A branch-and-cut algorithm for quadratic assignment problems based on linearizations


Erdogan, Gunes and Tansel, Barbaros (2007) A branch-and-cut algorithm for quadratic assignment problems based on linearizations. Computers & Operations Research, 34, (4), 1085-1106. (doi:10.1016/j.cor.2005.05.027).

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Description/Abstract

The quadratic assignment problem (QAP) is one of the hardest combinatorial optimization problems known. Exact solution attempts proposed for instances of size larger than 15 have been generally unsuccessful even though successful implementations have been reported on some test problems from the QAPLIB up to size 36. In this study, we focus on the Koopmans–Beckmann formulation and exploit the structure of the flow and distance matrices based on a flow-based linearization technique that we propose. We present two new IP formulations based on the flow-based linearization technique that require fewer variables and yield stronger lower bounds than existing formulations. We strengthen the formulations with valid inequalities and report computational experience with a branch-and-cut algorithm. The proposed method performs quite well on QAPLIB instances for which certain metrics (indices) that we proposed that are related to the degree of difficulty of solving the problem are relatively high (⩾0.3). Many of the well-known instances up to size 25 from the QAPLIB (e.g. nug24, chr25a) are in this class and solved in a matter of days on a single PC using the proposed algorithm

Item Type: Article
ISSNs: 0305-0548 (print)
Related URLs:
Subjects: H Social Sciences > HA Statistics
Divisions: Faculty of Business and Law > Southampton Management School > Management Science
ePrint ID: 204809
Date Deposited: 01 Dec 2011 15:10
Last Modified: 27 Mar 2014 19:48
URI: http://eprints.soton.ac.uk/id/eprint/204809

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