A Generalized Benders Decomposition for Mixed-Integer Nonlinear Programming: Theory and Applications
This paper comprehensively explains how to solve mixed-integer nonlinear programming (MINLP) models using the generalized benders decomposition (GBD) method. The MINLP problem is an optimization model in which some variables must be integers and the objective function or constraints are nonlinear. ...
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| Format: | Article |
| Language: | English |
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Mathematics Department UIN Maulana Malik Ibrahim Malang
2024-11-01
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| Series: | Cauchy: Jurnal Matematika Murni dan Aplikasi |
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| Online Access: | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/29398 |
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| author | Fadiah Hasna Nadiatul Haq Diah Chaerani Anita Triska |
| author_facet | Fadiah Hasna Nadiatul Haq Diah Chaerani Anita Triska |
| author_sort | Fadiah Hasna Nadiatul Haq |
| collection | DOAJ |
| description | This paper comprehensively explains how to solve mixed-integer nonlinear programming (MINLP) models using the generalized benders decomposition (GBD) method. The MINLP problem is an optimization model in which some variables must be integers and the objective function or constraints are nonlinear. The GBD method is an extension of the Benders Decomposition (BD) method, effectively handles the characteristics of the MINLP model, where the model has nonlinear properties and involves two types of variables, namely continuous variables and integer variables. The GBD method decomposes the problem into primal and master problems that are solved alternately until the optimal solution is found. The main difference between the GBD and BD methods is that GBD uses nonlinear duality in the main problem so that GBD can solve the nonlinear problem, whereas BD applies linear duality. This paper also presents some theorem proofs related to GBD that were not presented in detail in the previous literature. The application of the GBD method is also presented to demonstrate how the method can be effectively used to solve real-world MINLP problems. |
| format | Article |
| id | doaj-art-27b0ed18fa6949fc8a9285acb7af081a |
| institution | OA Journals |
| issn | 2086-0382 2477-3344 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Mathematics Department UIN Maulana Malik Ibrahim Malang |
| record_format | Article |
| series | Cauchy: Jurnal Matematika Murni dan Aplikasi |
| spelling | doaj-art-27b0ed18fa6949fc8a9285acb7af081a2025-08-20T02:13:45ZengMathematics Department UIN Maulana Malik Ibrahim MalangCauchy: Jurnal Matematika Murni dan Aplikasi2086-03822477-33442024-11-019232934010.18860/ca.v9i2.293988271A Generalized Benders Decomposition for Mixed-Integer Nonlinear Programming: Theory and ApplicationsFadiah Hasna Nadiatul Haq0Diah Chaerani1Anita Triska2Department of Mathematics, Universitas Padjadjaran, Jl. Raya Bandung Sumedang KM 21, Sumedang, IndonesiaDepartment of Mathematics, Universitas Padjadjaran, Jl. Raya Bandung Sumedang KM 21, Sumedang, IndonesiaDepartment of Mathematics, Universitas Padjadjaran, Jl. Raya Bandung Sumedang KM 21, Sumedang, IndonesiaThis paper comprehensively explains how to solve mixed-integer nonlinear programming (MINLP) models using the generalized benders decomposition (GBD) method. The MINLP problem is an optimization model in which some variables must be integers and the objective function or constraints are nonlinear. The GBD method is an extension of the Benders Decomposition (BD) method, effectively handles the characteristics of the MINLP model, where the model has nonlinear properties and involves two types of variables, namely continuous variables and integer variables. The GBD method decomposes the problem into primal and master problems that are solved alternately until the optimal solution is found. The main difference between the GBD and BD methods is that GBD uses nonlinear duality in the main problem so that GBD can solve the nonlinear problem, whereas BD applies linear duality. This paper also presents some theorem proofs related to GBD that were not presented in detail in the previous literature. The application of the GBD method is also presented to demonstrate how the method can be effectively used to solve real-world MINLP problems.https://ejournal.uin-malang.ac.id/index.php/Math/article/view/29398optimizationmixed-integer nonlinear programminggeneralized benders decomposition |
| spellingShingle | Fadiah Hasna Nadiatul Haq Diah Chaerani Anita Triska A Generalized Benders Decomposition for Mixed-Integer Nonlinear Programming: Theory and Applications Cauchy: Jurnal Matematika Murni dan Aplikasi optimization mixed-integer nonlinear programming generalized benders decomposition |
| title | A Generalized Benders Decomposition for Mixed-Integer Nonlinear Programming: Theory and Applications |
| title_full | A Generalized Benders Decomposition for Mixed-Integer Nonlinear Programming: Theory and Applications |
| title_fullStr | A Generalized Benders Decomposition for Mixed-Integer Nonlinear Programming: Theory and Applications |
| title_full_unstemmed | A Generalized Benders Decomposition for Mixed-Integer Nonlinear Programming: Theory and Applications |
| title_short | A Generalized Benders Decomposition for Mixed-Integer Nonlinear Programming: Theory and Applications |
| title_sort | generalized benders decomposition for mixed integer nonlinear programming theory and applications |
| topic | optimization mixed-integer nonlinear programming generalized benders decomposition |
| url | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/29398 |
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