A two‐stage network interdiction‐monitoring game

IF 1.6 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Networks Pub Date : 2022-12-04 DOI:10.1002/net.22136

D. Nguyen, Yongjia Song, J. Smith

{"title":"A two‐stage network interdiction‐monitoring game","authors":"D. Nguyen, Yongjia Song, J. Smith","doi":"10.1002/net.22136","DOIUrl":null,"url":null,"abstract":"We study a network interdiction problem involving two agents: a defender and an evader. The evader seeks to traverse a path from a source node to a terminus node in a directed network without being detected. The game takes place in two stages. In the first stage, the defender removes a set of arcs in the network. In the second stage, the defender and evader play a simultaneous game. The defender monitors a set of arcs, thus increasing the probability that the evader will be detected on that arc (if the evader uses the arc). The evader selects a source‐terminus path. Because the second stage is played simultaneously, both agents use mixed‐strategy solutions. We approach the solution of the second‐stage problem by proposing a constraint‐and‐column generation algorithm. We show that both the constraint‐generation and column‐generation problems are NP‐hard. Accordingly, we prescribe approximate versions of these problems that can be solved more efficiently. Our algorithm relies on solving the approximate versions until it is necessary to obtain an exact solution of the constraint‐generation and column‐generation problems. Then, to link the first‐ and second‐stage problems, we model the original problem using an epigraph reformulation, which we solve using a Benders‐decomposition based approach. The efficacy of our approach is demonstrated on a set of randomly generated test instances.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"81 1","pages":"334 - 358"},"PeriodicalIF":1.6000,"publicationDate":"2022-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Networks","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1002/net.22136","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, HARDWARE & ARCHITECTURE","Score":null,"Total":0}

引用次数: 0

Abstract

We study a network interdiction problem involving two agents: a defender and an evader. The evader seeks to traverse a path from a source node to a terminus node in a directed network without being detected. The game takes place in two stages. In the first stage, the defender removes a set of arcs in the network. In the second stage, the defender and evader play a simultaneous game. The defender monitors a set of arcs, thus increasing the probability that the evader will be detected on that arc (if the evader uses the arc). The evader selects a source‐terminus path. Because the second stage is played simultaneously, both agents use mixed‐strategy solutions. We approach the solution of the second‐stage problem by proposing a constraint‐and‐column generation algorithm. We show that both the constraint‐generation and column‐generation problems are NP‐hard. Accordingly, we prescribe approximate versions of these problems that can be solved more efficiently. Our algorithm relies on solving the approximate versions until it is necessary to obtain an exact solution of the constraint‐generation and column‐generation problems. Then, to link the first‐ and second‐stage problems, we model the original problem using an epigraph reformulation, which we solve using a Benders‐decomposition based approach. The efficacy of our approach is demonstrated on a set of randomly generated test instances.

查看原文本刊更多论文

两阶段网络拦截监控游戏

我们研究了一个涉及两个特工的网络拦截问题：一个是防御者，另一个是逃避者。逃避者试图在没有被检测到的情况下穿越定向网络中从源节点到终端节点的路径。比赛分两个阶段进行。在第一阶段，防守队员移除网络中的一组弧线。在第二阶段，防守队员和躲避队员同时进行比赛。防御者监视一组弧线，从而增加在该弧线上检测到躲避者的概率（如果躲避者使用该弧线）。躲避者选择一条源-终点路径。因为第二阶段是同时进行的，所以两个代理都使用混合策略解决方案。我们通过提出一种约束和列生成算法来解决第二阶段问题。我们证明了约束生成和列生成问题都是NP难问题。因此，我们规定了可以更有效地解决这些问题的近似版本。我们的算法依赖于求解近似版本，直到有必要获得约束生成和列生成问题的精确解。然后，为了将第一阶段和第二阶段的问题联系起来，我们使用题词重新表述对原始问题进行建模，并使用基于Benders分解的方法进行求解。我们的方法的有效性在一组随机生成的测试实例上得到了证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Networks 工程技术-计算机：硬件

CiteScore

4.40

自引率

9.50%

发文量

审稿时长

12 months

期刊介绍： Network problems are pervasive in our modern technological society, as witnessed by our reliance on physical networks that provide power, communication, and transportation. As well, a number of processes can be modeled using logical networks, as in the scheduling of interdependent tasks, the dating of archaeological artifacts, or the compilation of subroutines comprising a large computer program. Networks provide a common framework for posing and studying problems that often have wider applicability than their originating context. The goal of this journal is to provide a central forum for the distribution of timely information about network problems, their design and mathematical analysis, as well as efficient algorithms for carrying out optimization on networks. The nonstandard modeling of diverse processes using networks and network concepts is also of interest. Consequently, the disciplines that are useful in studying networks are varied, including applied mathematics, operations research, computer science, discrete mathematics, and economics. Networks publishes material on the analytic modeling of problems using networks, the mathematical analysis of network problems, the design of computationally eﬃcient network algorithms, and innovative case studies of successful network applications. We do not typically publish works that fall in the realm of pure graph theory (without signiﬁcant algorithmic and modeling contributions) or papers that deal with engineering aspects of network design. Since the audience for this journal is then necessarily broad, articles that impact multiple application areas or that creatively use new or existing methodologies are especially appropriate. We seek to publish original, well-written research papers that make a substantive contribution to the knowledge base. In addition, tutorial and survey articles are welcomed. All manuscripts are carefully refereed.