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...

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 ...

a new powerful optimization algorithm inspired from colonizing weeds is utilized to solve the well-known quadratic assignment problem (qap) which is of application in a large number of practical areas such as plant layout, machinery layout and so on. a set of reference numerical problems from qaplib is taken in order to evaluate the efficiency of the algorithm compared with the previous ones wh...

Changing the QAP's hard definition such that the facilities M are allowed to be mapped by a (single-valued, not necessarily injective) function π into the set of possible locations Y subject to a relation Π, π ⊆ Π, it arises the Semi-QAP that might be regarded as a relaxation of the QAP. In contrast to the Tree-QAP (flow graph F is a tree) the corresponding Semi-Tree-QAP is solvable in polynomi...

This paper aims at describing the state of the art on quadratic assignment problems (QAPs). It discusses the most important developments in all aspects of the QAP such as linearizations, QAP polyhedra, algorithms to solve the problem to optimality, heuristics, polynomially solvable special cases, and asymptotic behavior. Moreover, it also considers problems related to the QAP, e.g. the biquadra...

General quadratic matrix minimization problems, with orthogonal constraints, arise in continuous relaxations for the (discrete) quadratic assignment problem (QAP). Currently, bounds for QAP are obtained by treating the quadratic and linear parts of the objective function, of the relaxations, separately. This paper handles general objectives as one function. The objectives can be both nonhomogen...

We model the problem of monolingual textual alignment as a Quadratic Assignment Problem (QAP) which simultaneously maximizes the global lexicosemantic and syntactic similarities of two sentence-level texts. Because QAP is an NP-complete problem, we propose a branch-and-bound approach to efficiently find an optimal solution. When compared with other methods and studies, our results are competitive.

Since 2004, the Computational Optimization and Applications (COAP) editorial board has selected a paper from the preceding year’s COAP publications for the “Best Paper Award.” The award competition among papers published in 2008 culminated in a tie between two papers. This article concerns the award winning work of Peter Hahn, Bum-Jin Kim, Monique Guignard-Spielberg and Yi-Rong Zhu at the Unive...