DOI QR코드

DOI QR Code

New Mathematical Model and Parallel Hybrid Genetic Algorithm for the Optimal Assignment of Strike packages to Targets

공격편대군-표적 최적 할당을 위한 수리모형 및 병렬 하이브리드 유전자 알고리즘

  • Kim, Heungseob (Department of Systems Engineering, Republic of Korea Air Force Academy) ;
  • Cho, Yongnam (Department of Systems Engineering, Republic of Korea Air Force Academy)
  • 김흥섭 (공군사관학교 시스템공학과) ;
  • 조용남 (공군사관학교 시스템공학과)
  • Received : 2017.01.20
  • Accepted : 2017.06.16
  • Published : 2017.08.05

Abstract

For optimizing the operation plan when strike packages attack multiple targets, this article suggests a new mathematical model and a parallel hybrid genetic algorithm (PHGA) as a solution methodology. In the model, a package can assault multiple targets on a sortie and permitted the use of mixed munitions for a target. Furthermore, because the survival probability of a package depends on a flight route, it is formulated as a mixed integer programming which is synthesized the models for vehicle routing and weapon-target assignment. The hybrid strategy of the solution method (PHGA) is also implemented by the separation of functions of a GA and an exact solution method using ILOG CPLEX. The GA searches the flight routes of packages, and CPLEX assigns the munitions of a package to the targets on its way. The parallelism enhances the likelihood seeking the optimal solution via the collaboration among the HGAs.

