A new neural network for solving linear programming problems

Abstract We propose and analyse a new class of neural network models for solving linear programming (LP) problems in real time. We introduce a novel energy function that transforms linear programming into a system of nonlinear differential equations. This system of differential equations can be solved on-line by a simplified low-cost analog neural network containing only one single artificial neuron with adaptive synaptic weights. The network architecture is suitable for currently available CMOS VLSI implementations. An important feature of the proposed neural network architecture is its flexibility and universality. The correctness and performance of the proposed neural network is illustrated by extensive computer simulation experiments.

[1]  Andrzej Cichocki,et al.  Neural networks for linear inverse problems with incomplete data especially in applications to signal and image reconstruction , 1995, Neurocomputing.

[2]  John J. Hopfield,et al.  Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit , 1986 .

[3]  John A. Tomlin,et al.  Implementing the Simplex Method for the Optimization Subroutine Library , 1992, IBM Syst. J..

[4]  Jack B. Dennis,et al.  Mathematical Programming and Electrical Networks , 1959, The Mathematical Gazette.

[5]  M. R. Osborne.  Finite Algorithms in Optimization and Data Analysis , 1985 .

[6]  A. Cichocki,et al.  Neural Networks for Solving Linear Inequality Systems , 1997, Parallel Comput..

[7]  Stefen Hui,et al.  Neural networks for constrained optimization problems , 1993, Int. J. Circuit Theory Appl..

[8]  Clóvis C. Gonzaga,et al.  Path-Following Methods for Linear Programming , 1992, SIAM Rev..

[9]  Insley B. Pyne,et al.  Linear programming on an electronic analogue computer , 1956, Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics.

[10]  Michael A. Shanblatt,et al.  Improved Neural Networks For Linear and Nonlinear Programming , 1991, Int. J. Neural Syst..

[11]  Andrzej Cichocki,et al.  Neural networks for optimization and signal processing , 1993 .

[12]  Leon O. Chua,et al.  Nonlinear programming without computation , 1984 .

[13]  Anthony G. Constantinides,et al.  Lagrange Neural Networks for Linear Programming , 1992, J. Parallel Distributed Comput..

[14]  Marco Balsi.  Stability of cellular neural networks with one-dimensional templates , 1993, Int. J. Circuit Theory Appl..

[15]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[16]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, Comb..

[17]  Leon O. Chua,et al.  Neural networks for nonlinear programming , 1988 .

[18]  Andrzej Cichocki,et al.  Switched-capacitor neural networks for differential optimization , 1991, Int. J. Circuit Theory Appl..

[19]  Jun Wang.  Analysis and design of a recurrent neural network for linear programming , 1993 .

[20]  R. Perfetti,et al.  Neural network for real-time synthesis of FIR filters , 1989 .

[21]  Edgar Sanchez-Sinencio,et al.  Nonlinear switched capacitor 'neural' networks for optimization problems , 1990 .

[22]  Jun Wang,et al.  A deterministic annealing neural network for convex programming , 1994, Neural Networks.

[23]  Abdesselam Bouzerdoum,et al.  Neural network for quadratic optimization with bound constraints , 1993, IEEE Trans. Neural Networks.

[24]  Andrzej Cichocki,et al.  Simplified neural networks for solving linear least squares and total least squares problems in real time , 1994, IEEE Trans. Neural Networks.

[25]  Stefen Hui,et al.  Solving linear programming problems with neural networks: a comparative study , 1995, IEEE Trans. Neural Networks.