A solvable case of the quadratic assignment problem

Abstract

This short note investigates a restricted version of the quadratic assignment problem (QAP), where one of the coefficient matrices is a Kalmanson matrix, and where the other coefficient matrix is a symmetric circulant matrix that is generated by a decreasing function. This restricted version is called the Kalmanson-circulant QAP. We prove that - in strong contrast to the general QAP - this version can be solved easily. Our result naturally generalizes a well-known theorem of Kalmanson on the travelling salesman problem. © 1998 Elsevier Science B.V. All rights reserved.