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 ©...

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 research is concerned with the development of an exact algorithm for a general quadratic assignment problem (QAP), of which the Koopmans-Beckmann formulation, in the context of an analysis of the location of economic activities or facilities, is a special case. The algorithm is based on the linearization of a general QAP of size n into a linear assignment problem of size n(n-l)/2. The obje...

The Quadratic Assignment Problem (QAP) is an NP-Complete problem [1]. The multiobjective Quadratic Assignment Problem (mQAP) is the multiobjective version of the QAP and was formalized in 2002 [2]. The QAP has had extensive research, but mQAP research is still in its infancy. The mQAP has been been used to optimize communication for formations of heterogenous unmanned aerial vehicles (UAVs) thr...

This paper investigates a restricted version of the Quadratic Assignment Problem (QAP), where one of the coefficient matrices is an Anti-Monge matrix with non-decreasing rows and columns and the other coefficient matrix is a symmetric Toeplitz matrix. This restricted version is called the Anti-Monge–Toeplitz QAP. There are three well-known combinatorial problems that can be modeled via the Anti...

In this work, we introduce the variance expression for quadratic assignment problem (QAP) costs. We also de;ne classes of QAP instances, described by a common linear relaxation form. The use of the variance in these classes leads to the study of isomorphism and allows for a de;nition of a new di"culty index for QAP instances. This index is then compared to a classical measure found in the liter...

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.

In this paper we show that even for the case of 1:1 substitution ciphers—which encipher plaintext symbols by exchanging them with a unique substitute—finding the optimal decipherment with respect to a bigram language model is NP-hard. We show that in this case the decipherment problem is equivalent to the quadratic assignment problem (QAP). To the best of our knowledge, this connection between ...

Semidefinite relaxations of the quadratic assignment problem (QAP ) have recently turned out to provide good approximations to the optimal value of QAP . We take a systematic look at various conic relaxations of QAP . We first show that QAP can equivalently be formulated as a linear program over the cone of completely positive matrices. Since it is hard to optimize over this cone, we also look ...

The quadratic assignment problem (QAP) is one of the most difficult combinatorial optimization problems. An effective heuristic for obtaining approximate solutions to the QAP is simulated annealing (SA). Here we describe an SA implementation for the QAP which runs on a graphics processing unit (GPU). GPUs are composed of low cost commodity graphics chips which in combination provide a powerful ...