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A New Nonparametric Filled Function Method for Integer Programming Problems with Constraints

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  • Suxia Ma

    (School of Mathematics and Information Sciences, North Minzu University, Yinchuan 750021, China
    Ningxia Province Cooperative Innovation Center of Scientific Computing and Intelligent Information Processing, North Minzu University, Yinchuan 750021, China)

  • Yuelin Gao

    (Ningxia Province Cooperative Innovation Center of Scientific Computing and Intelligent Information Processing, North Minzu University, Yinchuan 750021, China
    Ningxia Province Key Laboratory of Intelligent Information and Data Processing, North Minzu University, Yinchuan 750021, China)

  • Bo Zhang

    (School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China)

  • Wenlu Zuo

    (School of Mathematics and Information Sciences, North Minzu University, Yinchuan 750021, China)

Abstract

In this paper, we investigate and develop a new filled function method for solving integer programming problems with constraints. By adopting the appropriate equivalent transformation method, these problems are transformed into a class of box-constrained integer programming problems. Then, an effective nonparametric filled function is constructed, and a new global optimization algorithm is designed using the discrete steepest descent method. Numerical experiments illustrate that this algorithm has effectiveness, feasibility, and better global optimization ability.

Suggested Citation

  • Suxia Ma & Yuelin Gao & Bo Zhang & Wenlu Zuo, 2022. "A New Nonparametric Filled Function Method for Integer Programming Problems with Constraints," Mathematics, MDPI, vol. 10(5), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:734-:d:758880
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    References listed on IDEAS

    as
    1. Qian Liu & Yuqing Xu & Yang Zhou, 2020. "A class of exact penalty functions and penalty algorithms for nonsmooth constrained optimization problems," Journal of Global Optimization, Springer, vol. 76(4), pages 745-768, April.
    2. Pirlot, Marc, 1996. "General local search methods," European Journal of Operational Research, Elsevier, vol. 92(3), pages 493-511, August.
    3. Shang, You-lin & Zhang, Lian-sheng, 2008. "Finding discrete global minima with a filled function for integer programming," European Journal of Operational Research, Elsevier, vol. 189(1), pages 31-40, August.
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