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Solving the production transportation problem via a deterministic annealing neural network method

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  • Wu, Zhengtian
  • Gao, Qing
  • Jiang, Baoping
  • Karimi, Hamid Reza

Abstract

The production transportation problem is a famous NP-hard problem which is a challenge to be solved. This study develops a deterministic annealing neural network method based on Lagrange-barrier functions and two neural network models to solve the problem of this kind. According to the problem’s formulation, the Lagrange function will be applied to deal with the linear equality constraints. At the same time, the barrier function will be applied to make the solution arrive at the near-global or global optimal solution. For each of the two neural network models, an iterative procedure to optimize the proposed neural network will be developed and the descent direction is obtained. Then two Lyapunov functions corresponding to the two neural network models are proposed. On the basis of the Lyapunov functions, this deterministic annealing neural network method are shown to converge to the stable equilibrium state and be completely stable. Finally, preliminary numerical results on a number of test problems show that the developed method is promising and could be expanded to other similar issues in the real world.

Suggested Citation

  • Wu, Zhengtian & Gao, Qing & Jiang, Baoping & Karimi, Hamid Reza, 2021. "Solving the production transportation problem via a deterministic annealing neural network method," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    • Handle: RePEc:eee:apmaco:v:411:y:2021:i:c:s009630032100607x
    DOI: 10.1016/j.amc.2021.126518
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    1. Kousik Bhattacharya & Sujit Kumar De & Anup Khan & Prasun Kumar Nayak, 2021. "Pollution sensitive global crude steel production–transportation model under the effect of corruption perception index," OPSEARCH, Springer;Operational Research Society of India, vol. 58(3), pages 636-660, September.
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    4. Sakawa, Masatoshi & Nishizaki, Ichiro & Uemura, Yoshio, 2001. "Fuzzy programming and profit and cost allocation for a production and transportation problem," European Journal of Operational Research, Elsevier, vol. 131(1), pages 1-15, May.
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    Cited by:

    1. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2023. "A general purpose exact solution method for mixed integer concave minimization problems," European Journal of Operational Research, Elsevier, vol. 309(3), pages 977-992.
    2. Qing, Nengneng & Yang, Yongqing & Luan, Xiaoli & Wan, Haiying, 2024. "Practical time-boundary consensus for fractional-order multi-agent systems under well-known and estimable topology," Applied Mathematics and Computation, Elsevier, vol. 464(C).

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