It was recently demonstrated that a well-known eigenvalue bound for the Quadratic Assignment Problem (QAP) actually corresponds to a semideenite programming (SDP) relaxation. However, for this bound to be computationally useful the assignment constraints of the QAP must rst be eliminated, and the bound then applied to a lower-dimensional problem. The resulting \projected eigenvalue bound" is on...

We describe a new convex quadratic programming bound for the quadratic assignment problem (QAP). The construction of the bound uses a semideenite programming representation of a basic eigenvalue bound for QAP. The new bound dominates the well-known projected eigenvalue bound, and appears to be competitive with existing bounds in the tradeoo between bound quality and computational eeort.

This paper reports heuristic and exact solution advances for the Quadratic Assignment Problem (QAP). QAP instances most often discussed in the literature are relatively well solved by heuristic approaches. Indeed, solutions at a fraction of one percent from the best known solution values are rapidly found by most heuristic methods. Exact methods are not able to prove optimality for these instan...

The quadratic assignment problem (QAP) is very challengeable and interesting problem that can model many real-life problems. In this paper, we will simply discuss the meaning of quadratic assignment problem, solving techniques and we will give a survey of some developments and researches.

Local search procedures are popular methods to solve combinatorial problems and neighborhood structures are the main part of those algorithms. This paper presents a new neighborhood for the Quadratic Assignment Problem. The proposed neighborhood is compared with the classical 2-exchange neighborhood.

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 ...