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A review of Hopfield neural networks for solving mathematical programming problems

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

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.

Suggested Citation

  • Wen, Ue-Pyng & Lan, Kuen-Ming & Shih, Hsu-Shih, 2009. "A review of Hopfield neural networks for solving mathematical programming problems," European Journal of Operational Research, Elsevier, vol. 198(3), pages 675-687, November.
    • Handle: RePEc:eee:ejores:v:198:y:2009:i:3:p:675-687
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    1. Iasson Karafyllis, 2014. "Feedback Stabilization Methods for the Solution of Nonlinear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 783-806, June.
    2. Veerasamy, Veerapandiyan & Abdul Wahab, Noor Izzri & Ramachandran, Rajeswari & Othman, Mohammad Lutfi & Hizam, Hashim & Devendran, Vidhya Sagar & Irudayaraj, Andrew Xavier Raj & Vinayagam, Arangarajan, 2021. "Recurrent network based power flow solution for voltage stability assessment and improvement with distributed energy sources," Applied Energy, Elsevier, vol. 302(C).
    3. Jayaraman Venkatesh & Alexander N. Pchelintsev & Anitha Karthikeyan & Fatemeh Parastesh & Sajad Jafari, 2023. "A Fractional-Order Memristive Two-Neuron-Based Hopfield Neuron Network: Dynamical Analysis and Application for Image Encryption," Mathematics, MDPI, vol. 11(21), pages 1-17, October.

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