Mạng nơ-ron hồi tiếp với sự hội tụ trong thời gian hữu hạn cho các bài toán lập trình hai mức hình chữ nhật lồi

Neural Computing and Applications - Tập 30 - Trang 3399-3408 - 2017
Jiqiang Feng1, Sitian Qin2, Fengli Shi2, Xiaoyue Zhao2
1Institute of Intelligent Computing Science, Shenzhen University, Shenzhen, People’s Republic of China
2Department of Mathematics, Harbin Institute of Technology, Weihai, People’s Republic of China

Tóm tắt

Trong bài báo này, một mạng nơ-ron hồi tiếp với một hàm kích hoạt có thể điều chỉnh mới được đề xuất để giải quyết một loại vấn đề lập trình hai mức hình chữ nhật lồi. Đã chứng minh rằng điểm cân bằng của mạng nơ-ron được đề xuất là ổn định theo nghĩa Lyapunov, và trạng thái của mạng nơ-ron đề xuất hội tụ tới một điểm cân bằng trong thời gian hữu hạn. So với các phương pháp liên quan đến động lực học nơ-ron hiện có, mạng nơ-ron được đề xuất trong bài báo này có khả năng giải quyết vấn đề lập trình hai mức hình chữ nhật lồi trong thời gian hữu hạn. Hơn nữa, thời gian hội tụ hữu hạn có thể được ước lượng định lượng. Cuối cùng, hai ví dụ số được trình bày để cho thấy tính hiệu quả của mạng nơ-ron hồi tiếp được đề xuất.

Từ khóa

#Mạng nơ-ron hồi tiếp #Lập trình hai mức #Động lực học nơ-ron #Thời gian hội tụ hữu hạn #Chứng minh ổn định Lyapunov

