Combat simulation using continuous time neural networks

Document Type : Original Article

Authors

1 PhD Student in Department of Mathematics, Faculty of Basic Sciences, Central Tehran Branch, Islamic Azad University, Tehran, Iran

2 Researcher in Institute for the Study of War, Army Command and Staff University,Tehran, Iran.

Abstract

This paper focuses on modeling the behavior of commanders in a combat simulation. A military mission is often associated with multiple conflicting goals, including task success, completion time, enemies’ elimination, and own forces survival. In this paper, considering defensive and non-defensive scenarios, and using multi-objective optimization, a model is presented in order to minimize own forces loss and to maximize enemies’ elimination. Also, based on the weighting method and the Karush-Kuhn-Tucker optimality conditions, a continuous time feedback neural network model is designed for solving the proposed multi-objective optimization problem. The main idea of the neural network approach for the proposed multi-objective optimization problem is to establish a dynamic system in the form of first order ordinary differential equations. The proposed neural network does not require any adjustable parameter and its structure enables a simple hardware implementation. The proposed method can act as a consultant for the commander who decides for its forces. Finally, the validity and efficiency of the proposed model are demonstrated by an example.

Keywords


  • Bazaraa, M. S., Sherali, H. D. & Shetty, C. M. (2005). Nonlinear Programming. John Wiley & Sons, Inc.
  • Boutselis, P. & Ringrose, T.J. (2013). GAMLSS and neural networks in combat simulation metamodelling: A case study. Expert Systems with Applications, 40(15): 6087-6093.
  • Bouzerdoum, A. & Pattison, T. R. (1993). Neural network for quadratic optimization with bound constraints. IEEE Transactions on Neural Networks, 4(2):  293–304.
  • Effati, S. & Moghaddas, M. (2016). A novel neural network based on NCP function for solving constrained nonconvex optimization problems. Complexity, 21(6):130–141.
  • Effati, S., Ghomashi, A., & Abbasi, M. (2011). A novel recurrent neural network for solving MLCPs and its application to linear and quadratic programming. Asia Pacific Journal of Operational Research, 28 (4): 523–541.
  • Gao, X. & Liao, L. Z. (2010). A new one-layer neural network for linear and quadratic programming. IEEE Transactions on Neural Networks, 21(6): 918–929.
  • Kennedy, M. & Chua, L. (1988). Neural networks for nonlinear programming. IEEE Transactions on Circuits and Systems, 35(5): 554–562.
  • Kilmer, R. A. (1996). Applications of artificial neural networks to combat simulations. Mathematical and Computer Modelling, 23(1–2): 91-99.
  • Law, A. & Kelton, W. (1991). Simulation Modeling and Analysis, McGraw-Hill, New York.
  • Maa, C. Y. & Shanblatt, M. A. (1992). A two-phase optimization neural network. IEEE Transactions on Neural Networks, 3(6):1003–1009.
  • Miller, R. & Michel, A. (1982). Ordinary Differential Equations. Academic Press, Inc.
  • Nazemi, A. & Effati, S. (2013). An application of a merit function for solving convex programming problems. Computers & Industrial Engineering, 66(2): 212–221.
  • Nazemi, A. (2012). A dynamic system model for solving convex nonlinear optimization problems. Communications in Nonlinear Science and Numerical Simulation, 17(4):1696-1705.
  • Oswalt, I. (1993). Current applications, trends, and organizations in the U.S. military simulation and gaming. Simulation and Gaming, 24(2):153-189.
  • Rodriguez-Vazquez, A., Dominguez-Castro, R., Rueda, A., Huertas, J., & Sanchez-Sinencio, E. (1990). Nonlinear switched capacitor ‘neural’ networks for optimization problems. IEEE Transactions on Circuits and Systems, 37(3): 384–398.
  • Sakawa, M‎.,) 1993. (Fuzzy Sets and Interactive Multiobjective Optimization. ‎Plenum Press‎, ‎New York and London‎‎.
  • Tank, D. & Hopfield, J.J. (1986). Simple ’neural’ optimization networks: An a/d converter, signal decision circuit, and a linear programming circuit. IEEE Transactions on Circuits and Systems, 33(5): 533–541.
  • Teng, T., Tan, A., Tan, Y., and Yeo, A. (2012). Self-organizing neural networks for learning air combat maneuvers, The 2012 International Joint Conference on Neural Networks (IJCNN), Brisbane, QLD, pp. 1-8.
  • Xia, Y. & Wang, J. (2004). A recurrent neural network for nonlinear convex optimization subject to nonlinear inequality constraints. IEEE Transactions on Circuits and Systems I: Regular Papers, 51(7): 1385–1394.
  • Xia, Y. & Wang, J. (2005). A recurrent neural network for solving nonlinear convex programs subject to linear constraints. IEEE Transactions on Neural Networks, 16(2): 379–386.
  • Xia, Y., Leung, H., and Wang, J. (2002). A projection neural network and its application to constrained optimization problems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 49(4), pp. 447–458.
  • Xue, Q. et al. (2010). Improved LMBP algorithm in the analysis and application of simulation data, International Conference on Computer Application and System Modeling (ICCASM 2010), Taiyuan, pp. 545–547.
  • Xue, X. & Bian, W. (2007). A project neural network for solving degenerate convex quadratic program. Neurocomputing, 70(13-15): 2449–2459.
  • Yu, P.L. (1973). A class of solutions for group decision problems. Management Science, 19: 936-946.

Zhang, S. & Constantinides, A. (1992). Lagrange programming neural networks. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 39(7): 441–452