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

Record type: Article

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

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Citation

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

More information

Published date: April 2007
Organisations: Centre of Excellence for International Banking, Finance & Accounting

Identifiers

Local EPrints ID: 204809
URI: http://eprints.soton.ac.uk/id/eprint/204809
ISSN: 0305-0548
PURE UUID: 48f0451d-50dd-4629-b50e-a41000c0e427

Catalogue record

Date deposited: 01 Dec 2011 15:10
Last modified: 18 Jul 2017 11:05

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Contributors

Author: Gunes Erdogan
Author: Barbaros Tansel

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