Skip to main content

Real-time heuristic algorithms for the static weapon target assignment problem


The problem of targeting and engaging individual missiles (targets) with an arsenal of interceptors (weapons) is known as the weapon target assignment problem. Many optimal solution techniques are applied to solve problem variants having linear approximations of the objective function, and their final solutions rarely yield optimal solutions to the original problem. Herein, we propose a nonlinear branch and bound algorithm to solve the untransformed problem. We also develop two heuristics respectively based on a branch and bound algorithm and the optimal solution to the quiz problem, and we compare them to a well-embraced heuristic from the literature. We test the three heuristics to solve a set of 15 problem sizes and 20 instances for each size, comparing their performance with respect to solution quality and required computational effort. The heuristic based upon the optimal solution to the quiz problem finds solutions within \(6\%\) of optimal for small problems and provides statistically similar results as one of the best heuristics found in the literature for larger problems, while solving these problems in ten thousandths of the time.

This is a preview of subscription content, access via your institution.

Fig. 1


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

  • Ahuja, R.K., Kumar, A., Jha, K.C., Orlin, J.B.: Exact and heuristic algorithms for the weapon-target assignment problem. Oper. Res. 55(6), 1136–1146 (2007)

    MathSciNet  Article  MATH  Google Scholar 

  • Barr, R., Golden, B., Kelly, J., Resende, M., Stewart, W.: Designing and reporting on computational experiments with heuristic methods. J. Heuristics 1(1), 9–32 (1995)

    Article  MATH  Google Scholar 

  • Bertsekas, D.P., Castañon, D.A.: Rollout algorithms for stochastic scheduling problems. J. Heuristics 5(1), 89–108 (1999)

    Article  MATH  Google Scholar 

  • Castañon, D.: Advanced weapon-target assignment algorithm quarterly report. Tr-337, ALPHA TECH Inc., Burlington, MA (1987)

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

  • Day, R.H.: Allocating weapons to target complexes by means of nonlinear programming. Oper. Res. 14(6), 992–1013 (1966)

    Article  Google Scholar 

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

    MathSciNet  Article  Google Scholar 

  • Flood, M.: Target-assignment model. In: Proceedings of the Princeton University Conference on Linear Programming. Princeton, NJ (1957)

  • Hongtao, L., Fengju, K.: Adaptive chaos parallel clonal selection algorithm for objective optimization in WTA application. Opt. Int. J. Light Electron Opt. 127(6), 3459–3465 (2016)

    Article  Google Scholar 

  • Hosein, P.A.: A class of dynamic nonlinear resource allocation problems. Tech. rep, Massachusetts Inst Of Tech Cambridge Lab For Information And Decision Systems (1989)

  • Johansson, F., Falkman, G.: An empirical investigation of the static weapon-target allocation problem. In: Proceedings of the 3rd Skövde Workshop on Information Fusion Topics (SWIFT2009). Sweden (2009)

  • Leboucher, C., Shin, H.S., Siarry, P., Chelouah, R., Le Ménec, S., Tsourdos, A.: A two-step optimisation method for dynamic weapon target assignment problem. In: Recent Advances on Meta-Heuristics and Their Application to Real Scenarios. InTech (2013)

  • Lee, Z.J., Lee, C.Y., Su, S.F.: An immunity-based ant colony optimization algorithm for solving weapon-target assignment problem. Appl. Soft Comput. 2(1), 39–47 (2002)

    Article  Google Scholar 

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

  • Ma, F., Ni, M., Gao, B., Yu, Z.: An efficient algorithm for the weapon target assignment problem. In: 2015 IEEE International Conference on Information and Automation, pp. 2093–2097. IEEE (2015)

  • Manne, A.S.: A target-assignment problem. Oper. Res. 6(3), 346–351 (1958)

    MathSciNet  Article  Google Scholar 

  • Matlin, S.: A review of the literature on the missile-allocation problem. Oper. Res. 18(2), 334–373 (1970)

    Article  Google Scholar 

  • Rosenberger, J.M., Hwang, H.S., Pallerla, R.P., Yucel, A., Wilson, R.L., Brungardt, E.G.: The generalized weapon target assignment problem. Tech. rep, DTIC Document (2005)

  • Shi-Jin, W., Bing-Hai, Z., Li-Feng, X.: A filtered-beam-search-based heuristic algorithm for flexible job-shop scheduling problem. Int. J. Prod. Res. 46(11), 3027–3058 (2008)

    Article  MATH  Google Scholar 

  • Sonuc, E., Sen, B., Bayir, S.: A parallel simulated annealing algorithm for weapon-target assignment problem. Int. J. Adv. Comput. Sci. Appl. (2017). (to appear in print)

  • Wacholder, E.: A neural network-based optimization algorithm for the static weapon-target assignment problem. ORSA J. Comput. 1(4), 232–246 (1989)

    Article  MATH  Google Scholar 

  • Walkup, D.W., MacLaren, M.D.: A multiple-assignment problem. Tech. rep, DTIC Document (1964)

  • Zhou, Y., Li, X., Zhu, Y., Wang, W.: A discrete particle swarm optimization algorithm applied in constrained static weapon-target assignment problem. In: 2016 12th World Congress on Intelligent Control and Automation (WCICA), pp. 3118–3123. IEEE (2016)

Download references


The authors gratefully thank the Editor-in-Chief and two reviewers for their constructive comments that greatly improved the presentation of this paper.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Darryl K. Ahner.

Additional information

The views expressed in this paper are those of the authors and do not reflect the official policy or position of the United States Army, the United States Air Force, the Department of Defense, or the United States Government.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kline, A.G., Ahner, D.K. & Lunday, B.J. Real-time heuristic algorithms for the static weapon target assignment problem. J Heuristics 25, 377–397 (2019).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Convex programming
  • Branch and bound
  • Global optimization
  • Quiz problem
  • Weapon target assignment problem