Journal of the Korean Society for Aeronautical & Space Sciences (한국항공우주학회지)

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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Optimal Weapon-Target Assignment of Multiple Dissimilar Closed-In Weapon Systems Using Mixed Integer Linear Programming

혼합정수선형계획법을 이용한 다수 이종 근접 방어 시스템의 최적 무장 할당

  • Received : 2019.06.03
  • Accepted : 2019.10.28
  • Published : 2019.11.01
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Abstract

In this paper, a Mixed Integer Linear Programming(MILP) approach for solving optimal Weapon-Target Assignment(WTA) problem of multiple dissimilar Closed-In Weapon Systems (CIWS) is proposed. Generally, WTA problems are formulated in nonlinear mixed integer optimization form, which often requires impractical exhaustive search to optimize. However, transforming the problem into a structured MILP problem enables global optimization with an acceptable computational load. The problem of interest considers defense against several threats approaching the asset from various directions, with different time of arrival. Moreover, we consider multiple dissimilar CIWSs defending the asset. We derive a MILP form of the given nonlinear WTA problem. The formulated MILP problem is implemented with a commercial optimizer, and the optimization result is proposed.

본 논문에서는 다수 이종 근접 방어 시스템(Closed-In Weapon System, CIWS)의 최적 무장 할당 문제를 제시하고, 이를 혼합정수선형계획법(Mixed Integer Linear Programming, MILP)으로 변형해 해결하는 기법을 제안한다. 일반적인 무장 할당 문제의 경우 다양한 경우의 수를 고려해야하기 때문에 계산 시간이 기하급수적으로 증가하는 경우가 잦다. 하지만 주어진 문제를 MILP와 같은 혼합정수 최적화 문제로 변형하면 준실시간 내에 전역 최적해를 찾을 수 있다. 본 논문에서는 다수 위협이 각각 다른 시점에 다른 방향에서 방어 자산을 공격하는 상황을 고려한다. 또한, 제원이 다른 다수 CIWS를 동시 운용하는 경우를 추가로 고려한다. 본 논문에서는 이와 같은 문제 상황을 비선형 혼합정수계획 문제로 정식화하고, 이를 MILP로 변형하는 기법을 제시하였다. 또한, 이를 상용 최적화 프로그램으로 구현해 최적화 성능을 검증하였다.

Keywords

References

  1. Jeon, I. S., Lee, J. I., and Tahk, M. J., "Impact-time-control guidance law for anti-ship missiles," IEEE Transaction on Control Systems Technology, Vol. 14, No. 2, March 2006, pp. 260-266. https://doi.org/10.1109/TCST.2005.863655
  2. Tahk, M. J., Shim, S. W., Hong, S. M., Lee, C. H., and Choi, H. L., "Impact time control based on time-to-go prediction for sea-skimming anti-ship missile," IEEE Transactions on Aerospace and Electronic Systems, Vol. 54, No. 4, August 2018, pp. 2043-2052. https://doi.org/10.1109/TAES.2018.2803538
  3. Rosenberger, J. M., et al, "The Generalized Weapon Target Assignment Problem," 10th International Command and Control Research and Technology Symposium, June 2005.
  4. Ma, F., Ni, M., Gao, B., and Yu. Z., "An Efficient Algorithm for the Weapon Target Assignment Problem," Proceeding of the 2015 IEEE International Conference on Information and Automation, August 2015, pp. 2093-2097.
  5. Xin, B., et al., "An Efficient Rule-Based Constructive Heuristic to Solve Dynamic Weapon Target Assignment Problem," IEEE Transactions on Systems, Man and Cybernetics - Part A: Systems and Humans, Vol. 41, No. 3, 2011, pp. 598-606. https://doi.org/10.1109/TSMCA.2010.2089511
  6. Leboucher, C., et al., "Optimal Weapon Target Assignment Based on an Geometric Approach," Proceedings of the 19th IFAC Symposium on Automatic Control in Aerospace, Vol. 46, Issue 19, 2013, pp. 341-346.
  7. Leboucher, C., et al., "Novel Evolutionary Game Based Multi-Objective Optimisation for Dynamic Weapon Target Assignment," Proceedings of the 19th IFAC World Congress, Vol. 47, Issue 3, 2014, pp. 3936-3941.
  8. Park, J. M., Roh, H., and Tahk, M. J., "Co-evolutionary Method For Dynamic Weapon- Target Assignment," Advances in Control and Optimization of Dynamic Systems, Hyderabad, India, February 2018.
  9. Mouton, H., Roodt, J., and le Roux, H., "Applying Reinforcement Learning to the Weapon Assignment Problem in Air Defence," Scientia Militaria, South African Journal of Military Studies, Vol. 39, No. 2, 2011, pp. 123-140.
  10. Ma, Y., and Chou, C., "Weapon Target Assignment Decision Based on Markov Decision Process in Air Defense," System Simulation and Scientific Computing, Vol. 327, 2012, pp. 353-360. https://doi.org/10.1007/978-3-642-34396-4_43
  11. Vielma, J. P., "Mixed Integer Linear Programming Formulation Techniques," SIAM Review, Vol. 57, No. 1, February 2015, pp. 3-57. https://doi.org/10.1137/130915303
  12. Wolsey, L. A., Nemhauser, G. L., Integer and Combinatorial Optimization, 1st Ed., John Wiley & Sons, New York, 1999.
  13. Richards, A., Schouwernaars, T., How, J. P., and Feron, E., "Spacecraft trajectory planning with avoidance constraints using mixed-integer linear programming," Journal of Guidance, Control, and Dynamics, Vol. 25, No. 4, 2002, pp. 755-764. https://doi.org/10.2514/2.4943
  14. Lee, D. R., and Yang, J. H., "A Study on the Allocation and Engagement Scheduling of Air Defense Missiles by Using Mixed Integer Programming," Korean Management Science Review, Vol. 32, No. 4, December 2015, pp. 109-133. https://doi.org/10.7737/KMSR.2015.32.4.109
  15. Roh, H., and Tahk, M. J., "Optimization of Closed-In Weapon System Target Assignment Using Mixed Integer Linear Programming," Proceeding of The Korean Society for Aeronautical and Space Sciences Spring Conference, April 2018, pp. 437-438.
  16. Gurobi Optimizer Reference Manual, Gurobi Optimization, LLC, http://www.gurobi.com, 2018.