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Finding discrete global minima with a filled function for integer programming

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  • Shang, You-lin
  • Zhang, Lian-sheng

Abstract

The filled function method is an approach to find the global minimum of multidimensional functions. This paper proposes a new definition of the filled function for integer programming problem. A filled function which satisfies this definition is presented. Furthermore, we discuss the properties of the filled function and design a new filled function algorithm. Numerical experiments on several test problems with up to 50 integer variables have demonstrated the applicability and efficiency of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:189:y:2008:i:1:p:31-40
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    References listed on IDEAS

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    1. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    2. Zanakis, Stelios H. & Evans, James R. & Vazacopoulos, Alkis A., 1989. "Heuristic methods and applications: A categorized survey," European Journal of Operational Research, Elsevier, vol. 43(1), pages 88-110, November.
    3. R. C. Jeroslow, 1973. "There Cannot be any Algorithm for Integer Programming with Quadratic Constraints," Operations Research, INFORMS, vol. 21(1), pages 221-224, February.
    4. Vassilev, Vassil & Genova, Krassimira, 1994. "An approximate algorithm for nonlinear integer programming," European Journal of Operational Research, Elsevier, vol. 74(1), pages 170-178, April.
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    Cited by:

    1. 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.

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