考虑信息隐藏策略的反恐应急设施选址模型
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摘要
恐怖袭击常以人流密集地区的平民对象作为袭击目标,极易造成严重后果.通过反恐应急设施的合理布局可以缩短救援时间并降低袭击损失.在设施选址过程中,政府还可通过选址信息的隐藏来获取信息优势,误导恐怖分子的袭击策略并改善效用.首先,对考虑信息隐藏策略的反恐应急设施选址问题进行描述,结合随机选择模型刻画恐怖分子的有限理性行为,并将该问题构建为一类双层规划模型;随后,针对模型分别设计精确解算法和遗传算法,并结合喀什地区交通网络进行仿真分析.结果发现:恐怖分子理性程度已知时,相比于选址信息的完全公开,隐藏部分信息后更有利于降低政府损失,信息隐藏的最优数量与恐怖分子理性程度相关;恐怖分子理性程度未知时,在其理性程度被低估的情形下,选址信息隐藏策略更能发挥作用.
As terrorists have a strong preference in attacking civilians in densely populated areas, terrorist attacks can easily cause serious consequences. In order to improve the rescue efficiency and reduce the loss of attacks, the State can locate emergency facilities in the transportation network. Since the one with information advantage is usually dominant in the game, the State can also mislead terrorist's actions and improve her utility by hiding some location information. First, we describe the research problem and address it to a bi-level programming model in which terrorists' bounded rational behaviors are depicted according to the random selection theory. Second, both exact solution method and genetic algorithm are proposed, and they are applied in a real-world case study of Kashi area. The result shows that: when the State is able to calculate the rationality of terrorists, compared with disclosing all location information,hiding some information is more beneficial for reducing the expected loss, and the degree of information hiding is highly related to the rationality of terrorists. Conversely, when the State isn't able to calculate the rationality of terrorists, the information hiding strategy always plays a more effective role in the case that the terrorist's rationality is underestimated.
As terrorists have a strong preference in attacking civilians in densely populated areas, terrorist attacks can easily cause serious consequences. In order to improve the rescue efficiency and reduce the loss of attacks, the State can locate emergency facilities in the transportation network. Since the one with information advantage is usually dominant in the game, the State can also mislead terrorist's actions and improve her utility by hiding some location information. First, we describe the research problem and address it to a bi-level programming model in which terrorists' bounded rational behaviors are depicted according to the random selection theory. Second, both exact solution method and genetic algorithm are proposed, and they are applied in a real-world case study of Kashi area. The result shows that: when the State is able to calculate the rationality of terrorists, compared with disclosing all location information,hiding some information is more beneficial for reducing the expected loss, and the degree of information hiding is highly related to the rationality of terrorists. Conversely, when the State isn't able to calculate the rationality of terrorists, the information hiding strategy always plays a more effective role in the case that the terrorist's rationality is underestimated.
引文
[1]刘霞,韩自,金仕根.国际恐怖活动的新特征及其发展趋势[J].中国软科学,2015, 11:1-10.Liu X, Han Z, Jin S G. New features and developing trend of international terrorism[J]. China Soft Science, 2015,11:1—10.
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[4] Labbe M, Ponce D, Puerto J. A comparative study of formulations and solution methods for the discrete ordered p-median problem[J]. Computers&Operations Research, 2017, 78:230-242.
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[7] Lu C C. Robust weighted vertex p-center model considering uncertain data:An application to emergency management[J]. European Journal of Operational Research, 2013, 230(1):113—121.
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[11]叶艳妹,张晓滨,林琼,等.基于加权集覆盖模型的农村居民点空间布局优化—以流泗镇为例[J].经济地理,2017,37(5):140-148.Ye Y M, Zhang X B, Lin Q, et al. A weighted set covering problem model for optimal spatial layout of rural settlements—A case of Liusi Town[J]. Economic Geography, 2017, 37(5):140-148.
[12]李双琳,马祖军,郑斌,等.震后初期应急物资配送的模糊多目标选址-多式联运问题[J].中国管理科学,2013, 21(2):144-151.Li S L, Ma Z J, Zheng B, et al. Fuzzy multi-objective location-multimodal transportation problem for relief delivery during the initial post-earthquake period[J]. Chinese Journal of Management Science, 2013, 21(2):144-151.
[13] Zarrinpoor N, Fallahnezhad M S, Pishvaee M S. Design of a reliable hierarchical location-allocation model under disruptions for health service networks:A two-stage robust approach[J]. Computers&Industrial Engineering,2017, 109:130-150.
