The quadratic assignment problem (QAP) was introduced in 1957 by
Koopmans and Beckmann to model a plant location problem. Since then the
QAP has been object of numerous investigations by mathematicians,
computers scientists, ope- tions researchers and practitioners. Nowadays
the QAP is widely considered as a classical combinatorial optimization
problem which is (still) attractive from many points of view. In our
opinion there are at last three main reasons which make the QAP a
popular problem in combinatorial optimization. First, the number of re-
life problems which are mathematically modeled by QAPs has been
continuously increasing and the variety of the fields they belong to is
astonishing. To recall just a restricted number among the applications
of the QAP let us mention placement problems, scheduling, manufacturing,
VLSI design, statistical data analysis, and parallel and distributed
computing. Secondly, a number of other well known c- binatorial
optimization problems can be formulated as QAPs. Typical examples are
the traveling salesman problem and a large number of optimization
problems in graphs such as the maximum clique problem, the graph
partitioning problem and the minimum feedback arc set problem. Finally,
from a computational point of view the QAP is a very difficult problem.
The QAP is not only NP-hard and - hard to approximate, but it is also
practically intractable: it is generally considered as impossible to
solve (to optimality) QAP instances of size larger than 20 within
reasonable time limits.
