A genetic algorithm using a finite search space for solving nonlinear/linear fractional bilevel programming problems
The bilevel programming problem is strongly NP-hard and non-convex, which implies that the problem is very challenging for most canonical optimization approaches using single-point search techniques to find global optima. In the present paper, a class of nonlinear bilevel programming problems are co...
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| Autor*in: |
Li, Hecheng [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Rechteinformationen: |
Nutzungsrecht: © Springer Science+Business Media New York 2015 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Annals of operations research - Dordrecht, The Netherlands : Springer Nature B.V., 1984, 235(2015), 1, Seite 543-558 |
|---|---|
| Übergeordnetes Werk: |
volume:235 ; year:2015 ; number:1 ; pages:543-558 |
| Links: |
|---|
| DOI / URN: |
10.1007/s10479-015-1878-5 |
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| 520 | |a The bilevel programming problem is strongly NP-hard and non-convex, which implies that the problem is very challenging for most canonical optimization approaches using single-point search techniques to find global optima. In the present paper, a class of nonlinear bilevel programming problems are considered where the follower is a linear fractional program. Based on a novel coding scheme, a genetic algorithm with global convergence was developed. First, potential bases of the follower’s problem were taken as individuals, and a genetic algorithm was used to explore these bases. In addition, in order to evaluate each individual, a fitness function was presented by making use of the optimality conditions of linear fractional programs. Also, the fitness evaluation, as a sub-procedure of optimization, can partly improve the leader’s objective. Finally, some computational examples were solved and the results show that the proposed algorithm is efficient and robust. | ||
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| 650 | 4 | |a Operation Research/Decision Theory | |
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| 650 | 4 | |a Bilevel programming | |
| 650 | 4 | |a Bases | |
| 650 | 4 | |a Combinatorics | |
| 650 | 4 | |a Business and Management | |
| 650 | 4 | |a Theory of Computation | |
| 650 | 4 | |a Operations research | |
| 650 | 4 | |a Studies | |
| 650 | 4 | |a Genetic algorithms | |
| 650 | 4 | |a Mathematical programming | |
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10.1007/s10479-015-1878-5 doi PQ20160617 (DE-627)OLC1956856536 (DE-599)GBVOLC1956856536 (PRQ)c2504-c7a6e70ee05ba4c421b205e3b159ece6fc67e36be0ac804ad37d37c6d48812b90 (KEY)0133795520150000235000100543geneticalgorithmusingafinitesearchspaceforsolvingn DE-627 ger DE-627 rakwb eng 004 DNB Li, Hecheng verfasserin aut A genetic algorithm using a finite search space for solving nonlinear/linear fractional bilevel programming problems 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The bilevel programming problem is strongly NP-hard and non-convex, which implies that the problem is very challenging for most canonical optimization approaches using single-point search techniques to find global optima. In the present paper, a class of nonlinear bilevel programming problems are considered where the follower is a linear fractional program. Based on a novel coding scheme, a genetic algorithm with global convergence was developed. First, potential bases of the follower’s problem were taken as individuals, and a genetic algorithm was used to explore these bases. In addition, in order to evaluate each individual, a fitness function was presented by making use of the optimality conditions of linear fractional programs. Also, the fitness evaluation, as a sub-procedure of optimization, can partly improve the leader’s objective. Finally, some computational examples were solved and the results show that the proposed algorithm is efficient and robust. Nutzungsrecht: © Springer Science+Business Media New York 2015 Genetic algorithm Operation Research/Decision Theory Optimal solutions Bilevel programming Bases Combinatorics Business and Management Theory of Computation Operations research Studies Genetic algorithms Mathematical programming Enthalten in Annals of operations research Dordrecht, The Netherlands : Springer Nature B.V., 1984 235(2015), 1, Seite 543-558 (DE-627)12964370X (DE-600)252629-3 (DE-576)018141862 0254-5330 volume:235 year:2015 number:1 pages:543-558 http://dx.doi.org/10.1007/s10479-015-1878-5 Volltext http://search.proquest.com/docview/1736311838 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT AR 235 2015 1 543-558 |
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10.1007/s10479-015-1878-5 doi PQ20160617 (DE-627)OLC1956856536 (DE-599)GBVOLC1956856536 (PRQ)c2504-c7a6e70ee05ba4c421b205e3b159ece6fc67e36be0ac804ad37d37c6d48812b90 (KEY)0133795520150000235000100543geneticalgorithmusingafinitesearchspaceforsolvingn DE-627 ger DE-627 rakwb eng 004 DNB Li, Hecheng verfasserin aut A genetic algorithm using a finite search space for solving nonlinear/linear fractional bilevel programming problems 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The bilevel programming problem is strongly NP-hard and non-convex, which implies that the problem is very challenging for most canonical optimization approaches using single-point search techniques to find global optima. In the present paper, a class of nonlinear bilevel programming problems are considered where the follower is a linear fractional program. Based on a novel coding scheme, a genetic algorithm with global convergence was developed. First, potential bases of the follower’s problem were