Graph Modeling for Quadratic Assignment Problems Associated with the Hypercube
- Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804 (United States)
- Department of Industrial and Enterprise System Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801 (United States)
- Department of Electrical and Computer Engineering, McMaster University, Ontario (Canada)
In the paper we consider the quadratic assignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at least n different optimal solutions to the underlying QAPs. Moreover, the inherent symmetries in the associated hypercube allow us to obtain partial information regarding the optimal solutions and thus shrink the search space and improve all the existing QAP solvers for the underlying QAPs.Secondly, we use graph modeling technique to derive a new integer linear program (ILP) models for the underlying QAPs. The new ILP model has n(n-1) binary variables and O(n{sup 3} log(n)) linear constraints. This yields the smallest known number of binary variables for the ILP reformulation of QAPs. Various relaxations of the new ILP model are obtained based on the graphical characterization of the hypercube, and the lower bounds provided by the LP relaxations of the new model are analyzed and compared with what provided by several classical LP relaxations of QAPs in the literature.
- OSTI ID:
- 21316827
- Journal Information:
- AIP Conference Proceedings, Vol. 1146, Issue 1; Conference: CMETP: International conference on modelling and engineering and technological problems; 9. biennial national conference of Indian Society of Industrial and Applied Mathematics (ISIAM), Agra (India), 14-16 Jan 2009; Other Information: DOI: 10.1063/1.3183570; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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