The Quadratic Assignment Problem is one of the hardest combinatorial optimization problems known. We present two new classes of instances of the Quadratic Assignment Problem that can be reduced to the Linear Assignment Problem and give polynomial time procedures to check whether or not an instance is an element of these classes. © 2011 Elsevier B.V. All rights reserved.

In this paper, a new concept distance called permutation distance is proposed and exploited in detail. We combine it with the hamming distance and propose a group of new neighborhood structures in VNS for QAP. Numerical tests running on the standard benchmark library QAPLIB show that this approach would dramatically improve the performance of VNS for QAP.

The molecular conformation problem is discussed, and a concave quadratic global minimization approach for solving it is described. This approach is based on a quadratic assignment formulation of a discrete approximation to the original problem.