[14] Wang H, Du L, Ma S. Multi-objective open location-routing model with split delivery for optimized relief distribution in post-earthquake[J]. Transportation Research Part E, 2014, 69(3):160-179.
[15]王海军,杜丽敬,马士华.震后应急物流系统中双目标开放式选址-路径问题模型与算法研究[J].管理工程学报,2016,30(2):108-115.Wang H J, Du L J, Ma S H. Model and algorithms for integrated open location and routing problem in emergency logistics under earthquake[J]. Journal of Industrial Engineering and Engineering Management, 2016, 30(2):108-115.
[16] Berman O, Gavious A. Location of terror response facilities:A game between state and terrorist[J]. European Journal of Operational Research, 2007, 177(2):1113-1133.
[17]韩传峰,孟令鹏,张超,等.基于完全信息动态博弈的反恐设施选址模型[J].系统工程理论与实践,2012, 32(2):366-372.Han C F, Meng L P, Zhang C, et al. Location of terror response facilities based on dynamic game of complete information[J]. Systems Engineering—Theory&Practice, 2012, 32(2):366-372.
[18]柴瑞瑞,孙康,陈静锋,等.连续恐怖袭击下反恐设施选址与资源调度优化模型及其应用[J].系统工程理论与实践,2016,36(2):464-472.Chai R R, Sun K, Chen J F, et al. Optimization model and application of anti-terrorist facilities location and resource scheduling under continuous terrorist attack[J]. Systems Engineering—Theory&Practice, 2016, 36(2):464-472.
[19] Meng L P, Kang Q, Han C F, et al. Determining the optimal location of terror response facilities under the risk of disruption[J]. IEEE Transactions on Intelligent Transportation System, 2017, 99:1—11.
[20] Simon H A. A behavioral model of rational choice[J]. The Quarterly Journal of Economics, 1955, 69(1):99-118.
[21]牟博佼,李岩,朱岩.基于有限理性假设的运营管理研究现状及发展趋势[J].清华大学学报(自然科学版),2012, 52(2):253-259.Mu B J, Li Y, Zhu Y. Current status and development trends in operations management using bounded rationality[J]. Journal of Tsinghua University(Science and Technology), 2012, 52(2):253-259.
[22]李睿.非对称信息博弈论与经济管理方法[J].情报理论与实践,1999, 22(3):148-149.Li R. Asymmetric information game theory and economic management method[J]. Information Studies:Theory&Application, 1999, 22(3):148-149.
[23] Zhuang J, Alagoz O. Modeling secrecy and deception in a multiple-period attacker-defender signaling game[J].European Journal of Operational Research, 2010, 203(2):409-418.
[24] Zhuang J, Bier V M. Secrecy and deception at equilibrium, with applications to anti-terrorism resource allocation[J]. Defence&Peace Economics, 2011, 22(1):43-61.
[25] Chen H C, Friedman J W, Thisse J F. Boundedly rational Nash equilibrium:A probabilistic choice approach[J].Games&Economic Behavior, 1997, 18(1):32-54.
[26] Espejo I, Marinb A. Closest assignment constraints in discrete location problems[J]. European Journal of Operational Research, 2012, 219(1):49-58.
[2]赵国军.“东突”恐怖活动常态化及其治理[J].国际展望,2015, 7(1):104-117.
[3] Hakimi S L. Optimum locations of switching centers and the absolute centers and medians of a graph[J]. Operations Research, 1964, 12(3):450-459.
[4] Labbe M, Ponce D, Puerto J. A comparative study of formulations and solution methods for the discrete ordered p-median problem[J]. Computers&Operations Research, 2017, 78:230-242.
[5] Karatas M, Yakici E. An analysis of p-median location problem:Effects of backup service level and demand assignment policy[J]. European Journal of Operational Research, 2018, 271(2):178-189.
[6] Hakimi S L. Optimum distribution of switching centers in a communication network and some related graph theoretic problems[J]. Operations Research, 1965, 13(3):462-475.
[7] Lu C C. Robust weighted vertex p-center model considering uncertain data:An application to emergency management[J]. European Journal of Operational Research, 2013, 230(1):113—121.
[8] Merino L M, Sambola M A, Chia A M. The probabilistic p-center problem:Planning service for potential customers[J]. European Journal of Operational Research, 2017, 262(2):509-520.
[9] Araz C, Selim H, Ozkarahan I. A fuzzy multi-objective covering-based vehicle location model for emergency services[J]. Computers&Operations Research, 2007, 34(3):705-726.
