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Backbone analysis and algorithm design for the quadratic assignment problem

  • He JiangEmail author
  • XianChao Zhang
  • GuoLiang Chen
  • MingChu Li
Article

Abstract

As the hot line in NP-hard problems research in recent years, backbone analysis is crucial for phase transition, hardness, and algorithm design. Whereas theoretical analysis of backbone and its applications in algorithm design are still at a beginning state yet, this paper took the quadratic assignment problem (QAP) as a case study and proved by theoretical analysis that it is NP-hard to find the backbone, i.e., no algorithm exists to obtain the backbone of a QAP in polynomial time. Results of this paper showed that it is reasonable to acquire approximate backbone by intersection of local optimal solutions. Furthermore, with the method of constructing biased instances, this paper proposed a new meta-heuristic—biased instance based approximate backbone (BI-AB), whose basic idea is as follows: firstly, construct a new biased instance for every QAP instance (the optimal solution of the new instance is also optimal for the original one); secondly, the approximate backbone is obtained by intersection of multiple local optimal solutions computed by some existing algorithm; finally, search for the optimal solutions in the reduced space by fixing the approximate backbone. Work of the paper enhanced the research area of theoretical analysis of backbone. The meta-heuristic proposed in this paper provided a new way for general algorithm design of NP-hard problems as well.

Keywords

quadratic assignment problem NP-hard backbone analysis biased instance meta-heuristic 

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Copyright information

© Science in China Press 2008

Authors and Affiliations

  • He Jiang
    • 1
    • 2
    Email author
  • XianChao Zhang
    • 1
  • GuoLiang Chen
    • 2
  • MingChu Li
    • 1
  1. 1.School of SoftwareDalian University of TechnologyDalianChina
  2. 2.Department of Computer ScienceUniversity of Science and Technology of ChinaHefeiChina

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