, each heuristic type offers a trade-off between solution quality and computational time. To illustrate our solution approach, we present an application for defending critical infrastructure to improve its resilience against intentional attacks. In this context we use a defender-attacker-defender model and apply it to electrical power grids. We also propose a modified implementation of a widely adopted enumeration algorithm in this area, with a warm-starting solution technique that significantly enhanced the computational performance of the enumeration algorithm. We test our solution approaches on three electrical transmission networks and present the results of our numerical computations as well as some insights.



中文翻译:

三级混合二元线性规划:关键基础设施防御的解决方法和应用

在通常遵循等级结构的不同组织中,分散的决策变得越来越普遍。为了对这些问题建模,已建议将多级编程作为对不同决策级别之间的交互进行建模的合适方法。然而,众所周知,即使对于双层的情况,多级编程也具有很强的N-难的。为了解决这个计算挑战,我们开发了三种不同的基于启发式的方法来解决特定类别的三级编程问题,其中领导者在一定程度上直接控制追随者的决策,并共享一个共同的目标函数水平。正如预期的那样,每种启发式类型都提供了解决方案质量和计算时间之间的权衡。为了说明我们的解决方案,我们展示了一个用于保护关键基础设施的应用程序,以提高其抵御蓄意攻击的弹性。在这种情况下,我们使用防御者-攻击者-防御者模型并将其应用于电网。我们还提出了该领域广泛采用的枚举算法的改进实现,采用热启动求解技术,显着增强了枚举算法的计算性能。我们在三个输电网络上测试了我们的解决方案,并展示了我们的数值计算结果以及一些见解。

更新日期:2021-07-24
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