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A review of Hopfield neural networks for solving mathematical programming problems

Ue-Pyng Wen, Kuen-Ming Lan and Hsu-Shih Shih

European Journal of Operational Research, 2009, vol. 198, issue 3, 675-687

Abstract: The Hopfield neural network (HNN) is one major neural network (NN) for solving optimization or mathematical programming (MP) problems. The major advantage of HNN is in its structure can be realized on an electronic circuit, possibly on a VLSI (very large-scale integration) circuit, for an on-line solver with a parallel-distributed process. The structure of HNN utilizes three common methods, penalty functions, Lagrange multipliers, and primal and dual methods to construct an energy function. When the function reaches a steady state, an approximate solution of the problem is obtained. Under the classes of these methods, we further organize HNNs by three types of MP problems: linear, non-linear, and mixed-integer. The essentials of each method are also discussed in details. Some remarks for utilizing HNN and difficulties are then addressed for the benefit of successive investigations. Finally, conclusions are drawn and directions for future study are provided.

Keywords: Hopfield; neural; networks; Energy; function; Mathematical; programming; penalty; function; Lagrange; multiplier; Primal; and; dual; functions (search for similar items in EconPapers)
Date: 2009
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European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

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