taken as individuals, and a genetic algorithm was used to explore these bases. In addition, in order to evaluate each individual, a fitness function was presented by making use of the optimality conditions of linear fractional programs. Also, the fitness evaluation, as a sub-procedure of optimization, can partly improve the leader’s objective. Finally, some computational examples were solved and the results show that the proposed algorithm is efficient and robust. Nutzungsrecht: © Springer Science+Business Media New York 2015 Genetic algorithm Operation Research/Decision Theory Optimal solutions Bilevel programming Bases Combinatorics Business and Management Theory of Computation Operations research Studies Genetic algorithms Mathematical programming Enthalten in Annals of operations research Dordrecht, The Netherlands : Springer Nature B.V., 1984 235(2015), 1, Seite 543-558 (DE-627)12964370X (DE-600)252629-3 (DE-576)018141862 0254-5330 volume:235 year:2015 number:1 pages:543-558 http://dx.doi.org/10.1007/s10479-015-1878-5 Volltext http://search.proquest.com/docview/1736311838 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT AR 235 2015 1 543-558 |
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10.1007/s10479-015-1878-5 doi PQ20160617 (DE-627)OLC1956856536 (DE-599)GBVOLC1956856536 (PRQ)c2504-c7a6e70ee05ba4c421b205e3b159ece6fc67e36be0ac804ad37d37c6d48812b90 (KEY)0133795520150000235000100543geneticalgorithmusingafinitesearchspaceforsolvingn DE-627 ger DE-627 rakwb eng 004 DNB Li, Hecheng verfasserin aut A genetic algorithm using a finite search space for solving nonlinear/linear fractional bilevel programming problems 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The bilevel programming problem is strongly NP-hard and non-convex, which implies that the problem is very challenging for most canonical optimization approaches using single-point search techniques to find global optima. In the present paper, a class of nonlinear bilevel programming problems are considered where the follower is a linear fractional program. Based on a novel coding scheme, a genetic algorithm with global convergence was developed. First, potential bases of the follower’s problem were taken as individuals, and a genetic algorithm was used to explore these bases. In addition, in order to evaluate each individual, a fitness function was presented by making use of the optimality conditions of linear fractional programs. Also, the fitness evaluation, as a sub-procedure of optimization, can partly improve the leader’s objective. Finally, some computational examples were solved and the results show that the proposed algorithm is efficient and robust. Nutzungsrecht: © Springer Science+Business Media New York 2015 Genetic algorithm Operation Research/Decision Theory Optimal solutions Bilevel programming Bases Combinatorics Business and Management Theory of Computation Operations research Studies Genetic algorithms Mathematical programming Enthalten in Annals of operations research Dordrecht, The Netherlands : Springer Nature B.V., 1984 235(2015), 1, Seite 543-558 (DE-627)12964370X (DE-600)252629-3 (DE-576)018141862 0254-5330 volume:235 year:2015 number:1 pages:543-558 http://dx.doi.org/10.1007/s10479-015-1878-5 Volltext http://search.proquest.com/docview/1736311838 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT AR 235 2015 1 543-558 |
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10.1007/s10479-015-1878-5 doi PQ20160617 (DE-627)OLC1956856536 (DE-599)GBVOLC1956856536 (PRQ)c2504-c7a6e70ee05ba4c421b205e3b159ece6fc67e36be0ac804ad37d37c6d48812b90 (KEY)0133795520150000235000100543geneticalgorithmusingafinitesearchspaceforsolvingn DE-627 ger DE-627 rakwb eng 004 DNB Li, Hecheng verfasserin aut A genetic algorithm using a finite search space for solving nonlinear/linear fractional bilevel programming problems 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The bilevel programming problem is strongly NP-hard and non-convex, which implies that the problem is very challenging for most canonical optimization approaches using single-point search techniques to find global optima. In the present paper, a class of nonlinear bilevel programming problems are considered where the follower is a linear fractional program. Based on a novel coding scheme, a genetic algorithm with global convergence was developed. First, potential bases of the follower’s problem were taken as individuals, and a genetic algorithm was used to explore these bases. In addition, in order to evaluate each individual, a fitness function was presented by making use of the optimality conditions of linear fractional programs. Also, the fitness evaluation, as a sub-procedure of optimization, can partly improve the leader’s objective. Finally, some computational examples were solved and the results show that the proposed algorithm is efficient and robust. Nutzungsrecht: © Springer Science+Business Media New York 2015 Genetic algorithm Operation Research/Decision Theory Optimal solutions Bilevel programming Bases Combinatorics Business and Management Theory of Computation Operations research Studies Genetic algorithms Mathematical programming Enthalten in Annals of operations research Dordrecht, The Netherlands : Springer Nature B.V., 1984 235(2015), 1, Seite 543-558 (DE-627)12964370X (DE-600)252629-3 (DE-576)018141862 0254-5330 volume:235 year:2015 number:1 pages:543-558 http://dx.doi.org/10.1007/s10479-015-1878-5 Volltext http://search.proquest.com/docview/1736311838 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT AR 235 2015 1 543-558 |
