A striking characteristic of high-tech products is the rapid decrease of their quality-adjusted prices. Empirical studies show that the rate of decrease of QAPs is typically not constant over time; QAPs decrease rapidly at early stages of the product and then the rate of decrease tapers o®. Studies also suggest that the QAP is positively correlated with the rate of product introductions: The fa...

In this paper, a new concept distance called permutation distance is proposed and exploited in detail. We combine it with the hamming distance and propose a group of new neighborhood structures in VNS for QAP. Numerical tests running on the standard benchmark library QAPLIB show that this approach would dramatically improve the performance of VNS for QAP.

The molecular conformation problem is discussed, and a concave quadratic global minimization approach for solving it is described. This approach is based on a quadratic assignment formulation of a discrete approximation to the original problem.

Finding global optimum of a non-convex quadratic function is in general a very difficult task even when the feasible set is a polyhedron. We show that when the feasible set of a quadratic problem consists of orthogonal matrices from Rn×k, then we can transform it into a semidefinite program in matrices of order kn which has the same optimal value. This opens new possibilities to get good lower ...

The quadratic assignment problem (denoted QAP), in the trace formulation over the permutation matrices, is min X2 tr(AXB + C)X t : Several recent lower bounds for QAP are discussed. These bounds are obtained by applying continuous optimization techniques to approximations of this combinatorial optimization problem, as well as by exploiting the special matrix structure of the problem. In particu...

Quadratic Assignment problems are in practice among the most diicult to solve in the class of NP-complete problems. The only successful approach hitherto has been Branch-and-Bound-based algorithms, but such algorithms are crucially dependent on good bound functions to limit the size of the space searched. Much work has been done to identify such functions for the QAP, but with limited success. ...

Quadratic Assignment is a basic problem in combinatorial optimization, which generalizes several other problems such as Traveling Salesman, Linear Arrangement, Dense k Subgraph, and Clustering with given sizes. The input to the Quadratic Assignment Problem consists of two n × n symmetric non-negative matrices W = (wi,j) and D = (di,j). Given matrices W , D, and a permutation π : [n] → [n], the ...

A typical example of the quadratic assignment problem (QAP) is the facility location problem, in which a set of n facilities are to be assigned, at minimum cost, to an equal number of locations. Between each pair of facilities, there is a given amount of flow, contributing a cost equal to the product of the flow and the distance between locations to which the facilities are assigned. Proving op...

We study a generalization of the quadratic assignment problem (QAP) by allowing multiple equipments to be assigned at a single location as long as resources at the location permit. This problem arises in many real world applications such as facility location problem and logistics network design. We call the problem as the generalized quadratic assignment problem (GQAP) and show that this relaxa...