یک مدل شبکه عصبی بازگشتی برای حل مدل CCR در تحلیل پوششی داده ها

Subject Areas : Data Envelopment Analysis

معصومه عباسی ¹ (گروه ریاضی، واحد کرمانشاه، دانشگاه آزاد اسلامی، کرمانشاه، ایران)
عباس قماشی ² (گروه ریاضی، واحد کرمانشاه، دانشگاه آزاد اسلامی، کرمانشاه، ایران)

Received: 2017-11-20 Accepted : 2018-04-24 Published : 2019-06-01

Keywords: شبکه عصبی بازگشتی-روش گرادیان-تحلیل پوششی داده ها-CCR-پایداری-همگرای عمومی,

Abstract :

در این مقاله ما یک شبکه عصبی برای حل مدل CCR در تحلیل پوششی داده ها (DEA) معرفی می کنیم. مدل شبکه عصبی پیشنهادی از یک مسئله مینیمم سازی نامقید حاصل می شود. از دیدگاه تئوری، نشان داده می شود که شبکه عصبی پیشنهادی به مفهوم لیاپانف پایدار و همگرای عمومی به جواب بهینه مدل CCR می باشد. مدل پیشنهادی ساختار تک لایه دارد. با یک مثال عددی موثر بودن مدل پیشنهادی برای حل مدل CCR در DEA نشان داده می شود.

References:

Charnes, A., Cooper, W. W., & Rhodes, E. (1979). Measuring the efficiency of decision-making units. European journal of operational research, 3(4), 339.

 Hu, X. (2009). Applications of the general projection neural network in solving extended linear-quadratic programming problems with linear constraints. Neurocomputing, 72 (4), 1131-1137.

 Hu, X., Zhang, B. (2009). A New Recurrent Neural Network for Solving Convex Quadratic Programming Problems with an Application to the-Winners-Take-All Problem. Neural Networks, IEEE Transactions on, 20(4), 654-664.

 Kennedy, M. P., Chua, L. O. (1988). Neural networks for nonlinear programming. Circuits and Systems, IEEE Transactions on, 35(5), 554-562.

Kinderlehrer, D., & Stampacchia, G. (1980). An introduction to variational inequalities and their applications (Vol. 31). Siam.

 Liu, Q., Wang, J. (2013). A one-layer projection neural network for nonsmooth optimization subject to linear equalities and bound constraints. Neural Networks and Learning Systems, IEEE Transactions on, 24(5), 812-824.

 Maa, C. Y., Shanblatt, M. A. (1992). Linear and quadratic programming neural network analysis. Neural Networks, IEEE Transactions on, 3(4), 580-594.

Miller, R. K., & Michel, A. N. (1982). Ordinary differential equations. Academic Press.

Nazemi, A. (2014). A neural network model for solving convex quadratic programming problems with some applications. Engineering Applications of Artificial Intelligence, 32, 54-62.

 Nazemi, A., Nazemi, M. (2014). A Gradient-Based Neural Network Method for Solving Strictly Convex Quadratic Programming Problems. Cognitive Computation. 1-12.

Ortega, J. M., & Rheinboldt, W. C. (1970). Iterative solution of nonlinear equations in several variables (Vol. 30). Siam.

 Rodriguez-Vazquez, A., Dominguez-Castro, R., Rueda, A., Huertas, J. L., Sanchez-Sinencio, E. (1990). Nonlinear switched capacitor neural networks for optimization problems.Circuits and Systems, IEEE Transactions on, 37(3), 384-398.

 Tank, D., Hopfield, J. J. (1986). Simple ’neural’ optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit. Circuits and Systems, IEEE Transactions on, 33(5), 533-541.

 Wu, X. Y., Xia, Y. S., Li, J., Chen, W. K. (1996). A high-performance neural network for solving linear and quadratic programming problems. Neural Networks, IEEE Transactions on, 7(3), 643-651.

 Xia, Y. (1996). A new neural network for solving linear and quadratic programming problems. Neural Networks, IEEE Transactions on, 7(6), 1544-1548.

 Xia, Y. (2009). A Compact Cooperative Recurrent Neural Network for Computing General Constrained Norm Estimators. Signal Processing, IEEE Transactions on, 57(9),3693-3697.

 Xia, Y. S., Wang, J. (2000a). On the stability of globally projected dynamical systems. Journal of Optimization Theory and Applications, 106(1), 129-150.

 Xia, Y., & Wang, J. (2016). A bi-projection neural network for solving constrained quadratic optimization problems. IEEE transactions on neural networks and learning systems, 27(2), 214-224.

 Xia, Y., Feng, G., Wang, J. (2004). A recurrent neural network with exponential convergence for solving convex quadratic program and related linear piecewise equations. Neural Networks, 17(7), 1003-1015.

 Xia, Y., Feng, G., Wang, J. (2008). A novel recurrent neural network for solving nonlinear optimization problems with inequality constraints. Neural Networks, IEEE Transactions on, 19(8), 1340-1353.

Xia, Y., Leung, H. (2014). A Fast Learning Algorithm for Blind Data Fusion Using a Novel-Norm Estimation. Sensors Journal, IEEE, 14(3), 666-672.

Xia, Y., Leung, H., Wang, J. (2002). A projection neural network and its application to constrained optimization problems. Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on, 49(4), 447-458.

 Xia, Y., Sun, C., Zheng, W. X. (2012). Discrete-time neural network for fast solving large linear estimation problems and its application to image restoration. Neural Networks and Learning Systems, IEEE Transactions on, 23(5), 812-820.

Xia, Y., Wang, J. (1998). A general methodology for designing globally convergent optimization neural networks. Neural Networks, IEEE Transactions on, 9(6), 1331-1343.

Xia, Y., Wang, J. (2000b). A recurrent neural network for solving linear projection equations. Neural Networks, 13(3), 337-350.

 Xia, Y., Wang, J. (2000c). Global exponential stability of recurrent neural networks for solving optimization and related problems. Neural Networks, IEEE Transactions on,11(4), 1017-1022.

 Xia, Y., Wang, J. (2004). A general projection neural network for solving monotone variational inequalities and related optimization problems. Neural Networks, IEEE Transactions on, 15(2), 318-328.

 Xia, Y., Wang, J. (2005). A recurrent neural network for solving nonlinear convex programs subject to linear constraints. Neural Networks, IEEE Transactions on, 16(2),379-386.

 Xue X, Bian W. (2007). A project neural network for solving degenerate convex quadratic program. Neurocomputing.70:244959. 46.

Yan, Y. (2014). A New Nonlinear Neural Network for Solving QP Problems. In Advances in Neural Networks ISNN 2014 (pp. 347-357). Springer International Publishing.

Yang Y, Cao J. (2008). A feedback neural network for solving convex constraint optimization problems. Appl Math Comput. 201: 34050. 47.

Yang, Y., Cao, J., Xu, X., Hu, M., & Gao, Y. (2014). A new neural network for solving quadratic programming problems with equality and inequality constraints. Mathematics and Computers in Simulation, 101, 103-112.

Zhang, J., & Zhang, L. (2010). An augmented Lagrangian method for a class of inverse quadratic programming problems. Applied Mathematics and Optimization, 61(1), 57.