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Optimal multi-stage allocation of weapons to targets using adaptive dynamic programming

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Abstract

We consider the optimal allocation of resources (weapons) to a collection of tasks (targets) with the objective of maximizing the reward for completing tasks (destroying targets). Tasks arrive in two stages, where the first stage tasks are known and the second stage task arrivals follow a random distribution. Given the distribution of these second stage task arrivals, simulation and mathematical programming are used within a dynamic programming framework to determine optimal allocation strategies. The special structure of the assignment problem is exploited to recursively update functional approximations representing future rewards using subgradient information. Through several theorems, optimality of the algorithm is proven for a two-stage Dynamic Weapon-Target Assignment Problem.

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References

  1. Ahner, D.K.: Planning and control of unmanned aerial vehicles in a stochastic environment. Doctor of Philosophy dissertation, Boston University (2005)

  2. Bertsekas, D.P.: Dynamic programming and optimal control, vol. 1. Athena Scientific (2012)

  3. Castanon, D.: Advanced weapon-target assignment algorithm quarterly report. Tr-337, ALPHA TECH Inc., Burlington, Massachusetts (1987)

  4. Chang, S., James, R., Shaw, J.: Assignment algorithm for kinetic energy weapons in boost phase defence. In: Decision and Control, 1987. 26th IEEE Conference on, vol. 26, pp. 1678–1683. IEEE (1987)

  5. Chen, J., Xin, B., Peng, Z., Dou, L., Zhang, J.: Evolutionary decision-makings for the dynamic weapon-target assignment problem. Sci China Ser F Inf Sci 52(11), 2006–2018 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. denBroeder Jr, G.G., Ellison, R.E., Emerling, L.: On optimum target assignments. Oper Res 7(3), 322–326 (1959)

    Article  MathSciNet  Google Scholar 

  7. Godfrey, G., Powell, W.: An adaptive dynamic programming algorithm for dynamic fleet management, i: single period travel times. Transp Sci 36(1), 21–39 (2002)

    Article  MATH  Google Scholar 

  8. Godfrey, G.A., Powell, W.B.: An adaptive, distribution-free algorithm for the newsvendor problem with censored demands, with applications to inventory and distribution. Manag Sci 47(8), 1101–1112 (2001)

    Article  MATH  Google Scholar 

  9. Hosein, P.A., Athans, M.: Some analytical results for the dynamic weapon-target allocation problem. Tech. rep., DTIC Document (1990)

  10. Hosein P.A., W.J., Athans, M.: Dynamic weapon-target assignment problems with vulnerable c2ì\(^3\) nodes (1988)

  11. Khosla, D.: Hybrid genetic approach for the dynamic weapon-target allocation problem. In: Proceedings of SPIE, vol. 4396, pp. 248–263. SHE (2001)

  12. Leboucher, C., Shin, H.S., Siarry, P., Chelouah, R., Le Ménec, S., Tsourdos, A.: Recent advances on meta-heuristics and their applications to real scenarios, chap. A two-step optimisation method for dynamic weapon target assignment problem, InTech (2013)

  13. Lloyd, S., Witsenhausen, H.: Weapons allocation is np-complete. In: 1986 Summer Computer Simulation Conference, pp. 1054–1058 (1986)

  14. Murphey, R.: Approximation and Complexity in Numerical Optimization Continuous and Discrete Problems, vol. 42, chap. An approximate algorithm for a weapon assignment stochastic program. Kluwer Academic (2000)

  15. Murphey, R.A.: An approximate algorithm for a weapon target assignment stochastic program. Nonconvex Optim Appl 42, 406–421 (2000)

    Article  MathSciNet  Google Scholar 

  16. Murphey, R.A.: Target-based weapon target assignment problems. In: Nonlinear Assignment Problems, pp. 39–53. Springer (2000)

  17. Orlin, D.: Optimal weapons allocation against layered defenses. Naval Res Logist (NRL) 34(5), 605–617 (1987)

    Article  Google Scholar 

  18. Powell, W.: Approximate Dynamic Programming: Solving the Curses of Dimensionality, vol. 703. Wiley (2007)

  19. Sikanen, T.: Solving weapon target assignment problem with dynamic programming. Tech. rep., Tech. Rep. 55670 A TFY. N Available: http://www.sal.tkkfi/Opinnot/Mat-2.108/pdf-files/esik08b.pdf. (2008)

  20. Soland, R.M.: Optimal terminal defense tactics when several sequential engagements are possible. Oper Res 35(4), 537–542 (1987)

    Article  Google Scholar 

  21. Wu, L., Wang, H., Lu, F., Jia, P.: An anytime algorithm based on modified ga for dynamic weapon-target allocation problem. In: Evolutionary Computation, 2008. CEC 2008. (IEEE World Congress on Computational Intelligence). IEEE Congress on, pp. 2020–2025. IEEE (2008)

  22. Xin, B., Chen, J., Peng, Z., Dou, L., Zhang, J.: An efficient rule-based constructive heuristic to solve dynamic weapon-target assignment problem. Syst Man Cybern Part A Syst Hum IEEE Trans 41(3), 598–606 (2011)

    Article  Google Scholar 

  23. Xin, B., Chen, J., Zhang, J., Dou, L., Peng, Z.: Efficient decision makings for dynamic weapon-target assignment by virtual permutation and tabu search heuristics. Syst Man Cybern Part C Appl Rev IEEE Trans 40(6), 649–662 (2010)

    Article  Google Scholar 

  24. Yanxia, W., Longjun, Q., Zhi, G., Lifeng, M.: Weapon target assignment problem satisfying expected damage probabilities based on ant colony algorithm. J Syst Eng Electron 19(5), 939–944 (2008)

    Article  MATH  Google Scholar 

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Acknowledgments

The authors would like to acknowledge the referees for the comments and suggestions which improved the clarity and presentation of the work contained herein.

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Authors and Affiliations

  1. Department of Operational Sciences, Center for Operational Analysis, Air Force Institute of Technology, Dayton, USA

    Darryl K. Ahner & Carl R. Parson

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  1. Darryl K. Ahner
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Correspondence to Carl R. Parson.

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Ahner, D.K., Parson, C.R. Optimal multi-stage allocation of weapons to targets using adaptive dynamic programming. Optim Lett 9, 1689–1701 (2015). https://doi.org/10.1007/s11590-014-0823-x

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  • DOI: https://doi.org/10.1007/s11590-014-0823-x

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