The quadratic assignment problem is a well studied and notoriously difficult combinatorial problem. Recently, a discrete linear formulation of the quadratic assignment problem was presented that solved five previously unsolved instances from the quadratic assignment library, QAPLIB, to optimality. That formulation worked especially well on sparse instances. In this paper we show how to tighten ...

This paper proposes a genetic algorithm based on a new replacement strategy to solve the quadratic assignment problems, which are NP-hard. The new replacement strategy aims to improve the performance of the genetic algorithm through well balancing the convergence of the searching process and the diversity of the population. In order to test the performance of the algorithm, the instances in QAP...

Variances of solution values that can be calculated in polynomial time may be associated with an instance of the Quadratic Assignment Problem (QAP). The problem of graph isomorphism can be modeled as a QAP, associating each data matrix with each graph. In this work, we look for invariant edge weight functions for the graphs composing the instances in order to try to find quantitative difference...

This paper presents a history of a difficult facility layout problem that falls into the category of the Koopmans-Beckmann variant of the Quadratic Assignment Problem (QAP), wherein 30 facilities are to be assigned to 30 locations. The problem arose in 1972 as part of the design of a German university hospital, Klinikum Regensburg. This problem, known as the Krarup30a upon its inclusion in the ...

This paper reports heuristic and exact solution advances for the Quadratic Assignment Problem (QAP). QAP instances frequently used 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 instances a...

This paper seeks to raise awareness of some negative phenomena in science. It happens more and more frequently that somebody carries out research in one field but finds that the results are not strong enough for publication and then submits them to be published in a related but not identical field as an application. The Quadratic Assignment Problem (QAP) is known as one of the most difficult pr...

We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans-Beckman form QAP(A,B), by showing that the identity permutation is optimal when A and B are respectively a Robinson similarity and dissimilarity matrix and one of A or B is a Toeplitz matrix. A Robinson (dis)similarity matrix is a symmetric matrix whose entries (increase) decrease monotonically along row...

The quadratic assignment problem (QAP) is among the hardest combinatorial optimization problems. Very few instances of this problem can be solved in polynomial time. In this paper we address the problem of allocating rooms among people in a suitable shape of corridor with some constraints of undesired neighborhood. We give a linear time algorithm for this problem that we formulate as a QAP. c ©...

Lower bounds on the bandwidth, the size of a vertex separator of general undirected graphs, and the largest common subgraph of two undirected (weighted) graphs are obtained. The bounds are based on a projection technique developed for the quadratic assignment problem, and once more demonstrate the importance of the extreme eigenvalues of the Laplacian. They will be shown to be strict for certai...

This paper presents the Anisotropic selection scheme for cellular Genetic Algorithms (cGA). This new scheme allows to enhance diversity and to control the selective pressure which are two important issues in Genetic Algorithms, especially when trying to solve difficult optimization problems. Varying the anisotropic degree of selection allows swapping from a cellular to an island model of parall...