A Recurrent Neural Network for Solving Bilevel Linear Programming Problem

In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems Vol. 25; no. 4; pp. 824 - 830
Main Authors: He, Xing, Li, Chuandong, Huang, Tingwen, Li, Chaojie, Huang, Junjian
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.04.2014
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Applied sciences
Artificial intelligence
Artificial neural networks
Bilevel linear programming problem (BLPP)
Computer science; control theory; systems
Computer Simulation
Connectionism. Neural networks
differential inclusions
Educational institutions
Exact sciences and technology
Feedback
Global analysis, analysis on manifolds
Inclusions
Learning
Linear programming
Logistics
Mathematical analysis
Mathematical models
Mathematics
Models, Theoretical
Neural networks
Neural Networks (Computer)
nonsmooth analysis
Operational research and scientific management
Operational research. Management science
Optimization
Ordinary differential equations
Pattern Recognition, Automated - methods
Programming profession
Programming, Linear
recurrent neural network (NN)
Recurrent neural networks
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Performance evaluation
Bilevel linear programming problem (BLPP)
Recurrence
Recurrent neural nets
Lyapunov method
Linear programming
Neural network
Modeling
Penalty method
Equilibrium point
recurrent neural network (NN)
Nonsmooth analysis
Optimal solution
Differential inclusion
differential inclusions
Logistics
ISSN:2162-237X, 2162-2388, 2162-2388
Online Access:Get full text
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Summary:In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2013.2280905