A multilevel algorithm for large unconstrained binary quadratic optimization

Authors:
Yang Wang;Zhipeng Lü;Fred Glover;Jin-Kao Hao
Affiliations:
LERIA, Université d'Angers, Angers Cedex 01, France;School of Computer Science and Technology, Huazhong University, of Science and Technology, Wuhan, China;OptTek Systems, Inc., CO;LERIA, Université d'Angers, Angers Cedex 01, France
Venue:
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Year:
2012

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Abstract

The unconstrained binary quadratic programming (UBQP) problem is a general NP-hard problem with various applications. In this paper, we present a multilevel algorithm designed to approximate large UBQP instances. The proposed multilevel algorithm is composed of a backbone-based coarsening phase, an asymmetric uncoarsening phase and a memetic refinement phase, where the backbone-based procedure and the memetic refinement procedure make use of tabu search to obtain improved solutions. Evaluated on a set of 11 largest instances from the literature (with 5000 to 7000 variables), the proposed algorithm proves to be able to attain all the best known values with a computing effort less than any existing approach.