Performance ratio of polynomial heuristics for triangle inequality quadratic assignment problems

  • Authors:

  • Maurice Queyranne

  • Affiliations:

  • University of British Columbia, Vancouver, B.C., Canada V6T 1 W5

  • Venue:
  • Operations Research Letters
  • Year:
  • 1986

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Abstract

We consider the Koopman's-Beckmann version of the Quadratic Assignment Problem, with a distance matrix satisfying the triangle inequality. It is shown that, unless P = NP, no polynomial heuristic can have a bounded performance ratio. This result holds when candidate locations can be arbitrary (distinct) points on the line, or in a metric space. It is not known to hold when candidate locations are regularly spaced points on the line - the Linear Arrangement Problem, grid points in the plane, or otherwise regularly spaced points in a metric space. Other open problems are the Triangle Inequality Asymmetric Travelling Salesman Problem, and the Unit Cost Triangle Inequality Quadratic Assignment Problem.