[10]陈志宗,关贤军.灾害应急反应的枢纽集覆盖模型及枢纽最大覆盖模型[J].运筹与管理,2016,25(5):15-20.Chen Z Z, Guan X J. Hub set-covering model and hub maximal coverage model for disaster emergency response[J].Operations Research and Management Science, 2016, 25(5):15-22.
[11]叶艳妹,张晓滨,林琼,等.基于加权集覆盖模型的农村居民点空间布局优化—以流泗镇为例[J].经济地理,2017,37(5):140-148.Ye Y M, Zhang X B, Lin Q, et al. A weighted set covering problem model for optimal spatial layout of rural settlements—A case of Liusi Town[J]. Economic Geography, 2017, 37(5):140-148.
[12]李双琳,马祖军,郑斌,等.震后初期应急物资配送的模糊多目标选址-多式联运问题[J].中国管理科学,2013, 21(2):144-151.Li S L, Ma Z J, Zheng B, et al. Fuzzy multi-objective location-multimodal transportation problem for relief delivery during the initial post-earthquake period[J]. Chinese Journal of Management Science, 2013, 21(2):144-151.
[13] Zarrinpoor N, Fallahnezhad M S, Pishvaee M S. Design of a reliable hierarchical location-allocation model under disruptions for health service networks:A two-stage robust approach[J]. Computers&Industrial Engineering,2017, 109:130-150.
[14] Wang H, Du L, Ma S. Multi-objective open location-routing model with split delivery for optimized relief distribution in post-earthquake[J]. Transportation Research Part E, 2014, 69(3):160-179.
[15]王海军,杜丽敬,马士华.震后应急物流系统中双目标开放式选址-路径问题模型与算法研究[J].管理工程学报,2016,30(2):108-115.Wang H J, Du L J, Ma S H. Model and algorithms for integrated open location and routing problem in emergency logistics under earthquake[J]. Journal of Industrial Engineering and Engineering Management, 2016, 30(2):108-115.
[16] Berman O, Gavious A. Location of terror response facilities:A game between state and terrorist[J]. European Journal of Operational Research, 2007, 177(2):1113-1133.
[17]韩传峰,孟令鹏,张超,等.基于完全信息动态博弈的反恐设施选址模型[J].系统工程理论与实践,2012, 32(2):366-372.Han C F, Meng L P, Zhang C, et al. Location of terror response facilities based on dynamic game of complete information[J]. Systems Engineering—Theory&Practice, 2012, 32(2):366-372.
[18]柴瑞瑞,孙康,陈静锋,等.连续恐怖袭击下反恐设施选址与资源调度优化模型及其应用[J].系统工程理论与实践,2016,36(2):464-472.Chai R R, Sun K, Chen J F, et al. Optimization model and application of anti-terrorist facilities location and resource scheduling under continuous terrorist attack[J]. Systems Engineering—Theory&Practice, 2016, 36(2):464-472.
[19] Meng L P, Kang Q, Han C F, et al. Determining the optimal location of terror response facilities under the risk of disruption[J]. IEEE Transactions on Intelligent Transportation System, 2017, 99:1—11.
[20] Simon H A. A behavioral model of rational choice[J]. The Quarterly Journal of Economics, 1955, 69(1):99-118.
[21]牟博佼,李岩,朱岩.基于有限理性假设的运营管理研究现状及发展趋势[J].清华大学学报(自然科学版),2012, 52(2):253-259.Mu B J, Li Y, Zhu Y. Current status and development trends in operations management using bounded rationality[J]. Journal of Tsinghua University(Science and Technology), 2012, 52(2):253-259.
[22]李睿.非对称信息博弈论与经济管理方法[J].情报理论与实践,1999, 22(3):148-149.Li R. Asymmetric information game theory and economic management method[J]. Information Studies:Theory&Application, 1999, 22(3):148-149.
[23] Zhuang J, Alagoz O. Modeling secrecy and deception in a multiple-period attacker-defender signaling game[J].European Journal of Operational Research, 2010, 203(2):409-418.
[24] Zhuang J, Bier V M. Secrecy and deception at equilibrium, with applications to anti-terrorism resource allocation[J]. Defence&Peace Economics, 2011, 22(1):43-61.
[25] Chen H C, Friedman J W, Thisse J F. Boundedly rational Nash equilibrium:A probabilistic choice approach[J].Games&Economic Behavior, 1997, 18(1):32-54.
[26] Espejo I, Marinb A. Closest assignment constraints in discrete location problems[J]. European Journal of Operational Research, 2012, 219(1):49-58.