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The Quadratic Assignment Problem

  • Rainer E. Burkard
  • Eranda Çela
  • Panos M. Pardalos
  • Leonidas S. Pitsoulis
Chapter

Abstract

The quadratic assignment problem (QAP) was introduced by Koopmans and Beckmann in 1957 as a mathematical model for the location of a set of indivisible economical activities [113]. Consider the problem of allocating a set of facilities to a set of locations, with the cost being a function of the distance and flow between the facilities, plus costs associated with a facility being placed at a certain location. The objective is to assign each facility to a location such that the total cost is minimized. Specifically, we are given three n x n input matrices with real elements F = (f ij ), D = (d kl ) and B = (b ik ), where f ij is the flow between the facility i and facility j, d kl is the distance between the location k and location l, and b ik is the cost of placing facility i at location k. The Koopmans-Beckmann version of the QAP can be formulated as follows: Let n be the number of facilities and locations and denote by N the set N = {1, 2,..., n}.

Keywords

Tabu Search Travel Salesman Problem Travel Salesman Problem Master Problem Greedy Randomize Adaptive Search Procedure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Rainer E. Burkard
    • 1
  • Eranda Çela
    • 1
  • Panos M. Pardalos
    • 2
  • Leonidas S. Pitsoulis
    • 2
  1. 1.Institute of MathematicsTechnical University GrazGrazAustria
  2. 2.Center for Applied Optimization, Industrial and Systems Engineering DepartmentUniversity of FloridaGainesvilleUSA

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