Autocorrelation Measures for the Quadratic Assignment Problem

Abstract

In this article we provide an exact expression for computing the autocorrelation coefficient $\xi$ and the autocorrelation length $\ell$ of any arbitrary instance of the Quadratic Assignment Problem (QAP) in polynomial time using its elementary landscape decomposition. We also provide empirical evidence of the autocorrelation length conjecture in QAP and compute the parameters $\xi$ and $\ell$ for the 137 instances of the QAPLIB. Our goal is to better characterize the difficulty of this important class of problems to ease the future definition of new optimization methods. Also, the advance that this represents helps to consolidate QAP as an interesting and now better understood problem.