A Level-2 Reformulation–Linearization Technique Bound for the Quadratic Assignment Problem

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dc.contributor.authorAdams, Warren P
dc.contributor.authorGuignard, Monique
dc.contributor.authorHahn, Peter M
dc.contributor.authorHightower, William L
dc.date2023-05-17T15:30:46.000
dc.date.accessioned2023-05-23T00:16:45Z
dc.date.available2023-05-23T00:16:45Z
dc.date.issued2007-08-01
dc.date.submitted2016-09-08T09:30:53-07:00
dc.description.abstractThis paper studies polyhedral methods for the quadratic assignment problem. Bounds on the objective value are obtained using mixed 0–1 linear representations that result from a reformulation–linearization technique (rlt). The rlt provides different “levels” of representations that give increasing strength. Prior studies have shown that even the weakest level-1 form yields very tight bounds, which in turn lead to improved solution methodologies. This paper focuses on implementing level-2. We compare level-2 with level-1 and other bounding mechanisms, in terms of both overall strength and ease of computation. In so doing, we extend earlier work on level-1 by implementing a Lagrangian relaxation that exploits block-diagonal structure present in the constraints. The bounds are embedded within an enumerative algorithm to devise an exact solution strategy. Our computer results are notable, exhibiting a dramatic reduction in nodes examined in the enumerative phase, and allowing for the exact solution of large instances.
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/42237
dc.legacy.articleid1267
dc.legacy.fields10.1016/j.ejor.2006.03.051
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1267&context=oid_papers&unstamped=1
dc.rights© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.source.beginpage983
dc.source.endpage996
dc.source.issue48
dc.source.issue3
dc.source.journalOperations, Information and Decisions Papers
dc.source.journaltitleEuropean Journal of Operational Research
dc.source.peerreviewedtrue
dc.source.statuspublished
dc.source.volume180
dc.subject.othercombinatorial optimization
dc.subject.otherassignment
dc.subject.otherbranch and bound
dc.subject.otherquadratic assignment problem
dc.subject.otherreformulation–linearization technique
dc.subject.otherOther Mathematics
dc.titleA Level-2 Reformulation–Linearization Technique Bound for the Quadratic Assignment Problem
dc.typeArticle
digcom.contributor.authorAdams, Warren P
digcom.contributor.authorGuignard, Monique
digcom.contributor.authorHahn, Peter M
digcom.contributor.authorHightower, William L
digcom.identifieroid_papers/48
digcom.identifier.contextkey9091996
digcom.identifier.submissionpathoid_papers/48
digcom.typearticle
dspace.entity.typePublication
upenn.schoolDepartmentCenterOperations, Information and Decisions Papers
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