A new relaxation framework for quadratic assignment problems based on matrix splitting

Jiming Peng, Hans Mittelmann, Xiaoxue Li

Research output: Contribution to journalArticle

17 Scopus citations


Quadratic assignment problems (QAPs) are known to be among the hardest discrete optimization problems. Recent study shows that even obtaining a strong lower bound for QAPs is a computational challenge. In this paper, we first discuss how to construct new simple convex relaxations of QAPs based on various matrix splitting schemes. Then we introduce the so-called symmetric mappings that can be used to derive strong cuts for the proposed relaxation model. We show that the bounds based on the new models are comparable to some strong bounds in the literature. Promising experimental results based on the new relaxations are reported.

Original languageEnglish (US)
Pages (from-to)59-77
Number of pages19
JournalMathematical Programming Computation
Issue number1
StatePublished - Mar 8 2010



  • Lower bound
  • Matrix splitting
  • Quadratic assignment problem (QAP)
  • Relaxation
  • Semidefinite programming (SDP)

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software

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