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A Branch and Bound Algorithm for the Quadratic Assignment Problem using a Lower Bound Based on Linear Programming

  • K. G. Ramakrishnan
  • Mauricio G. C. Resende
  • Panos M. Pardalos
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 7)

Abstract

In this paper, we study a branch and bound algorithm for the quadratic assignment problem (QAP) that uses a lower bound based on the linear programming (LP) relaxation of a classical integer programming formulation of the QAP. We report on computational experience with the branch and bound algorithm on all QAP test problems of dimension n ≤ 15 of QAPLIB, a standard library of QAP test problems. The linear programming relaxations are solved with an implementation of an interior point algorithm that uses a preconditioned conjugate gradient algorithm to compute directions. The branch and bound algorithm is compared with a similar branch and bound algorithm that uses the Gilmore-Lawler lower bound (GLB) instead of the LP-based bound. The LP-based algorithm examines a small portion of the nodes explored by the GLB-based algorithm. Extensions to the implementation are discussed.

Keywords

Branch and Bound Combinatorial Optimization Interior Point Methods Linear Programming Lower Bounds Quadratic Assignment Problem 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • K. G. Ramakrishnan
    • 1
  • Mauricio G. C. Resende
    • 2
  • Panos M. Pardalos
    • 3
  1. 1.AT&T Bell LaboratoriesUSA
  2. 2.AT&T Bell LaboratoriesUSA
  3. 3.University of FloridaUSA

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