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Path relinking for unconstrained binary quadratic programming

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  • Wang, Yang
  • Lü, Zhipeng
  • Glover, Fred
  • Hao, Jin-Kao
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    Abstract

    This paper presents two path relinking algorithms to solve the unconstrained binary quadratic programming (UBQP) problem. One is based on a greedy strategy to generate the relinking path from the initial solution to the guiding solution and the other operates in a random way. We show extensive computational results on five sets of benchmarks, including 31 large random UBQP instances and 103 structured instances derived from the MaxCut problem. Comparisons with several state-of-the-art algorithms demonstrate the efficacy of our proposed algorithms in terms of both solution quality and computational efficiency. It is noteworthy that both algorithms are able to improve the previous best known results for almost 40 percent of the 103 MaxCut instances.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 223 (2012)
    Issue (Month): 3 ()
    Pages: 595-604

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    Handle: RePEc:eee:ejores:v:223:y:2012:i:3:p:595-604

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    Related research

    Keywords: UBQP; Path relinking; Tabu search; MaxCut;

    References

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    1. R. D. McBride & J. S. Yormark, 1980. "An Implicit Enumeration Algorithm for Quadratic Integer Programming," Management Science, INFORMS, vol. 26(3), pages 282-296, March.
    2. Lü, Zhipeng & Glover, Fred & Hao, Jin-Kao, 2010. "A hybrid metaheuristic approach to solving the UBQP problem," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1254-1262, December.
    3. Katayama, Kengo & Narihisa, Hiroyuki, 2001. "Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem," European Journal of Operational Research, Elsevier, vol. 134(1), pages 103-119, October.
    4. Fred Glover & Gary A. Kochenberger & Bahram Alidaee, 1998. "Adaptive Memory Tabu Search for Binary Quadratic Programs," Management Science, INFORMS, vol. 44(3), pages 336-345, March.
    5. Alidaee, Bahram & Kochenberger, Gary & Lewis, Karen & Lewis, Mark & Wang, Haibo, 2008. "A new approach for modeling and solving set packing problems," European Journal of Operational Research, Elsevier, vol. 186(2), pages 504-512, April.
    6. Lodi, Andrea & Allemand, Kim & Liebling, Thomas M., 1999. "An evolutionary heuristic for quadratic 0-1 programming," European Journal of Operational Research, Elsevier, vol. 119(3), pages 662-670, December.
    7. Delorme, Xavier & Gandibleux, Xavier & Rodriguez, Joaquin, 2004. "GRASP for set packing problems," European Journal of Operational Research, Elsevier, vol. 153(3), pages 564-580, March.
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