A performance comparison of utility functions for game theory based weapon-target assignment

Year 2024, Volume: 66 Issue: 1, 45 - 63, 14.06.2024

Oguzkan Akbel Aykut Kalaycıoğlu

https://doi.org/10.33769/aupse.1301383

Abstract

The weapon-target assignment problem has been considered as an essential issue for military applications to provide a protection for defended assets. The goal of a typical weapon-target assignment problem is to maximize the expected survivability of the valuable assets. In this study, defense of naval vessels that encounter aerial targets is considered. The vessels are assumed to have different types of weapons having various firepower and cost as well as the incoming targets may have different attack capabilities. In a typical scenario, in addition to protecting assets, it is also desirable to minimize the cost of weapons. Therefore, an asset-based static weapon-target assignment problem is considered in order to both maximize the expected survivability of the assets and minimize the weapon budget. Thus, a co-operative game theory based solution is proposed which relates the utilities of the individuals to the global utility and reach the Nash equilibrium.

Keywords

Game, weapon, assignment, optimization, utility

References

• Roux, J. and Vuuren, H. V., Threat evalution and weapon assignment decision Support: A review of the state of art, Orion, 23 (2) (2007), 151-187, https://doi.org/10.5784/232-54.
• Lötter, D. and Vuuren, J. V., Weapon assignment decision support in a surface based air defence environment, (2013), https://www.vuuren.co.za/papers/MORSPaper.pdf.
• Arslan, G., Marden, J. R. and Shamma, J. S., Autonomous vehicle-target assignment: A game-therotical formulation, Trans. ASME,129 (2007), 584-596.
• Kline, A., Ahner, D. and Hill, R., The weapon-target assignment problem, Comput. Oper. Res., pp., 5 (2019), 226-236, https://doi.org/10.1016/j.cor.2018.10.015.
• Shi, Y., Xing, Y., Mou, C. and Kuang, Z., An optimization model based on game theory, J. Multimed., 9 (4) (2014) 583-589, https://doi.org/10.4304/jmm.9.4.583-589.
• Karasakal, O., Air defense missile-target allocation models for a naval task group, Comput. Oper. Res., 35 (2008), 1759-1770, https://doi.org/10.1016/j.cor.2006.09.011.
• Li, X, Zhou, D., Pan, Q., Tang Y. and Huang, J., Weapon-target asignment problem by multiobjective evolutionary algorithm based on decomposition, Complexity, 2018 (2018), 1-19, https://doi.org/10.1155/2018/8623051.
• Aplak, H. S. and Türkbey, O., Fuzzy logic based game theory applications in multi criteria decision making process, J. Intell. Fuzzy Syst., 25 (2) (2013), 359-371.
• Taghavi, R. and Ranjbar, M., Weapon scheduling in naval combat systems for maximization of defense capabilities, Iran. J. Op. Res., 6 (2) (2015), 87-99.
• Şahin, M. A. and Leblebicioğlu, K., Approximating the optimal mapping for weapon target assignment by fuzzy reasoning, Inf. Sci., 255( 2014), 30-44.
• Johansson, F. and Falkman, G., Real-time allocation of firing units to hostile targets, J. Adv. Inf. Fusion, 6 (2) (2011), 187-199.
• Paradis, S., Benaskeur, A. and Cutler, P., Threat evalution and weapon allocation in network-centric warefare, Proceedings of the Seventh International Conferance on Information Fusion, (2005).
• Ng, Y. K., Expected subjective utility: Is the neumann-morgenstern utility the same as neoclassical's?, Soc. Choice Welf., 1 (1984), 177-186.
• Monderer, D. and Shapley, L. S., Potential games, Games Econ. Behav., 14 (1996), 124-143, https://doi.org/10.1006/game.1996.0044.
• Roughtgarden, T., Algorithmic game theory, Communications of the ACM, 53 (7) (2010), 78-86.
• Yang, Y. and Wang, F. Y., Budget Constraints and Optimization in Sponsored Search Auctions, Academic Press, 2014.
• Wonnacott, W. M., Modelling In The Design and Analysis of a Hit-To-Kill Rocket Guidance Kit, Thesis, Monterey, California: Naval Postgraduate School, 1997.
• Washburn, A. R., Notes On Firing Theory, Naval Post Graduate School, Monterey, California, 2002.
• US. Defence Documentation Center, Scientific and Technical Information, Alexandria, Virginia, 1963.
• Glazebrook, K. and Washburn, A. R., Shoot-Look-Shoot: A review and extension, Op. Res., 6 (2004), 454-463. Chatterjee, B., An optimization formulation to compute Nash equilibrium in finite games, 2009 Proceeding of International Conference on Methods and Models in Computer Science, (2009), https://doi.org/10.1109/ICM2CS.2009.5397970.