Stackelberg博弈下海盗活动地区海军护航选择优化
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摘要
为了优化海军在海盗活动区域的护航选择决策,更好地保护过往船舶,维护海上运输安全,在对实际护航行动涉及的海军与海盗两方主体博弈关系分析的基础上,建立了一个包括海军和海盗双方在内的非合作非零和Stackelberg博弈对双方行为进行描述,并选取双层规划模型将博弈关系进行数学转换.针对该双层规划模型的特点,采用基于灵敏度分析的启发式算法(SAB)对反应函数具体形式进行计算,并进行模型求解算法设计.最后,以索马里海盗活动区域为例进行实例分析,得出海军继续选择亚丁湾进行护航,海盗活动区域将向红海转移的结果,结果也说明了模型与算法的合理性.
To optimize the zone selection of naval escort for enhancing maritime security in pirates active areas. Firstly, the decision behaviors of the naval force and pirates in such areas are systematically analyzed.Secondly, a non- cooperative non- zero sum Stackelberg game is developed. The game builds the interactive relationships among the naval force and a pirate, which also can be described as a bi-level programming model. In order to solve this model, a heuristic algorithm called SAB is designed. Finally, the Somali pirates are taken as an example to implement the calculation. The results show that the best selection of naval escort zone is still the Gulf of Aden, while the pirates will be more willing to choose the Red sea area. The results also prove the rationality of models and the algorithm.
To optimize the zone selection of naval escort for enhancing maritime security in pirates active areas. Firstly, the decision behaviors of the naval force and pirates in such areas are systematically analyzed.Secondly, a non- cooperative non- zero sum Stackelberg game is developed. The game builds the interactive relationships among the naval force and a pirate, which also can be described as a bi-level programming model. In order to solve this model, a heuristic algorithm called SAB is designed. Finally, the Somali pirates are taken as an example to implement the calculation. The results show that the best selection of naval escort zone is still the Gulf of Aden, while the pirates will be more willing to choose the Red sea area. The results also prove the rationality of models and the algorithm.
引文
[1]Anja Shortland,Marc Vothknecht.Combating"maritime terrorism"off the coast of Somalia[J].European Journal of Political Economy,2011,27:133-151.
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[3]陈钢铁,帅斌.非合作下危险物品运输网络的双层模型及博弈研究[J].兰州交通大学学报,2011,30(3):71-74.[CHEN G T,SHUAI B.Bi-level network model and game of non-cooperation dangerous goods transport[J].Journal of Lanzhou Jiaotong University,2011,30(3):71-74.]
[4]Allison Reilly,Linda Nozick,Ningxiong Xu,et al.Game theory-based identification of facility use restrictions for the movement of hazardous materials under terrorist threat[J].Transportation Research Part E,2012,48:115-131.
[5]黄松,杨超,杨珺.基于Stackelberg博弈的变质物品分销网络设计模型[J].中国管理科学,2009,17(6):122-129.[HUANG S,YANG C,YANG J.Distribution network design model for deteriorating items based on stackelberg game[J].Chinese Journal of Management Science.2009;17(6):122-129.]
[6]李昌兵,杜茂康,付德强.求解双层规划问题的层次混沌量子遗传算法[J].系统工程学报,2013,28(2):159-166.[LI C B,DU M K,FU D Q.Hierarchical chaotic quantum-inspired genetic algorithm solving bi-level programming problem[J].Journal of Systems Engineering,2013,28(2):159-166.]
[7]曹守华,袁振洲,李艳红,等.交通流诱导条件下的路网随机平衡双层规划模型[J].交通运输系统工程与信息,2007,7(4):36-42.[CAO S H,YUAN Z Z,LI YH,et al.A Model for road network stochastic user equilibrium based on bilevel programming under the action of traffic flow guidance system[J],Journal of Transportation Systems Engineering and Information Technology,2007,7(4):36-42.]
[8]Juan Carlos Sevillano,David Rios Insua,Jesus Rios.Adversarial risk analysis the Somali pirates ease[J].Decision Analysis,2012,06:1-10.
[2]Brishti Guha,Ashok S Guha.Pirates and traders:Some economics of pirate-infested seas[J].Economics Letters,2011,111:147-158.
[3]陈钢铁,帅斌.非合作下危险物品运输网络的双层模型及博弈研究[J].兰州交通大学学报,2011,30(3):71-74.[CHEN G T,SHUAI B.Bi-level network model and game of non-cooperation dangerous goods transport[J].Journal of Lanzhou Jiaotong University,2011,30(3):71-74.]
[4]Allison Reilly,Linda Nozick,Ningxiong Xu,et al.Game theory-based identification of facility use restrictions for the movement of hazardous materials under terrorist threat[J].Transportation Research Part E,2012,48:115-131.
[5]黄松,杨超,杨珺.基于Stackelberg博弈的变质物品分销网络设计模型[J].中国管理科学,2009,17(6):122-129.[HUANG S,YANG C,YANG J.Distribution network design model for deteriorating items based on stackelberg game[J].Chinese Journal of Management Science.2009;17(6):122-129.]
[6]李昌兵,杜茂康,付德强.求解双层规划问题的层次混沌量子遗传算法[J].系统工程学报,2013,28(2):159-166.[LI C B,DU M K,FU D Q.Hierarchical chaotic quantum-inspired genetic algorithm solving bi-level programming problem[J].Journal of Systems Engineering,2013,28(2):159-166.]
[7]曹守华,袁振洲,李艳红,等.交通流诱导条件下的路网随机平衡双层规划模型[J].交通运输系统工程与信息,2007,7(4):36-42.[CAO S H,YUAN Z Z,LI YH,et al.A Model for road network stochastic user equilibrium based on bilevel programming under the action of traffic flow guidance system[J],Journal of Transportation Systems Engineering and Information Technology,2007,7(4):36-42.]
[8]Juan Carlos Sevillano,David Rios Insua,Jesus Rios.Adversarial risk analysis the Somali pirates ease[J].Decision Analysis,2012,06:1-10.