IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v198y2009i3p675-687.html
   My bibliography  Save this article

A review of Hopfield neural networks for solving mathematical programming problems

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00978-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. I. N. da Silva & W. C. Amaral & L. V. R. Arruda, 2006. "Neural Approach for Solving Several Types of Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 128(3), pages 563-580, March.
    2. Sexton, Randall S. & Alidaee, Bahram & Dorsey, Robert E. & Johnson, John D., 1998. "Global optimization for artificial neural networks: A tabu search application," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 570-584, April.
    3. G. A. Croes, 1958. "A Method for Solving Traveling-Salesman Problems," Operations Research, INFORMS, vol. 6(6), pages 791-812, December.
    4. Smith, Kate & Palaniswami, M. & Krishnamoorthy, M., 1996. "Traditional heuristic versus Hopfield neural network approaches to a car sequencing problem," European Journal of Operational Research, Elsevier, vol. 93(2), pages 300-316, September.
    5. Kate A. Smith, 1999. "Neural Networks for Combinatorial Optimization: A Review of More Than a Decade of Research," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 15-34, February.
    6. Sexton, Randall S. & Dorsey, Robert E. & Johnson, John D., 1999. "Optimization of neural networks: A comparative analysis of the genetic algorithm and simulated annealing," European Journal of Operational Research, Elsevier, vol. 114(3), pages 589-601, May.
    7. Papageorgiou, G. & Likas, A. & Stafylopatis, A., 1998. "Improved exploration in Hopfield network state-space through parameter perturbation driven by simulated annealing," European Journal of Operational Research, Elsevier, vol. 108(2), pages 283-292, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pendharkar, Parag C., 2001. "An empirical study of design and testing of hybrid evolutionary-neural approach for classification," Omega, Elsevier, vol. 29(4), pages 361-374, August.
    2. B Dengiz & C Alabas-Uslu & O Dengiz, 2009. "A tabu search algorithm for the training of neural networks," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(2), pages 282-291, February.
    3. Pendharkar, Parag C., 2002. "A computational study on the performance of artificial neural networks under changing structural design and data distribution," European Journal of Operational Research, Elsevier, vol. 138(1), pages 155-177, April.
    4. Asaju La’aro Bolaji & Aminu Ali Ahmad & Peter Bamidele Shola, 2018. "Training of neural network for pattern classification using fireworks algorithm," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(1), pages 208-215, February.
    5. Ilkyeong Moon & Sanghyup Lee & Moonsoo Shin & Kwangyeol Ryu, 2016. "Evolutionary resource assignment for workload-based production scheduling," Journal of Intelligent Manufacturing, Springer, vol. 27(2), pages 375-388, April.
    6. Giard, Vincent & Jeunet, Jully, 2010. "Optimal sequencing of mixed models with sequence-dependent setups and utility workers on an assembly line," International Journal of Production Economics, Elsevier, vol. 123(2), pages 290-300, February.
    7. Nair, D.J. & Grzybowska, H. & Fu, Y. & Dixit, V.V., 2018. "Scheduling and routing models for food rescue and delivery operations," Socio-Economic Planning Sciences, Elsevier, vol. 63(C), pages 18-32.
    8. Geraint Johnes, 2000. "Up Around the Bend: Linear and nonlinear models of the UK economy compared," International Review of Applied Economics, Taylor & Francis Journals, vol. 14(4), pages 485-493.
    9. Pan-Li Zhang & Xiao-Bo Sun & Ji-Quan Wang & Hao-Hao Song & Jin-Ling Bei & Hong-Yu Zhang, 2022. "The Discrete Carnivorous Plant Algorithm with Similarity Elimination Applied to the Traveling Salesman Problem," Mathematics, MDPI, vol. 10(18), pages 1-34, September.
    10. Arthur Charpentier & Romuald Élie & Carl Remlinger, 2023. "Reinforcement Learning in Economics and Finance," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 425-462, June.
    11. Racha El-Hajj & Rym Nesrine Guibadj & Aziz Moukrim & Mehdi Serairi, 2020. "A PSO based algorithm with an efficient optimal split procedure for the multiperiod vehicle routing problem with profit," Annals of Operations Research, Springer, vol. 291(1), pages 281-316, August.
    12. Monfared, M.A.S. & Etemadi, M., 2006. "The impact of energy function structure on solving generalized assignment problem using Hopfield neural network," European Journal of Operational Research, Elsevier, vol. 168(2), pages 645-654, January.
    13. Joo, Rocío & Bertrand, Sophie & Chaigneau, Alexis & Ñiquen, Miguel, 2011. "Optimization of an artificial neural network for identifying fishing set positions from VMS data: An example from the Peruvian anchovy purse seine fishery," Ecological Modelling, Elsevier, vol. 222(4), pages 1048-1059.
    14. CASTRO, Marco & SÖRENSEN, Kenneth & VANSTEENWEGEN, Pieter & GOOS, Peter, 2012. "A simple GRASP+VND for the travelling salesperson problem with hotel selection," Working Papers 2012024, University of Antwerp, Faculty of Business and Economics.
    15. Eric Larsen & Sébastien Lachapelle & Yoshua Bengio & Emma Frejinger & Simon Lacoste-Julien & Andrea Lodi, 2022. "Predicting Tactical Solutions to Operational Planning Problems Under Imperfect Information," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 227-242, January.
    16. Eric Bonabeau & Florian Henaux & Sylvain Gu'erin & Dominique Snyers & Pascale Kuntz & Guy Theraulaz, 1998. "Routing in Telecommunications Networks with ``Smart'' Ant-Like Agents," Working Papers 98-01-003, Santa Fe Institute.
    17. Stanimirović, Predrag & Gerontitis, Dimitris & Tzekis, Panagiotis & Behera, Ratikanta & Sahoo, Jajati Keshari, 2021. "Simulation of Varying Parameter Recurrent Neural Network with application to matrix inversion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 614-628.
    18. Zachariadis, Emmanouil E. & Tarantilis, Christos D. & Kiranoudis, Christos T., 2009. "A Guided Tabu Search for the Vehicle Routing Problem with two-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 195(3), pages 729-743, June.
    19. Z P Fan & Y Chen & J Ma & S Zeng, 2011. "Erratum: A hybrid genetic algorithmic approach to the maximally diverse grouping problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1423-1430, July.
    20. Luc Muyldermans & Patrick Beullens & Dirk Cattrysse & Dirk Van Oudheusden, 2005. "Exploring Variants of 2-Opt and 3-Opt for the General Routing Problem," Operations Research, INFORMS, vol. 53(6), pages 982-995, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:198:y:2009:i:3:p:675-687. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.