We consider transformations of the (metric) Quadratic Assignment Problem (QAP), that exploit the metric structure of a given instance. We show in particular, how the structural properties of rectangular grids can be used to improve a given lower bound. Our work is motivated by previous research of G.S. Palubetskes, and it extends a bounding approach proposed by J. Chakrapani and J. Skorin-Kapov...

Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan Leeds School of Business, University of Colorado at Boulder, Campus Box 419, Boulder, Colorado 80309-0419, USA [email protected] • [email protected]...

We address the exact solution of the famous esc instances of the quadratic assignment problem. These are extremely hard instances that remained unsolved—even allowing for a tremendous computing power—by using all previous techniques from the literature. During this challenging task we found that three ideas were particularly useful, and qualified as a breakthrough for our approach. The present ...

An assignment problem (AP) is a meticulous case ofa transportation problem, in which the goal to allocate number of facilities an equal activities at overall maximum profit (or minimum cost, distance, time). It occupies verysignificantrole real physical world. The well-known method applied solve APs Hungarian method, generates optimal solution given AP. A little bit difficulty cover all zero en...