An algorithm for a multicriteria optimization problem and its application to a facility location problem
In this paper, a new algorithm is proposed for solving a multicriteria optimization problem where the feasible set is an $m-$dimensional cube. In fact, the idea of the multicriteria big cube small cube method is employed to develop the new algorithm. It is proved that, for a given epsilon vector, th...
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| Format: | Article |
| Language: | English |
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Shahid Bahonar University of Kerman
2022-11-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_3481_254404c947893008b5355039a1ab3531.pdf |
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| author | Nemat Ghafari M.A. Yaghoobi |
| author_facet | Nemat Ghafari M.A. Yaghoobi |
| author_sort | Nemat Ghafari |
| collection | DOAJ |
| description | In this paper, a new algorithm is proposed for solving a multicriteria optimization problem where the feasible set is an $m-$dimensional cube. In fact, the idea of the multicriteria big cube small cube method is employed to develop the new algorithm. It is proved that, for a given epsilon vector, the output of the suggested algorithm involves all epsilon efficient solutions as well as all efficient solutions. Furthermore, the algorithm is applied to a multicriteria location problem. The results show that the recommended algorithm can obtain more epsilon efficient solutions in comparison with the main multicriteria big cube small cube method. |
| format | Article |
| id | doaj-art-a19f6ebcf545470ca4da5beee3389c16 |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2022-11-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-a19f6ebcf545470ca4da5beee3389c162025-01-07T10:26:24ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052022-11-0111319721310.22103/jmmr.2022.19734.12823481An algorithm for a multicriteria optimization problem and its application to a facility location problemNemat Ghafari0M.A. Yaghoobi1Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranDepartment of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranIn this paper, a new algorithm is proposed for solving a multicriteria optimization problem where the feasible set is an $m-$dimensional cube. In fact, the idea of the multicriteria big cube small cube method is employed to develop the new algorithm. It is proved that, for a given epsilon vector, the output of the suggested algorithm involves all epsilon efficient solutions as well as all efficient solutions. Furthermore, the algorithm is applied to a multicriteria location problem. The results show that the recommended algorithm can obtain more epsilon efficient solutions in comparison with the main multicriteria big cube small cube method.https://jmmrc.uk.ac.ir/article_3481_254404c947893008b5355039a1ab3531.pdfmulticriteria optimizationefficient solutionsepsilon efficient solutionsmulticriteria facility location |
| spellingShingle | Nemat Ghafari M.A. Yaghoobi An algorithm for a multicriteria optimization problem and its application to a facility location problem Journal of Mahani Mathematical Research multicriteria optimization efficient solutions epsilon efficient solutions multicriteria facility location |
| title | An algorithm for a multicriteria optimization problem and its application to a facility location problem |
| title_full | An algorithm for a multicriteria optimization problem and its application to a facility location problem |
| title_fullStr | An algorithm for a multicriteria optimization problem and its application to a facility location problem |
| title_full_unstemmed | An algorithm for a multicriteria optimization problem and its application to a facility location problem |
| title_short | An algorithm for a multicriteria optimization problem and its application to a facility location problem |
| title_sort | algorithm for a multicriteria optimization problem and its application to a facility location problem |
| topic | multicriteria optimization efficient solutions epsilon efficient solutions multicriteria facility location |
| url | https://jmmrc.uk.ac.ir/article_3481_254404c947893008b5355039a1ab3531.pdf |
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