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10.1007/s10479-015-1878-5 doi PQ20160617 (DE-627)OLC1956856536 (DE-599)GBVOLC1956856536 (PRQ)c2504-c7a6e70ee05ba4c421b205e3b159ece6fc67e36be0ac804ad37d37c6d48812b90 (KEY)0133795520150000235000100543geneticalgorithmusingafinitesearchspaceforsolvingn DE-627 ger DE-627 rakwb eng 004 DNB Li, Hecheng verfasserin aut A genetic algorithm using a finite search space for solving nonlinear/linear fractional bilevel programming problems 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The bilevel programming problem is strongly NP-hard and non-convex, which implies that the problem is very challenging for most canonical optimization approaches using single-point search techniques to find global optima. In the present paper, a class of nonlinear bilevel programming problems are considered where the follower is a linear fractional program. Based on a novel coding scheme, a genetic algorithm with global convergence was developed. First, potential bases of the follower’s problem were taken as individuals, and a genetic algorithm was used to explore these bases. In addition, in order to evaluate each individual, a fitness function was presented by making use of the optimality conditions of linear fractional programs. Also, the fitness evaluation, as a sub-procedure of optimization, can partly improve the leader’s objective. Finally, some computational examples were solved and the results show that the proposed algorithm is efficient and robust. Nutzungsrecht: © Springer Science+Business Media New York 2015 Genetic algorithm Operation Research/Decision Theory Optimal solutions Bilevel programming Bases Combinatorics Business and Management Theory of Computation Operations research Studies Genetic algorithms Mathematical programming Enthalten in Annals of operations research Dordrecht, The Netherlands : Springer Nature B.V., 1984 235(2015), 1, Seite 543-558 (DE-627)12964370X (DE-600)252629-3 (DE-576)018141862 0254-5330 volume:235 year:2015 number:1 pages:543-558 http://dx.doi.org/10.1007/s10479-015-1878-5 Volltext http://search.proquest.com/docview/1736311838 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT AR 235 2015 1 543-558 |
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A genetic algorithm using a finite search space for solving nonlinear/linear fractional bilevel programming problems |
| abstract |
The bilevel programming problem is strongly NP-hard and non-convex, which implies that the problem is very challenging for most canonical optimization approaches using single-point search techniques to find global optima. In the present paper, a class of nonlinear bilevel programming problems are considered where the follower is a linear fractional program. Based on a novel coding scheme, a genetic algorithm with global convergence was developed. First, potential bases of the follower’s problem were taken as individuals, and a genetic algorithm was used to explore these bases. In addition, in order to evaluate each individual, a fitness function was presented by making use of the optimality conditions of linear fractional programs. Also, the fitness evaluation, as a sub-procedure of optimization, can partly improve the leader’s objective. Finally, some computational examples were solved and the results show that the proposed algorithm is efficient and robust. |
| abstractGer |
The bilevel programming problem is strongly NP-hard and non-convex, which implies that the problem is very challenging for most canonical optimization approaches using single-point search techniques to find global optima. In the present paper, a class of nonlinear bilevel programming problems are considered where the follower is a linear fractional program. Based on a novel coding scheme, a genetic algorithm with global convergence was developed. First, potential bases of the follower’s problem were taken as individuals, and a genetic algorithm was used to explore these bases. In addition, in order to evaluate each individual, a fitness function was presented by making use of the optimality conditions of linear fractional programs. Also, the fitness evaluation, as a sub-procedure of optimization, can partly improve the leader’s objective. Finally, some computational examples were solved and the results show that the proposed algorithm is efficient and robust. |
| abstract_unstemmed |
The bilevel programming problem is strongly NP-hard and non-convex, which implies that the problem is very challenging for most canonical optimization approaches using single-point search techniques to find global optima. In the present paper, a class of nonlinear bilevel programming problems are considered where the follower is a linear fractional program. Based on a novel coding scheme, a genetic algorithm with global convergence was developed. First, potential bases of the follower’s problem were taken as individuals, and a genetic algorithm was used to explore these bases. In addition, in order to evaluate each individual, a fitness function was presented by making use of the optimality conditions of linear fractional programs. Also, the fitness evaluation, as a sub-procedure of optimization, can partly improve the leader’s objective. Finally, some computational examples were solved and the results show that the proposed algorithm is efficient and robust. |
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| title_short |
A genetic algorithm using a finite search space for solving nonlinear/linear fractional bilevel programming problems |
| url |
http://dx.doi.org/10.1007/s10479-015-1878-5 http://search.proquest.com/docview/1736311838 |
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| doi_str |
10.1007/s10479-015-1878-5 |
| up_date |
2024-07-03T22:14:13.075Z |
| _version_ |
1803597751861116928 |
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7.400075 |