An O(n2)-Variables Linear Formulation for the Quadratic Assignment Problem

We present the first linear formulation using distance variables (used previously for the Linear Arrangement Problem) to solve the Quadratic Assignment Problem (QAP). The model involves O(n2) variables. It has been stengthened by facets and valid inequalities, and numerically tested with QAPLIB instances whose distance matrices are given by the shortest paths in grid graphs. For all the instances, the formulation provides competitive lower bound, in a fewer computational time, in comparison to other litterature techniques. For two of them, our model outperforms the existing techniques both in lower bound quality as well as in CPU time.