Date of this Version
European Journal of Operational Research
This 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.
© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
combinatorial optimization, assignment, branch and bound, quadratic assignment problem, reformulation–linearization technique
Adams, W. P., Guignard, M., Hahn, P. M., & Hightower, W. L. (2007). A Level-2 Reformulation–Linearization Technique Bound for the Quadratic Assignment Problem. European Journal of Operational Research, 180 (3), 983-996. http://dx.doi.org/10.1016/j.ejor.2006.03.051
Date Posted: 27 November 2017
This document has been peer reviewed.