A novel approach for solving bi-level mono-objective and multi-objective programming problems using evolutionary algorithms
Bi-level programming problems (BLP) constitute an important class of non-convex optimization problems, which makes it challenging to find a global optimal solution. In this article, we propose an efficient technique to solve this category of problems. We reformulated the initial problem as a single...
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| Format: | Article |
| Language: | English |
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Universidade Federal de Viçosa (UFV)
2024-12-01
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| Series: | The Journal of Engineering and Exact Sciences |
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| Online Access: | https://periodicos.ufv.br/jcec/article/view/20661 |
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| author | Wafa Bouguern Smail Addoune Hanene Debbiche |
| author_facet | Wafa Bouguern Smail Addoune Hanene Debbiche |
| author_sort | Wafa Bouguern |
| collection | DOAJ |
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Bi-level programming problems (BLP) constitute an important class of non-convex optimization problems, which makes it challenging to find a global optimal solution. In this article, we propose an efficient technique to solve this category of problems. We reformulated the initial problem as a single-level optimization problem using the optimal value function of the lower-level problem. To solve the latter, we employed a technique based on -dense curves to approximate the value function of the lower-level problem. Two evolutionary algorithms were then used to solve the reformulated problem. Furthermore, we extended our method to address multi-objective bi-level programming problems with a single objective at the upper level and multiple objectives at the lower level, known as a semi-vectorial bi-level programming problem. Several numerical experiments on nonlinear BLP show the outstanding efficiency of our approach.
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| format | Article |
| id | doaj-art-714a8fa92c524a519cc796337ee860a5 |
| institution | Kabale University |
| issn | 2527-1075 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Universidade Federal de Viçosa (UFV) |
| record_format | Article |
| series | The Journal of Engineering and Exact Sciences |
| spelling | doaj-art-714a8fa92c524a519cc796337ee860a52025-02-02T19:53:05ZengUniversidade Federal de Viçosa (UFV)The Journal of Engineering and Exact Sciences2527-10752024-12-0110910.18540/jcecvl10iss9pp20661A novel approach for solving bi-level mono-objective and multi-objective programming problems using evolutionary algorithmsWafa Bouguern0Smail Addoune1Hanene Debbiche2Mathematical Analysis and Applications Laboratory, Department of Mathematics, University Mohamed El Bachir El Ibrahimi of Bordj Bou Arreridj, El Anasser 34030, AlgeriaMathematical Analysis and Applications Laboratory, Department of Mathematics, University Mohamed El Bachir El Ibrahimi of Bordj Bou Arreridj, El Anasser 34030, AlgeriaMathematical Analysis and Applications Laboratory, Department of Mathematics, University Mohamed El Bachir El Ibrahimi of Bordj Bou Arreridj, El Anasser 34030, Algeria Bi-level programming problems (BLP) constitute an important class of non-convex optimization problems, which makes it challenging to find a global optimal solution. In this article, we propose an efficient technique to solve this category of problems. We reformulated the initial problem as a single-level optimization problem using the optimal value function of the lower-level problem. To solve the latter, we employed a technique based on -dense curves to approximate the value function of the lower-level problem. Two evolutionary algorithms were then used to solve the reformulated problem. Furthermore, we extended our method to address multi-objective bi-level programming problems with a single objective at the upper level and multiple objectives at the lower level, known as a semi-vectorial bi-level programming problem. Several numerical experiments on nonlinear BLP show the outstanding efficiency of our approach. https://periodicos.ufv.br/jcec/article/view/20661Nonlinear bi-level programmingMulticriteria optimizationoptimization |
| spellingShingle | Wafa Bouguern Smail Addoune Hanene Debbiche A novel approach for solving bi-level mono-objective and multi-objective programming problems using evolutionary algorithms The Journal of Engineering and Exact Sciences Nonlinear bi-level programming Multicriteria optimization optimization |
| title | A novel approach for solving bi-level mono-objective and multi-objective programming problems using evolutionary algorithms |
| title_full | A novel approach for solving bi-level mono-objective and multi-objective programming problems using evolutionary algorithms |
| title_fullStr | A novel approach for solving bi-level mono-objective and multi-objective programming problems using evolutionary algorithms |
| title_full_unstemmed | A novel approach for solving bi-level mono-objective and multi-objective programming problems using evolutionary algorithms |
| title_short | A novel approach for solving bi-level mono-objective and multi-objective programming problems using evolutionary algorithms |
| title_sort | novel approach for solving bi level mono objective and multi objective programming problems using evolutionary algorithms |
| topic | Nonlinear bi-level programming Multicriteria optimization optimization |
| url | https://periodicos.ufv.br/jcec/article/view/20661 |
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