Face Dimensions of General-Purpose Cutting Planes for Mixed-Integer Linear Programs

Matthias Walter

doi:10.1007/978-3-030-73879-2_28

Face Dimensions of General-Purpose Cutting Planes for Mixed-Integer Linear Programs

Matthias Walter^*

^*Corresponding author for this work

Mathematics of Operations Research

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

Cutting planes are a key ingredient to successfully solve mixed-integer linear programs. For specific problems, their strength is often theoretically assessed by showing that they are facet-defining for the corresponding mixed-integer hull. In this paper we experimentally investigate the dimensions of faces induced by general-purpose cutting planes generated by a state-of-the-art solver. Therefore, we relate the dimension of each cutting plane to its impact in a branch-and-bound algorithm.

Original language	English
Title of host publication	Integer Programming and Combinatorial Optimization
Subtitle of host publication	22nd International Conference, IPCO 2021, Atlanta, GA, USA, May 19–21, 2021, Proceedings
Editors	Mohit Singh, David P. Williamson
Publisher	Springer
Pages	399-412
Number of pages	14
ISBN (Electronic)	978-3-030-73879-2
ISBN (Print)	978-3-030-73878-5
DOIs	https://doi.org/10.1007/978-3-030-73879-2_28
Publication status	Published - 9 Jun 2021
Event	22nd International Conference on Integer Programming and Combinatorial Optimization, IPCO 2021 - Virtual, Online Duration: 19 May 2021 → 21 May 2021 Conference number: 22

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	12707
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	22nd International Conference on Integer Programming and Combinatorial Optimization, IPCO 2021
Abbreviated title	IPCO 2021
City	Virtual, Online
Period	19/05/21 → 21/05/21

Keywords

2022 OA procedure

Access to Document

10.1007/978-3-030-73879-2_28

ArticleFinal published version, 582 KBLicence: Taverne

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Walter, M. (2021). Face Dimensions of General-Purpose Cutting Planes for Mixed-Integer Linear Programs. In M. Singh, & D. P. Williamson (Eds.), Integer Programming and Combinatorial Optimization: 22nd International Conference, IPCO 2021, Atlanta, GA, USA, May 19–21, 2021, Proceedings (pp. 399-412). (Lecture Notes in Computer Science; Vol. 12707). Springer. https://doi.org/10.1007/978-3-030-73879-2_28

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abstract = "Cutting planes are a key ingredient to successfully solve mixed-integer linear programs. For specific problems, their strength is often theoretically assessed by showing that they are facet-defining for the corresponding mixed-integer hull. In this paper we experimentally investigate the dimensions of faces induced by general-purpose cutting planes generated by a state-of-the-art solver. Therefore, we relate the dimension of each cutting plane to its impact in a branch-and-bound algorithm.",

keywords = "2022 OA procedure",

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doi = "10.1007/978-3-030-73879-2\_28",

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booktitle = "Integer Programming and Combinatorial Optimization",

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Walter, M 2021, Face Dimensions of General-Purpose Cutting Planes for Mixed-Integer Linear Programs. in M Singh & DP Williamson (eds), Integer Programming and Combinatorial Optimization: 22nd International Conference, IPCO 2021, Atlanta, GA, USA, May 19–21, 2021, Proceedings. Lecture Notes in Computer Science, vol. 12707, Springer, pp. 399-412, 22nd International Conference on Integer Programming and Combinatorial Optimization, IPCO 2021, Virtual, Online, 19/05/21. https://doi.org/10.1007/978-3-030-73879-2_28

Face Dimensions of General-Purpose Cutting Planes for Mixed-Integer Linear Programs. / Walter, Matthias.
Integer Programming and Combinatorial Optimization: 22nd International Conference, IPCO 2021, Atlanta, GA, USA, May 19–21, 2021, Proceedings. ed. / Mohit Singh; David P. Williamson. Springer, 2021. p. 399-412 (Lecture Notes in Computer Science; Vol. 12707).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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N2 - Cutting planes are a key ingredient to successfully solve mixed-integer linear programs. For specific problems, their strength is often theoretically assessed by showing that they are facet-defining for the corresponding mixed-integer hull. In this paper we experimentally investigate the dimensions of faces induced by general-purpose cutting planes generated by a state-of-the-art solver. Therefore, we relate the dimension of each cutting plane to its impact in a branch-and-bound algorithm.

AB - Cutting planes are a key ingredient to successfully solve mixed-integer linear programs. For specific problems, their strength is often theoretically assessed by showing that they are facet-defining for the corresponding mixed-integer hull. In this paper we experimentally investigate the dimensions of faces induced by general-purpose cutting planes generated by a state-of-the-art solver. Therefore, we relate the dimension of each cutting plane to its impact in a branch-and-bound algorithm.

KW - 2022 OA procedure

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AN - SCOPUS:85106183804

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BT - Integer Programming and Combinatorial Optimization

A2 - Singh, Mohit

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T2 - 22nd International Conference on Integer Programming and Combinatorial Optimization, IPCO 2021

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Walter M. Face Dimensions of General-Purpose Cutting Planes for Mixed-Integer Linear Programs. In Singh M, Williamson DP, editors, Integer Programming and Combinatorial Optimization: 22nd International Conference, IPCO 2021, Atlanta, GA, USA, May 19–21, 2021, Proceedings. Springer. 2021. p. 399-412. (Lecture Notes in Computer Science). doi: 10.1007/978-3-030-73879-2_28

Face Dimensions of General-Purpose Cutting Planes for Mixed-Integer Linear Programs

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Face Dimensions of General-Purpose Cutting Planes for Mixed-Integer Linear Programs

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