A Dual Framework for Lower Bounds of the Quadratic Assignment Problem Based on Linearization

Abstract.

A dual framework allowing the comparison of various bounds for the quadratic assignment problem (QAP) based on linearization, e.g. the bounds of Adams and Johnson, Carraresi and Malucelli, and Hahn and Grant, is presented. We discuss the differences of these bounds and propose a new and more general bounding procedure based on the dual of the linearization of Adams and Johnson. The new procedure has been applied to problems of dimension up to $n=72$, and the computational results indicate that the new bound competes well with existing linearization bounds and yields a good trade off between computation time and bound quality.