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Path relinking for unconstrained binary quadratic programming

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

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.

Suggested Citation

  • Wang, Yang & Lü, Zhipeng & Glover, Fred & Hao, Jin-Kao, 2012. "Path relinking for unconstrained binary quadratic programming," European Journal of Operational Research, Elsevier, vol. 223(3), pages 595-604.
  • Handle: RePEc:eee:ejores:v:223:y:2012:i:3:p:595-604
    DOI: 10.1016/j.ejor.2012.07.012
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
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    Cited by:

    1. repec:spr:annopr:v:238:y:2016:i:1:d:10.1007_s10479-015-2076-1 is not listed on IDEAS
    2. Punnen, Abraham P. & Wang, Yang, 2016. "The bipartite quadratic assignment problem and extensions," European Journal of Operational Research, Elsevier, vol. 250(3), pages 715-725.
    3. Gili Rosenberg & Mohammad Vazifeh & Brad Woods & Eldad Haber, 2016. "Building an iterative heuristic solver for a quantum annealer," Computational Optimization and Applications, Springer, vol. 65(3), pages 845-869, December.
    4. Glover, Fred & Ye, Tao & Punnen, Abraham P. & Kochenberger, Gary, 2015. "Integrating tabu search and VLSN search to develop enhanced algorithms: A case study using bipartite boolean quadratic programs," European Journal of Operational Research, Elsevier, vol. 241(3), pages 697-707.
    5. Wang, Yang & Wu, Qinghua & Glover, Fred, 2017. "Effective metaheuristic algorithms for the minimum differential dispersion problem," European Journal of Operational Research, Elsevier, vol. 258(3), pages 829-843.

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    Keywords

    UBQP; Path relinking; Tabu search; MaxCut;

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