Keywords

References

  1. A. S. Manne, “A Target-Assignment Problem,” Operations Research, Vol. 6, No. 3, pp. 346-351, 1958. https://doi.org/10.1287/opre.6.3.346
  2. B. J. Griggs, "An Air Mission Planning Algorithm for a Theater Level Combat Model," M.S. Thesis, Graduate School of Engineering, Air Force Institue of Technology, 1994.
  3. D. R. Castro, "Optimization Models for Allocation of Air Strike Assets with Persistence," M.S. Thesis, Naval Postgraduate School, 2002.
  4. D. R. Lee and J. Yang, "The Optimal Allocation of Aircrafts to Targets by Using Mixed Integer Programming", Korean Management Science Review, Vol. 25, No. 1, pp. 55-74, 2008.
  5. 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, No. 5, pp. 662-676, 1997. https://doi.org/10.1287/opre.45.5.662
  6. J. J. Heo and C. Y. Kim, “A Study of Optimal Aircraft Allocation Model for Attacking Fixed Target,” Military Operations Research Society Of Korea, Vol. 12, No. 2, pp. 22-36, 1986.
  7. B. J. Jeong and C. Y. Kim, “Aircraft Allocation Model : Application of the Goal Programming,” Military Operations Research Society Of Korea, Vol. 20, No. 1, pp. 49-79, 1994.
  8. V. C. Li, G. L. Curry and E. A. Boyd, “Towards the Real Time Solution of Strike Force Asset Allocation Problems,” Computers & Operations Research, Vol. 31, No. 2, pp. 273-291, 2004. https://doi.org/10.1016/S0305-0548(02)00192-2
  9. J. M. Rosenberger, H. S. Hwang, R. P. Pallerla, A. Yucel, R. L. Wilson and E. G. Brungardt, "The Generalized Weapon Target Assignment Problem," 10th International Command and Control Research and Technology Symposium, McLean, VA, June 13-16, 2005.
  10. M. Ash, “Flood's Assignment Model for Small Kill Levels,” Operations Research, Vol. 7, No. 2, pp. 258-260, 1959. https://doi.org/10.1287/opre.7.2.258
  11. R. H. Day, “Allocating Weapons to Target Complexes by Means of Nonlinear Programming,” Operations Research, Vol. 14, No. 6, pp. 992-1013, 1966. https://doi.org/10.1287/opre.14.6.992
  12. Y. Owechko and S. Shams, "Comparison of Neural Network and Genetic Algorithms for a Resource Allocation Problem", IEEE World Congress on Computational Intelligence, Vol. 7, pp. 4655-4660, 1994.
  13. J. D. Katter, "A Solution of the Multi-Weapon, Mult-Target Assignment Problem," Working Paper 26957, MITRE, McLean, VA.
  14. S. C. Chang, R. M. James and J. J. Shaw, "Assignment Algorithm for Kinetic Energy Weapons in Boost Defense," In Proceedings of IEEE 26th Conference Decision and Control, Los Angeles, CA, pp. 1678-1683, 1987.
  15. D. Orlin, “Optimal Weapons Allocation against Layered Defenses,” Naval Research Logistics, Vol. 34, No. 5, pp. 605-616, 1987. https://doi.org/10.1002/1520-6750(198710)34:5<605::AID-NAV3220340502>3.0.CO;2-L
  16. J. Lee and M. Shin, “Stochastic Weapon Target Assignment Problem under Uncertainty in Targeting Accuracy,” Journal of Korea Operations Research and Management Science, Vol. 41, No. 3, pp. 23-36, 2016. https://doi.org/10.7737/JKORMS.2016.41.3.023
  17. O. Kwon, D. Kang, K. Lee and S. Park, “Lagrangian Relaxation Approach to the Targeting Problem,” Naval Research Logistics, Vol. 46, No. 6, pp. 640-653, 1999. https://doi.org/10.1002/(SICI)1520-6750(199909)46:6<640::AID-NAV3>3.0.CO;2-Q
  18. D. Ahner and C. Parson, "Weapon Tradeoff Analysis using Dynamic Programming for a Dynamic Weapon Target Assignment Problem Within a Simulation," Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, pp. 2831-2841, 2013.
  19. C. R. Parson, "Approximate Dynamic Programming for Military Resource Allocation," Ph.D. Thesis, Air Force Institute of Technology, 2014.
  20. R. K. Ahuja, A. Kumar, K. C. Jha and J. B. Orlin, “Exact and Heuristic Algorithms for the Weapon-Target Assignment Problem,” Operations Research, Vol. 55, No. 6, pp. 1136-1146, 2007. https://doi.org/10.1287/opre.1070.0440
  21. Z. J. Lee, S. F. Su and C. Y. Lee, “A Genetic Algorithm with Domain Knowledge for Weapon-Target Assignment Problems,” Journal of the Chinese Institute of Engineers, Vol. 25, No. 3, pp. 287-295, 2002. https://doi.org/10.1080/02533839.2002.9670703
  22. Z. J. Lee, S. F. Su and C. Y. Lee, “Efficiently Solving General Weapon-Target Assignment Problem by Genetic Algorithms with Greedy Eugenics,” IEEE Transactions on Systems, Man, and Cybernetics, Part B(Cybernetics), Vol. 33, No. 1, pp. 113-121, 2003. https://doi.org/10.1109/TSMCB.2003.808174
