Classes of quadratic assignment problem instances: isomorphism and difficulty measure using a statistical approach

In this work, we introduce the variance expression for quadratic assignment problem (QAP) costs. We also de;ne classes of QAP instances, described by a common linear relaxation form. The use of the variance in these classes leads to the study of isomorphism and allows for a de;nition of a new di"culty index for QAP instances. This index is then compared to a classical measure found in the literature. ? 2002 Elsevier Science B.V. All rights reserved.