Entry optimization using mixed integer linear programming

详细信息    查看全文

• 作者：Seungmin Baek ; Sungwon Moon ; H. Jin Kim
• 关键词：Decision making ; game theory ; military operation ; MILP (mixed integer linear programming) ; resource allocation
• 刊名：International Journal of Control, Automation and Systems
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：14
• 期：1
• 页码：282-290
• 全文大小：610 KB
• 参考文献：[1]A. K. Dixit, and B. J. Nalebuff, Think Strategically, Norton, 1993.
  [2]P. R. Thie, and G. E. Keough, An Introduction to Linear Programming and Game Theory, 2nd ed. Wiley, New York, 2008. [click]CrossRef MATH
  [3]O. G. Haywood, “Military decision and game theory,” Journal of the Operations Research Society of America, vol. 2, pp. 365–385, 1954. [click]CrossRef
  [4]F. Austin, et al., “Game theory for automated maneuvering during air-to-air combat,” Journal of Guidance, vol. 13, pp. 1143–1149, 1990. [click]CrossRef MATH
  [5]J. B. Cruz, et al., “Game-theoretic modeling and control of a military air operation,” IEEE Transactions on Aerospace and Electronic Systems, vol. 37, no. 4, pp. 1393–1404, 2001. [click]CrossRef MathSciNet
  [6]J. B. Cruz, et al., “Moving horizon nash strategies for a military air operation,” IEEE Transactions on Aerospace and Electronic Systems, vol. 38, no. 3, pp. 989–997, 2002. [click]CrossRef MathSciNet
  [7]D. Ghose, J. L. Speyer, and J. S. Shamma, “A game theoretical multiple resource interaction approach to resource allocation in an air campaign,” Annals of Operations Research, vol. 109, pp. 15–40, 2002. [click]CrossRef MathSciNet MATH
  [8]P. S. Sheeba, and D. Ghose, “A resource based game theoretical model for military conflicts,” DRDO-IISc Programme on Advanced Research in Mathematical Engineering, 2005.
  [9]A. Bemporad and M. Moran, “Control of systems integrating logic, dynamics, and constraints,” Automatica, vol. 35, pp. 407–427 1999. [click]CrossRef MATH
  [10]J. C. Smith, and Z. C. Taskin, A tutorial guide to mixedinteger programming models and solution techniques, University of Florida, 2007.
  [11]B. J. Griggs, G. S. Parnell, and L. J. Lehmkuhl, “An air mission planning algorithm using decision analysis and mixed integer programming,” Operations Research, vol. 45, pp. 662–676, 1997. [click]CrossRef MATH
  [12]G. Brown, et al., “A two-sided optimization for theater ballistic missile defense,” Operations Research, vol. 53, pp. 745–763, 2005. [click]CrossRef MathSciNet MATH
  [13]C. C. Murray and M. H. Karwan, “An extensible modeling framework for dynamic reassignment and rerouting in cooperative airborne operations,” Naval Research Logistics, vol. 57, 6 pp. 34–652, 2010. [click]MathSciNet
  [14]J. A. Sundali, et al., “Coordination in market entry games with symmetric players,” Organizational Behavior and Human Decision Processes, vol. 64, no. 2, pp. 203–218, 1995. [click]CrossRef
  [15]A. Rapoprt, et al., “Equilibrium play in large group market entry games,” Management Science, vol. 44, no. 1, pp. 119–141, 1998. [click]CrossRef
  [16]J. Duffy and E. Hopkins, “Learning, information, and sorting in merket entry games: theory and evidence,” Games and economic behavior, vol. 51, no. 1, pp. 31–62, 2005. [click]CrossRef MathSciNet MATH
  [17]P. Lichocki, et al., “Evolving Team Compositions by Agent Swapping,” IEEE Transactions on Evolutionary Computation, vol. 17, no. 2, pp. 282–298, 2013. [click]CrossRef
  [18]M. Waibel, L. Keller, and F. Floreano, “Genetic Team Composition and Level of Selection in the Evolution of Cooperation,” IEEE Transactions on Evolutionary Computation, vol. 13, no. 3, pp. 648–660, 2009. [click]CrossRef
  [19]T. Basarand G. J. Olsder, Dynamic noncooperative game theory, Academic, London, 1982. [click]
  [20]P. K. Dutta, Strategies and games: theory and practice, The MIT Press, 1999.
  [21]J. S. Shamma, Cooperative control of distributed multiagent systems, John Wiley & Sons, 2007. [click]CrossRef
  [22]L. A. Wolsey, Integer programming, Wiley, New York, 1998.MATH
  [23]I. Ravid, “Military decision, game theory and intelligence: An anecdote,” Operations Research, vol. 38, no. 2, pp. 260–264, 1990 [click].CrossRef
  
• 作者单位：Seungmin Baek (1)
  Sungwon Moon (1)
  H. Jin Kim (1)
  
  1. School of Mechanical and Aerospace Engineering and Institute of Advanced Aerospace Technology, Seoul National University, Seoul, 151-742, Korea
  
• 刊物类别：Engineering
• 刊物主题：Control Engineering
  
• 出版者：The Institute of Control, Robotics and Systems Engineers and The Korean Institute of Electrical Engi
• ISSN：2005-4092

文摘

An appropriate selection of agents to participate in a confrontation such as a game or combat depends on the types of the opposing team. This paper investigates the problem of determining a combination of agents to fight in a combat between two forces. When the types of enemy agents committed to the combat are not known, game theory provides the best response to the opponent. The entry game is solved by using mixed integer linear programming (MILP) to consider the constraints on resources in a game theoretic approach. Simulations for the examples involving three different sets of military forces are performed using an optimization tool, which demonstrates that the optimal entry is properly selected corresponding to the opposing force. Keywords Decision making game theory military operation MILP (mixed integer linear programming) resource allocation