Quantized hopfield networks for reliability optimization

Abstract The use of neural networks in the reliability optimization field is rare. This paper presents an application of a recent kind of neural networks in a reliability optimization problem for a series system with multiple-choice constraints incorporated at each subsystem, to maximize the system reliability subject to the system budget. The problem is formulated as a nonlinear binary integer programming problem and characterized as an NP-hard problem. Our design of neural network to solve efficiently this problem is based on a quantized Hopfield network. This network allows us to obtain optimal design solutions very frequently and much more quickly than others Hopfield networks.

[1]  Geoffrey E. Hinton,et al.  A Learning Algorithm for Boltzmann Machines , 1985, Cogn. Sci..

[2]  C. S. Sung,et al.  Reliability optimization of a series system with multiple-choice and budget constraints , 2000, Eur. J. Oper. Res..

[3]  Joon-Eon Yang,et al.  Application of genetic algorithm for reliability allocation in nuclear power plants , 1999 .

[4]  Daoud Aït-Kadi,et al.  Availability Optimization of Fault-Tolerant Systems , 2003, J. Decis. Syst..

[5]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Enrico Zio,et al.  Genetic algorithms and Monte Carlo simulation for optimal plant design , 2000, Reliab. Eng. Syst. Saf..

[7]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Prabhakant Sinha,et al.  The Multiple-Choice Knapsack Problem , 1979, Oper. Res..

[9]  P. A. Joyce,et al.  Application of Genetic Algorithms to Optimum Offshore Plant Design , 1998 .

[10]  J. J. Hopfield,et al.  “Neural” computation of decisions in optimization problems , 1985, Biological Cybernetics.

[11]  C. S. Sung,et al.  A branch-and-bound approach for spare unit allocation in a series system , 1994 .

[12]  E. W. Page,et al.  Learning in systematically designed networks , 1989, International 1989 Joint Conference on Neural Networks.

[13]  Satoshi Matsuda,et al.  "Optimal" Hopfield network for combinatorial optimization with linear cost function , 1998, IEEE Trans. Neural Networks.

[14]  Laura Painton,et al.  Genetic algorithms in optimization of system reliability. , 1995 .

[15]  A. Saidane,et al.  Optimal Reliability Design: Fundamentals and Applications , 2001 .

[16]  David W. Coit,et al.  Reliability optimization of series-parallel systems using a genetic algorithm , 1996, IEEE Trans. Reliab..

[17]  R. Nauss.  The 0–1 knapsack problem with multiple choice constraints☆ , 1978 .

[18]  Alice E. Smith,et al.  Genetic Optimization Using A Penalty Function , 1993, ICGA.

[19]  Satoshi Matsuda,et al.  Quantized Hopfield networks for integer programming , 1999, Systems and Computers in Japan.