Improved mixed-integer programming models for the multiprocessor scheduling problem with communication delays
We revise existing and introduce new mixed-integer programming models for the Multiprocessor scheduling problem with communication delays. The basis for both is the identification of two major modeling strategies one of which can be considered ordering -based, and the other assignment -based. We fir...
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| Published in | Journal of combinatorial optimization Vol. 36; no. 3; pp. 871 - 895 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.10.2018
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1382-6905 1573-2886 |
| DOI | 10.1007/s10878-017-0199-9 |
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| Abstract | We revise existing and introduce new mixed-integer programming models for the Multiprocessor scheduling problem with communication delays. The basis for both is the identification of two major modeling strategies one of which can be considered
ordering
-based, and the other
assignment
-based. We first reveal redundancies in the encoding of feasible solutions found in present formulations and discuss how they can be avoided. For the assignment-based approach, we propose new inequalities that lead to provably stronger continuous relaxations and better performance in practice. Moreover, we derive a third, novel modeling strategy and show how to more compactly linearize assignment formulations with quadratic constraints. In a comprehensive experimental comparison of representative models that reflect the state-of-the-art in terms of strength and size, we evaluate not only running times but also the obtained lower and upper bounds on the makespan for the harder instances of a large scale benchmark set. |
|---|---|
| AbstractList | We revise existing and introduce new mixed-integer programming models for the Multiprocessor scheduling problem with communication delays. The basis for both is the identification of two major modeling strategies one of which can be considered ordering-based, and the other assignment-based. We first reveal redundancies in the encoding of feasible solutions found in present formulations and discuss how they can be avoided. For the assignment-based approach, we propose new inequalities that lead to provably stronger continuous relaxations and better performance in practice. Moreover, we derive a third, novel modeling strategy and show how to more compactly linearize assignment formulations with quadratic constraints. In a comprehensive experimental comparison of representative models that reflect the state-of-the-art in terms of strength and size, we evaluate not only running times but also the obtained lower and upper bounds on the makespan for the harder instances of a large scale benchmark set. We revise existing and introduce new mixed-integer programming models for the Multiprocessor scheduling problem with communication delays. The basis for both is the identification of two major modeling strategies one of which can be considered ordering -based, and the other assignment -based. We first reveal redundancies in the encoding of feasible solutions found in present formulations and discuss how they can be avoided. For the assignment-based approach, we propose new inequalities that lead to provably stronger continuous relaxations and better performance in practice. Moreover, we derive a third, novel modeling strategy and show how to more compactly linearize assignment formulations with quadratic constraints. In a comprehensive experimental comparison of representative models that reflect the state-of-the-art in terms of strength and size, we evaluate not only running times but also the obtained lower and upper bounds on the makespan for the harder instances of a large scale benchmark set. |
| Author | Mallach, Sven |
| Author_xml | – sequence: 1 givenname: Sven surname: Mallach fullname: Mallach, Sven email: mallach@informatik.uni-koeln.de organization: Institut für Informatik, Universität zu Köln |
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| CitedBy_id | crossref_primary_10_1016_j_parco_2021_102815 crossref_primary_10_1007_s10878_023_01037_2 crossref_primary_10_1109_TCAD_2024_3447473 crossref_primary_10_1016_j_cor_2023_106212 crossref_primary_10_1016_j_jpdc_2020_07_005 crossref_primary_10_1007_s10288_023_00537_5 crossref_primary_10_1109_TPDS_2020_2989767 crossref_primary_10_31857_S0005231023080093 crossref_primary_10_1007_s10288_020_00460_z crossref_primary_10_1109_TCAD_2023_3274050 |
| Cites_doi | 10.1016/0020-0190(87)90231-6 10.1109/71.503776 10.1016/S0167-8191(96)00041-5 10.1016/S1383-7621(03)00011-0 10.1007/BF00129784 10.1145/66451.66454 10.1016/0167-8191(94)90121-X 10.1016/j.cor.2005.01.005 10.1007/s11227-007-0139-z 10.1007/s11227-010-0395-1 10.1016/0167-8191(93)90079-Z 10.1007/s10288-006-0015-3 10.1016/0743-7315(90)90042-N 10.1016/0167-8191(90)90056-F 10.1016/0166-218X(87)90042-4 10.1109/TPDS.2014.2308175 10.1109/71.207593 10.1016/0166-218X(83)90018-5 10.1145/344588.344618 10.1109/71.308533 10.1137/0218016 10.1007/978-3-540-72584-8_36 10.1016/S0167-5060(08)70356-X 10.1109/DATE.2007.364567 10.1007/3-540-61680-2_48 10.1007/978-3-642-33078-0_10 10.1109/SPDP.1995.530662 10.1109/ICPPW.2003.1240360 10.1007/s11590-014-0802-2 10.1007/978-3-319-50106-2_17 10.1145/125826.126138 10.1109/ICPP.1996.537394 10.1109/ICPP.1994.14 |
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| Keywords | Multiprocessor scheduling Integer programming Communication delays |
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publication-title: IEEE Trans Parallel Distrib Syst doi: 10.1109/TPDS.2014.2308175 – volume-title: Scheduling theory and its applications, chap 4 year: 1995 ident: 199_CR3 – ident: 199_CR27 doi: 10.1109/ICPP.1996.537394 – ident: 199_CR31 doi: 10.1109/ICPP.1994.14 – volume: 16 start-page: 173 issue: 2 year: 1990 ident: 199_CR41 publication-title: Parallel Comput doi: 10.1016/0167-8191(90)90056-F |
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| SubjectTerms | Combinatorics Convex and Discrete Geometry Formulations Integer programming Mathematical Modeling and Industrial Mathematics Mathematical models Mathematical programming Mathematics Mathematics and Statistics Modelling Multiprocessing Operations Research/Decision Theory Optimization Production scheduling Scheduling Theory of Computation Upper bounds |
| Title | Improved mixed-integer programming models for the multiprocessor scheduling problem with communication delays |
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