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A heuristic method to find a quick feasible solution based on the ratio programming

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Listed:
  • M. N. Yarahmadi

    (Amirkabir University of Technology (Tehran Polytechnic))

  • S. A. MirHassani

    (Amirkabir University of Technology (Tehran Polytechnic))

  • F. Hooshmand

    (Amirkabir University of Technology (Tehran Polytechnic))

Abstract

The feasibility pump is a successful rounding-based heuristic to find a feasible solution to mixed-integer programming (MIP) problems. This paper presents a novel method to find a high-quality feasible solution to 0–1 MIPs in a reasonable time. This method is based on a ratio programming model, which we refer to as a feasible-finder model (FFM). It proves that the optimal solution to FFM is feasible for the original MIP problem. An efficient ratio programming method is adopted to solve FFM by solving a sequence of linear programming problems. Then, to improve the quality of the feasible solution, a quality-controlling cut is generated and added in each iteration. Computational results over instances of CORAL and MIPLIB confirm the effectiveness of our method.

Suggested Citation

  • M. N. Yarahmadi & S. A. MirHassani & F. Hooshmand, 2023. "A heuristic method to find a quick feasible solution based on the ratio programming," Operational Research, Springer, vol. 23(3), pages 1-19, September.
    • Handle: RePEc:spr:operea:v:23:y:2023:i:3:d:10.1007_s12351-023-00777-7
    DOI: 10.1007/s12351-023-00777-7
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    References listed on IDEAS

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    1. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2013. "A new class of functions for measuring solution integrality in the Feasibility Pump approach: Complete Results," DIAG Technical Reports 2013-05, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    2. H. P. Benson, 2010. "Branch-and-Bound Outer Approximation Algorithm for Sum-of-Ratios Fractional Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 1-18, July.
    3. Yuelin Gao & Siqiao Jin, 2013. "A Global Optimization Algorithm for Sum of Linear Ratios Problem," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, June.
    4. YongJin Kim & YunChol Jong & JinWon Yu, 2021. "A parametric solution method for a generalized fractional programming problem," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(4), pages 971-989, December.
    5. X. Liu & Y.L. Gao & B. Zhang & F.P. Tian, 2019. "A New Global Optimization Algorithm for a Class of Linear Fractional Programming," Mathematics, MDPI, vol. 7(9), pages 1-21, September.
    6. Ruslan Sadykov & François Vanderbeck & Artur Pessoa & Issam Tahiri & Eduardo Uchoa, 2019. "Primal Heuristics for Branch and Price: The Assets of Diving Methods," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 251-267, April.
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