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

Jiming Peng, Hans Mittelmann, Xiaoxue Li

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

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
Volume2
Issue number1
DOIs
StatePublished - 2010

Fingerprint

Matrix Splitting
Quadratic Assignment Problem
Convex Relaxation
Discrete Optimization
Lower bound
Optimization Problem
Experimental Results
Model
Framework

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software

Cite this

A new relaxation framework for quadratic assignment problems based on matrix splitting. / Peng, Jiming; Mittelmann, Hans; Li, Xiaoxue.

In: Mathematical Programming Computation, Vol. 2, No. 1, 2010, p. 59-77.

Research output: Contribution to journalArticle

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