A novel algorithm for generating Pareto frontier of bi-level multi-objective rough nonlinear programming problem
This paper discusses a new algorithm for generating the Pareto frontier for bi-level multi-objective rough nonlinear programming problem (BL-MRNPP). In this algorithm, the uncertainty exists in constraints which are modeled as a rough set. Initially, BL-MRNPP is transformed into four deterministic m...
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| Veröffentlicht in: | Ain Shams Engineering Journal Jg. 12; H. 2; S. 2125 - 2133 |
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| Sprache: | Englisch |
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Elsevier B.V
01.06.2021
Elsevier |
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| ISSN: | 2090-4479 |
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| Abstract | This paper discusses a new algorithm for generating the Pareto frontier for bi-level multi-objective rough nonlinear programming problem (BL-MRNPP). In this algorithm, the uncertainty exists in constraints which are modeled as a rough set. Initially, BL-MRNPP is transformed into four deterministic models. The weighted method and the Karush-Kuhn-Tucker optimality condition are combined to obtain the Pareto front of each model. The nature of the problem solutions is characterized according to newly proposed definitions. The location of efficient solutions depending on the lower/upper approximation set is discussed. The aim of the proposed solution procedure for the BL-MRNPP is to avoid solving four problems. A numerical example is solved to indicate the applicability of the proposed algorithm. |
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| AbstractList | This paper discusses a new algorithm for generating the Pareto frontier for bi-level multi-objective rough nonlinear programming problem (BL-MRNPP). In this algorithm, the uncertainty exists in constraints which are modeled as a rough set. Initially, BL-MRNPP is transformed into four deterministic models. The weighted method and the Karush-Kuhn-Tucker optimality condition are combined to obtain the Pareto front of each model. The nature of the problem solutions is characterized according to newly proposed definitions. The location of efficient solutions depending on the lower/upper approximation set is discussed. The aim of the proposed solution procedure for the BL-MRNPP is to avoid solving four problems. A numerical example is solved to indicate the applicability of the proposed algorithm. |
| Author | Elsisy, M.A. El Sayed, M.A. Abo-Elnaga, Y. |
| Author_xml | – sequence: 1 givenname: M.A. surname: Elsisy fullname: Elsisy, M.A. organization: Department of Basic Engineering Sciences, Benha Faculty of Engineering, Benha University, ElQalyoubia, Egypt – sequence: 2 givenname: M.A. surname: El Sayed fullname: El Sayed, M.A. organization: Department of Basic Engineering Sciences, Benha Faculty of Engineering, Benha University, ElQalyoubia, Egypt – sequence: 3 givenname: Y. surname: Abo-Elnaga fullname: Abo-Elnaga, Y. organization: Department of Basic Sciences, Higher Technological Institute, Tenth of Ramadan City, Egypt |
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| Keywords | Multi-objective programming Bi-level programming KKT optimality Rough set |
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| SubjectTerms | Bi-level programming KKT optimality Multi-objective programming Rough set |
| Title | A novel algorithm for generating Pareto frontier of bi-level multi-objective rough nonlinear programming problem |
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