On Various Approaches for Bi-level Optimization Problems

Mohamed Aly El Sayed; Farahat Abdo Allah Farahat

doi:doi:10.11648/j.ijmfs.20190503.11

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On Various Approaches for Bi-level Optimization Problems

Mohamed Aly El Sayed, Farahat Abdo Allah Farahat

Published in International Journal of Management and Fuzzy Systems (Volume 5, Issue 3)

Received: 23 September 2019 Accepted: 18 October 2019 Published: 25 October 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.

Published in	International Journal of Management and Fuzzy Systems (Volume 5, Issue 3)
DOI	10.11648/j.ijmfs.20190503.11
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), 2019. Published by Science Publishing Group

Keywords

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

References

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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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - On Various Approaches for Bi-level Optimization Problems
AU  - Mohamed Aly El Sayed
AU  - Farahat Abdo Allah Farahat
Y1  - 2019/10/25
PY  - 2019
N1  - https://doi.org/10.11648/j.ijmfs.20190503.11
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
SP  - 47
EP  - 63
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

Mohamed Aly El Sayed

Department of Basic Engineering Sciences, Benha University, ElQalyoubia, Egypt
Farahat Abdo Allah Farahat

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

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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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - On Various Approaches for Bi-level Optimization Problems
AU  - Mohamed Aly El Sayed
AU  - Farahat Abdo Allah Farahat
Y1  - 2019/10/25
PY  - 2019
N1  - https://doi.org/10.11648/j.ijmfs.20190503.11
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
SP  - 47
EP  - 63
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  -

Copy | Download