A multiple objective programming approach to linear bilevel multi-follower programming
In this paper, we investigate the relationship between a certain class of linear bilevel multifollower programming problems and multiple objective programming. We introduce two multiple objective linear programming problems with different objective functions and the same constraint region. We show t...
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AIMS Press
2019-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2019.3.763/fulltext.html |
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doaj-80b0bd524b59441eae30023331dcb7db2020-11-25T01:51:04ZengAIMS PressAIMS Mathematics2473-69882019-07-014376377810.3934/math.2019.3.763A multiple objective programming approach to linear bilevel multi-follower programmingHabibe Sadeghi0Fatemeh Moslemi1Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, IranDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, IranIn this paper, we investigate the relationship between a certain class of linear bilevel multifollower programming problems and multiple objective programming. We introduce two multiple objective linear programming problems with different objective functions and the same constraint region. We show that the extreme points of the set of efficient solutions for both problems are the same as those of the set of feasible solutions to the linear bilevel multi-follower programming problem. Based on this relationship, a new algorithm to find an optimal solution for the linear bilevel multifollower programming problem is developed. Some numerical examples are presented to show the feasibility of the proposed algorithm.https://www.aimspress.com/article/10.3934/math.2019.3.763/fulltext.htmllinear bilevel programmingmulti-followermultiple objective programmingefficient set |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Habibe Sadeghi Fatemeh Moslemi |
| spellingShingle |
Habibe Sadeghi Fatemeh Moslemi A multiple objective programming approach to linear bilevel multi-follower programming AIMS Mathematics linear bilevel programming multi-follower multiple objective programming efficient set |
| author_facet |
Habibe Sadeghi Fatemeh Moslemi |
| author_sort |
Habibe Sadeghi |
| title |
A multiple objective programming approach to linear bilevel multi-follower programming |
| title_short |
A multiple objective programming approach to linear bilevel multi-follower programming |
| title_full |
A multiple objective programming approach to linear bilevel multi-follower programming |
| title_fullStr |
A multiple objective programming approach to linear bilevel multi-follower programming |
| title_full_unstemmed |
A multiple objective programming approach to linear bilevel multi-follower programming |
| title_sort |
multiple objective programming approach to linear bilevel multi-follower programming |
| publisher |
AIMS Press |
| series |
AIMS Mathematics |
| issn |
2473-6988 |
| publishDate |
2019-07-01 |
| description |
In this paper, we investigate the relationship between a certain class of linear bilevel multifollower programming problems and multiple objective programming. We introduce two multiple objective linear programming problems with different objective functions and the same constraint region. We show that the extreme points of the set of efficient solutions for both problems are the same as those of the set of feasible solutions to the linear bilevel multi-follower programming problem. Based on this relationship, a new algorithm to find an optimal solution for the linear bilevel multifollower programming problem is developed. Some numerical examples are presented to show the feasibility of the proposed algorithm. |
| topic |
linear bilevel programming multi-follower multiple objective programming efficient set |
| url |
https://www.aimspress.com/article/10.3934/math.2019.3.763/fulltext.html |
| work_keys_str_mv |
AT habibesadeghi amultipleobjectiveprogrammingapproachtolinearbilevelmultifollowerprogramming AT fatemehmoslemi amultipleobjectiveprogrammingapproachtolinearbilevelmultifollowerprogramming AT habibesadeghi multipleobjectiveprogrammingapproachtolinearbilevelmultifollowerprogramming AT fatemehmoslemi multipleobjectiveprogrammingapproachtolinearbilevelmultifollowerprogramming |
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