International Journal of Management and Fuzzy Systems

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On Various Approaches for Bi-level Optimization Problems

Received: Sep. 23, 2019    Accepted: Oct. 18, 2019    Published: Oct. 25, 2019
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Abstract

In this paper we review some different basic approaches for solving bi-level optimization problems (BLOP). Firstly, the formulation and some basic concepts of such BLOP are presented. Secondly, some conventional approaches for solving the BLOP such as; vertex enumeration method, branch and bound algorithm, Karush Kuhn-Tucker (KKT) transformation are exhibited. The vertex enumeration based approaches which use the important characteristic that at least one global optimal solution is attained at an extreme point of the constraints set. The KKT approaches in which a BLOP is transformed into a single level problem that solves the upper level decision maker (ULDM) problem while including the lower level decision maker (LLDM) optimality conditions as extra constraints. Fuzzy programming approach mainly based on the fuzzy set theory. Finally, formulation of the bi-level multi-objective decision making (BL-MODM) problem and recently developed approaches, such as; fuzzy goal programming (FGP) and technique for order preference by similarity to ideal solution (TOPSIS) approach, for solving such problem are presented. Numerical illustrations are presented for each technique to ensure the applicability and efficiency.

DOI 10.11648/j.ijmfs.20190503.11
Published in International Journal of Management and Fuzzy Systems ( Volume 5, Issue 3, September 2019 )
Page(s) 47-63
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Bi-level Programming, Multi-objective Programming, KKT Transformation, FGP, TOPSIS

References
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  • APA Style

    Mohamed Aly El Sayed, Farahat Abdo Allah Farahat. (2019). On Various Approaches for Bi-level Optimization Problems. International Journal of Management and Fuzzy Systems, 5(3), 47-63. https://doi.org/10.11648/j.ijmfs.20190503.11

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    ACS Style

    Mohamed Aly El Sayed; Farahat Abdo Allah Farahat. On Various Approaches for Bi-level Optimization Problems. Int. J. Manag. Fuzzy Syst. 2019, 5(3), 47-63. doi: 10.11648/j.ijmfs.20190503.11

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    AMA Style

    Mohamed Aly El Sayed, Farahat Abdo Allah Farahat. On Various Approaches for Bi-level Optimization Problems. Int J Manag Fuzzy Syst. 2019;5(3):47-63. doi: 10.11648/j.ijmfs.20190503.11

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  • @article{10.11648/j.ijmfs.20190503.11,
      author = {Mohamed Aly El Sayed and Farahat Abdo Allah Farahat},
      title = {On Various Approaches for Bi-level Optimization Problems},
      journal = {International Journal of Management and Fuzzy Systems},
      volume = {5},
      number = {3},
      pages = {47-63},
      doi = {10.11648/j.ijmfs.20190503.11},
      url = {https://doi.org/10.11648/j.ijmfs.20190503.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijmfs.20190503.11},
      abstract = {In this paper we review some different basic approaches for solving bi-level optimization problems (BLOP). Firstly, the formulation and some basic concepts of such BLOP are presented. Secondly, some conventional approaches for solving the BLOP such as; vertex enumeration method, branch and bound algorithm, Karush Kuhn-Tucker (KKT) transformation are exhibited. The vertex enumeration based approaches which use the important characteristic that at least one global optimal solution is attained at an extreme point of the constraints set. The KKT approaches in which a BLOP is transformed into a single level problem that solves the upper level decision maker (ULDM) problem while including the lower level decision maker (LLDM) optimality conditions as extra constraints. Fuzzy programming approach mainly based on the fuzzy set theory. Finally, formulation of the bi-level multi-objective decision making (BL-MODM) problem and recently developed approaches, such as; fuzzy goal programming (FGP) and technique for order preference by similarity to ideal solution (TOPSIS) approach, for solving such problem are presented. Numerical illustrations are presented for each technique to ensure the applicability and efficiency.},
     year = {2019}
    }
    

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    T1  - On Various Approaches for Bi-level Optimization Problems
    AU  - Mohamed Aly El Sayed
    AU  - Farahat Abdo Allah Farahat
    Y1  - 2019/10/25
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    DO  - 10.11648/j.ijmfs.20190503.11
    T2  - International Journal of Management and Fuzzy Systems
    JF  - International Journal of Management and Fuzzy Systems
    JO  - International Journal of Management and Fuzzy Systems
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    PB  - Science Publishing Group
    SN  - 2575-4947
    UR  - https://doi.org/10.11648/j.ijmfs.20190503.11
    AB  - In this paper we review some different basic approaches for solving bi-level optimization problems (BLOP). Firstly, the formulation and some basic concepts of such BLOP are presented. Secondly, some conventional approaches for solving the BLOP such as; vertex enumeration method, branch and bound algorithm, Karush Kuhn-Tucker (KKT) transformation are exhibited. The vertex enumeration based approaches which use the important characteristic that at least one global optimal solution is attained at an extreme point of the constraints set. The KKT approaches in which a BLOP is transformed into a single level problem that solves the upper level decision maker (ULDM) problem while including the lower level decision maker (LLDM) optimality conditions as extra constraints. Fuzzy programming approach mainly based on the fuzzy set theory. Finally, formulation of the bi-level multi-objective decision making (BL-MODM) problem and recently developed approaches, such as; fuzzy goal programming (FGP) and technique for order preference by similarity to ideal solution (TOPSIS) approach, for solving such problem are presented. Numerical illustrations are presented for each technique to ensure the applicability and efficiency.
    VL  - 5
    IS  - 3
    ER  - 

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Author Information
  • Department of Basic Engineering Sciences, Benha University, ElQalyoubia, Egypt

  • Higher Technological Institute, Tenth of Ramadan City, Cairo, Egupt

  • Section