  23. H. Lu, H. Zhang, X. Zhang and R. Han, "An Improved Genetic Algorithm for Target Assignment, Optimization of Naval Fleet Air Defense," 6th World Congress on Intelligent Control and Automation, Vol. 1, pp. 3401-3405, 2006.
  24. P. Li, W. Ling and F. Lu, "A Mutation-Based GA for Weapon-Target Allocation Problem Subject to Spatial Constraints," International Workshop on Intelligent Systems and Applications, pp. 1-4, 2009.
  25. L. Jinjun, C. Rong and X. Jiguangt, “Dynamic WTA Optimization Model of Air Defense Operation of Warships' Formation,” Journal of Systems Engineering and Electronics, Vol. 17, No. 1, pp. 126-131, 2006. https://doi.org/10.1016/S1004-4132(06)60023-6
  26. Z. J. Lee, C. Y. Lee and S. F. Su, “An Immunity-Based Ant Colony Optimization Algorithm for Solving Weapon-Target Assignment Problem,” Applied Soft Computing, Vol. 2, No. 1, pp. 39-47, 2002. https://doi.org/10.1016/S1568-4946(02)00027-3
  27. Y. Wang, L. Qian, Z. Guo and L. Ma, “Weapon Target Assignment Problem Satisfying Expected Damage Probabilities based on ant Colony Algorithm,” Systems Engineering & Electronics, Vol. 19, No. 5, pp. 939-944, 2008. https://doi.org/10.1016/S1004-4132(08)60179-6
  28. A. Tokgoz and S. Bulkan, “Weapon Target Assignment with Combinatorial Optimization Techniques,” International Journal of Advanced Research in Artificial Intelligence, Vol. 2, No. 7, pp. 39-50, 2013.
  29. H. Naeem and A. Masood, “An Optimal Dynamic Threat Evaluation and Weapon Scheduling Technique,” Knowledge-Based Systems, Vol. 23, No. 4, pp. 337-342, 2010. https://doi.org/10.1016/j.knosys.2009.11.012
  30. G. Shang, Z. Zaiyue, Z. Xiaoru and C. Cungen, "Immune Genetic Algorithm for Weapon-Target Assignment Problem," Workshop on Intelligent Information Technology Application(IITA 2007), 2007.
  31. Z. Song, F. Zhu and D. Zhang, "A Heuristic Genetic Algorithm for Solving Constrained Weapon-Target Assignment Problem," IEEE International Conference on Intelligent Computing and Intelligent Systems, Vol. 1, pp. 336-341, 2009.
  32. D. L. Luo, C. L. Shen, B. Wang and W. H. Wu, "Air Combat Decision-Making for Cooperative Multiple Target Attack using Heuristic Adaptive Genetic Algorithm," International Conference on Machine Learning and Cybernetics, Vol. 1, pp. 473-478, 2005.
  33. P. Toth and D. Vigo, "Vehicle Routing: Problems, Methods, and Applications(Vol. 18)," Siam, Philadelphia, 2014.
  34. I. Karaoglan, F. Altiparmak, I. Kara and B. Dengiz, “The Location-Routing Problem with Simultaneous Pickup and Delivery: Formulations and a Heuristic Approach,” Omega, Vol. 40, No. 4, pp. 465-477, 2012. https://doi.org/10.1016/j.omega.2011.09.002
  35. K. T. Kim and G. W. Jeon, “Hybrid Parallel Genetic Algorithm for Traveling Salesman Problem,” Journal of Korea Safety Management & Science, Vol. 13, No. 3, pp. 107-114, 2011.
  36. Z. H. Ahmed, “An Experimental Study of a Hybrid Genetic Algorithm for the Maximum Traveling Salesman Problem,” Mathematical Sciences, Vol. 7, No. 1, pp. 7-10, 2013. https://doi.org/10.1186/2251-7456-7-7
  37. A. R. V. da Silva and L. S. Ochi, “An Efficient Hybrid Algorithm for the Traveling Car Renter Problem,” Expert Systems with Applications, Vol. 64, No. 1, pp. 132-140, 2016. https://doi.org/10.1016/j.eswa.2016.07.038
  38. S. Gulcu, M. Mahi, O. K. Baykan and H. Kodaz, "A Parallel Cooperative Hybrid Method based on ant Colony Optimization and 3-Opt Algorithm for Solving Traveling Salesman Problem," Soft Computing, pp. 1-17, 2016.
  39. Y. Wang, "The Hybrid Genetic Algorithm with Two Local Optimization Strategies for Traveling Salesman Problem," Computers & Industrial Engineering, Vol. 70, pp. 124-133, 2014. https://doi.org/10.1016/j.cie.2014.01.015
  40. B. Lin, X. Sun and S. Salous, "Solving Travelling Salesman Problem with an Improved Hybrid Genetic Algorithm," Journal of Computer and Communications, Vol. 4, pp. 98-106, 2016.
  41. H. Kim, “Optimization Methodology for Determining the Locations of Logistics Support Units and Supply Line,” Journal of the Korean Society of Supply Chain Management, Vol. 16, No. 2, pp. 35-45, 2016.
  42. S, Yuan, B. Skinner, S. Huang and D. Liu, “A New Crossover Approach for Solving the Multiple Travelling Salesmen Problem using Genetic Algorithms,” European Journal of Operational Research, Vol. 228, No. 1, pp. 72-82, 2013. https://doi.org/10.1016/j.ejor.2013.01.043