Academic Journal
From an Interior Point to a Corner Point: Smart Crossover.
| Τίτλος: | From an Interior Point to a Corner Point: Smart Crossover. |
|---|---|
| Συγγραφείς: | Ge, Dongdong1 (AUTHOR) ddge@sjtu.edu.cn, Wang, Chengwenjian2 (AUTHOR) wcwj@umn.edu, Xiong, Zikai3 (AUTHOR) zikai@mit.edu, Ye, Yinyu4 (AUTHOR) yyye@stanford.edu |
| Πηγή: | INFORMS Journal on Computing. Nov/Dec2025, Vol. 37 Issue 6, p1670-1688. 19p. |
| Θεματικοί όροι: | *Linear programming, *Mathematical programming, *Problem solving, *Algorithms, Mixed integer linear programming, Spanning trees, Optimization algorithms, Graph theory |
| Περίληψη: | Identifying optimal basic feasible solutions to linear programming problems is a critical task for mixed integer programming and other applications. The crossover method, which aims at deriving an optimal extreme point from a suboptimal solution (the output of a starting method such as interior-point methods or first-order methods), is crucial in this process. This method, compared with the starting method, frequently represents the primary computational bottleneck in practical applications. We propose approaches to overcome this bottleneck by exploiting problem characteristics and implementing customized strategies. For problems arising from network applications and exhibiting network structures, we take advantage of the graph structure of the problem and the tree structure of the optimal solutions. Based on these structures, we propose a tree-based crossover method, aiming to recovering basic solutions by identifying nearby spanning tree structures. For general linear programs, we propose recovering an optimal basic solution by identifying the optimal face and employing controlled perturbations based on the suboptimal solution provided by interior-point methods. We prove that an optimal solution for the perturbed problem is an extreme point, and its objective value is at least as good as that of the initial interior-point solution. Computational experiments show significant speed-ups achieved by our methods compared with state-of-the-art commercial solvers on classical linear programming problem benchmarks, network flow problem benchmarks, and optimal transport problems. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Funding: D. Ge was supported by the National Natural Science Foundation of China [Grants 72150001, 72225009, 72394360, and 72394365]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0291) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0291). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR] |
| Copyright of INFORMS Journal on Computing is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
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| Header | DbId: bsx DbLabel: Business Source Index An: 189856738 RelevancyScore: 1451 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1451.22045898438 |
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| Items | – Name: Title Label: Title Group: Ti Data: From an Interior Point to a Corner Point: Smart Crossover. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Ge%2C+Dongdong%22">Ge, Dongdong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ddge@sjtu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Chengwenjian%22">Wang, Chengwenjian</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> wcwj@umn.edu</i><br /><searchLink fieldCode="AR" term="%22Xiong%2C+Zikai%22">Xiong, Zikai</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> zikai@mit.edu</i><br /><searchLink fieldCode="AR" term="%22Ye%2C+Yinyu%22">Ye, Yinyu</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> yyye@stanford.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22INFORMS+Journal+on+Computing%22">INFORMS Journal on Computing</searchLink>. Nov/Dec2025, Vol. 37 Issue 6, p1670-1688. 19p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Linear+programming%22">Linear programming</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+programming%22">Mathematical programming</searchLink><br />*<searchLink fieldCode="DE" term="%22Problem+solving%22">Problem solving</searchLink><br />*<searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Mixed+integer+linear+programming%22">Mixed integer linear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Spanning+trees%22">Spanning trees</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Identifying optimal basic feasible solutions to linear programming problems is a critical task for mixed integer programming and other applications. The crossover method, which aims at deriving an optimal extreme point from a suboptimal solution (the output of a starting method such as interior-point methods or first-order methods), is crucial in this process. This method, compared with the starting method, frequently represents the primary computational bottleneck in practical applications. We propose approaches to overcome this bottleneck by exploiting problem characteristics and implementing customized strategies. For problems arising from network applications and exhibiting network structures, we take advantage of the graph structure of the problem and the tree structure of the optimal solutions. Based on these structures, we propose a tree-based crossover method, aiming to recovering basic solutions by identifying nearby spanning tree structures. For general linear programs, we propose recovering an optimal basic solution by identifying the optimal face and employing controlled perturbations based on the suboptimal solution provided by interior-point methods. We prove that an optimal solution for the perturbed problem is an extreme point, and its objective value is at least as good as that of the initial interior-point solution. Computational experiments show significant speed-ups achieved by our methods compared with state-of-the-art commercial solvers on classical linear programming problem benchmarks, network flow problem benchmarks, and optimal transport problems. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Funding: D. Ge was supported by the National Natural Science Foundation of China [Grants 72150001, 72225009, 72394360, and 72394365]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0291) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0291). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of INFORMS Journal on Computing is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1287/ijoc.2022.0291 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 19 StartPage: 1670 Subjects: – SubjectFull: Linear programming Type: general – SubjectFull: Mathematical programming Type: general – SubjectFull: Problem solving Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Mixed integer linear programming Type: general – SubjectFull: Spanning trees Type: general – SubjectFull: Optimization algorithms Type: general – SubjectFull: Graph theory Type: general Titles: – TitleFull: From an Interior Point to a Corner Point: Smart Crossover. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Ge, Dongdong – PersonEntity: Name: NameFull: Wang, Chengwenjian – PersonEntity: Name: NameFull: Xiong, Zikai – PersonEntity: Name: NameFull: Ye, Yinyu IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov/Dec2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 10919856 Numbering: – Type: volume Value: 37 – Type: issue Value: 6 Titles: – TitleFull: INFORMS Journal on Computing Type: main |
| ResultId | 1 |