Tài liệu tham khảo

Aboussoror A, Adly S, Saissi FE (2016) Strong-weak nonlinear bilevel problems: existence of solutions in a sequential setting. Set-Valued Var Anal 1:1–20 Aiyoshi E, Shimizu K (1981) Hierarchical decentralized systems and its new solution by a barrier method. IEEE Trans Syst Man Cybern 11(6):444–449 Bard J (1998) Practical bilevel optimization: algorithm and applications. Kluwer, Dordrecht Bard JF (1988) Convex two-level optimization. Math Progr 40(1–3):15–27 Bard JF, Falk JE (1982) An explicit solution to the multi-level programming problem. Comput Oper Res 9(1):77–100 Bhat SP, Bernstein DS (2000) Finite-time stability of continuous autonomous systems. SIAM J Control Optim 38(3):751–766 Bracken J, McGill JT (1973) Mathematical programs with optimization problems in the constraints. Oper Res 21(1):37–44 Brotcorne L, Marcotte P, Savard G (2008) Bilevel programming: the montreal school. Infor 46(4):231–246 Calvete HI, Gale C (2011) On linear bilevel problems with multiple objectives at the lower level. Omega 39(1):33–40 Candler W, Townsley R (1982) A linear two-level programming problem. Comput Oper Res 9(1):59–76 Colson B, Marcotte P, Savard G (2005) A trust-region method for nonlinear bilevel programming: algorithm and computational experience. Comput Optim Appl 30(3):211–227 Colson B, Marcotte P, Savard G (2007) An overview of bilevel optimization. Ann Oper Res 153(1):235–256 Dempe S (2002) Foundation of bilevel programming. Kluwer, London Dempe S, Kue FM (2016) Solving discrete linear bilevel optimization problems using the optimal value reformulation. J Glob Optim 2016:1–23 Gao XB (2004) A novel neural network for nonlinear convex programming. IEEE Trans Neural Netw 15(3):613–621 Guo D, Zhang Y (2014) Li-function activated ZNN with finite-time convergence applied to redundant-manipulator kinematic control via time-varying Jacobian matrix pseudoinversion. Appl Soft Comput 24(2014):158–168 He X, Li C, Huang T, Li C (2014) Neural network for solving convex quadratic bilevel programming problems. Neural Netw 51:17–25 He X, Li C, Huang T, Li C, Huang J (2014) A recurrent neural network for solving bilevel linear programming problem. IEEE Trans Neural Netw Learn Syst 25(4):824–830 Lan KM, Wen UP, Shih HS, Lee ES (2007) A hybrid neural network approach to bilevel programming problems. Appl Math Lett 20(8):880–884 Li H, Fang L (2013) An efficient genetic algorithm for interval linear bilevel programming problems. In: 9th International conference on computational intelligence and security (CIS), 2013. pp 41–44 Li S, Li Y, Wang Z (2013) A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application. Neural Netw 39(1):27–39 Lv Y, Chen Z, Wan Z (2010) A neural network for solving a convex quadratic bilevel programming problem. J Comput Appl Math 234(2):505–511 Lv Y, Hu T, Wang G, Wan Z (2008) A neural network approach for solving nonlinear bilevel programming problem. Comput Math Appl 55(12):2823–2829 Miao P, Shen Y, Huang Y, Wang YW (2014) Solving time-varying quadratic programs based on finite-time Zhang neural networks and their application to robot tracking. Neural Comput Appl 26(3):693–703 Miao P, Shen Y, Xia X (2014) Finite time dual neural networks with a tunable activation function for solving quadratic programming problems and its application. Neurocomputing 143(16):80–89 Qin S, Le X, Wang J (2016) A neurodynamic optimization approach to bilevel quadratic programming. IEEE Trans Neural Netw Learn Syst 1–12 Qin S, Xue X (2015) A two-layer recurrent neural network for nonsmooth convex optimization problems. IEEE Trans Neural Netw Learn Syst 26(6):1149–1160 Qin S, Yang X, Xue X, Song J (2016) A one-layer recurrent neural network for pseudoconvex optimization problems with equality and inequality constraints. IEEE Trans Cybern 1–12 Qin S, Le X, Wang J (2015) A neurodynamic optimization approach to bilevel linear programming. Advances in neural networks - ISNN. Springer Qin S, Xue X (2009) Global exponential stability and global convergence in finite time of neural networks with discontinuous activations. Neural Process Lett 29(3):189–204 Qin S, Xue X, Wang P (2013) Global exponential stability of almost periodic solution of delayed neural networks with discontinuous activations. Inf Sci 220:367–378 Rastovic D (2008) Fractional fokkercplanck equations and artificial neural networks for stochastic control of tokamak. J Fusion Energy 27(3):182–187 Rastovic D (2009) Fuzzy scaling and stability of tokamaks. J Fusion Energy 28(1):101–106 Rastovic D (2012) Targeting and synchronization at tokamak with recurrent artificial neural networks. Neural Comput Appl 21(5):1065–1069 Shen Y, Huang Y (2012) Global finite-time stabilisation for a class of nonlinear systems. Int J Syst Sci 43(1):73–78 Shen Y, Xia X (2008) Semi-global finite-time observers for nonlinear systems. Automatica 44(12):3152–3156 Shih HS, Wen UP, Lee S, Lan KM, Hsiao HC (2004) A neural network approach to multiobjective and multilevel programming problems. Comput Math Appl 48(1–2):95–98 Sinha A, Malo P, Deb K, Korhonen P (2015) Solving bilevel multicriterion optimization problems with lower level decision uncertainty. IEEE Trans Evolut Comput 20(2):199–217 Ugranli F, Karatepe E, Nielsen AH (2016) Milp approach for bilevel transmission and reactive power planning considering wind curtailment. IEEE Trans Power Syst 32(1):652–661 Vicente L, Savard G, Júdice J (1994) Descent approaches for quadratic bilevel programming. J Optim Theory Appl 81(2):379–399 Wang M, Zhang R, Zhu X (2017) A bi-level programming approach to the decision problems in a vendor-buyer eco-friendly supply chain. Comput Ind Eng 105:299–312 Xiao L, Lu R (2015) Finite-time solution to nonlinear equation using recurrent neural dynamics with a specially-constructed activation function. Neurocomputing 151:246–251 Zhang G, Zhang G, Gao Y, Lu J (2011) Competitive strategic bidding optimization in electricity markets using bilevel programming and swarm technique. IEEE Trans Ind Electron 58(6):2138–2146