Operations, Information and Decisions Papers

Document Type

Journal Article

Date of this Version

8-2007

Publication Source

European Journal of Operational Research

Volume

180

Issue

3

Start Page

983

Last Page

996

DOI

10.1016/j.ejor.2006.03.051

Abstract

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.

Copyright/Permission Statement

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

combinatorial optimization, assignment, branch and bound, quadratic assignment problem, reformulation–linearization technique

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Date Posted: 27 November 2017

This document has been peer reviewed.