The issue tackled is testing whether a given solution of a quadratic 0-1 problem is optimal. The paper presents an algorithm based on the necessary and sufficient optimality condition introduced by Hirriart-Urruty for general convex problems. A measure of the quality of the solution is provided. Computational results show the applicability of the method. The method is extended to constrained qu...

This study uses data on campaign contributions and methods of network analysis to investigate the significance of interlocking directorates for political cohesion among corporate elites. Using quadratic assignment procedure (QAP) regression, the author shows that social ties formed through common membership on corporate boards contribute more to similarity of political behavior than commonaliti...

The quadratic assignment problem (QAP) is arguably one of the hardest NP-hard discrete optimization problems. Problems of dimension greater than 25 are still considered to be large scale. Current successful solution techniques use branch-and-bound methods, which rely on obtaining strong and inexpensive bounds. In this paper, we introduce a new semidefinite programming (SDP) relaxation for gener...

Recent progress in solving quadratic assignment problems (QAPs) from the QAPLIB test set has come from mixed integer linear or quadratic programming models that are solved in a branchand-bound framework. Semide nite programming bounds for QAP have also been studied in some detail, but their computational impact has been limited so far, mostly due to the restrictive size of the early relaxations...

The Vehicle Positioning Problem (VPP) is a classical combinato-rial optimization problem that has a natural formulation as an integer quadratic program. This MIQCP is closely related to the Quadratic Assignment Problem and, as far as we know, has not received any attention yet. We show in this article that such a formulation has interesting theoretical properties. Its QP relaxation produces, in...

The quadratic assignment problem (QAP) is one of the great challenges in combinatorial optimization. Linearization for QAP is to transform the quadratic objective function into a linear one. Numerous QAP linearizations have been proposed, most of which yield mixed integer linear programs (MILP). Kauffmann and Broeckx’s linearization (KBL) is the current smallest one in terms of the number of va...

In this paper we show that the optimization of several ranking-based performance measures, such as precision-at-k and average-precision, is intimately related to the solution of quadratic assignment problems. Both the task of test-time prediction of the best ranking and the task of constraint generation in estimators based on structured support vector machines can all be seen as special cases o...

The quadratic assignment problem (QAP) belongs to the class of NP -hard combinatorial optimization problems. Although it has been studied extensively over the past 35 years, problems of size n 15 still prove to be intractable. Since good lower bounds are necessary to solve larger problem instances, we discuss the class of eigenvalue bounds for QAP and extend previous results of these continuous...

We investigate a special case of the maximum quadratic assignment problem where one matrix is a product matrix and the other matrix is the distance matrix of a one-dimensional point set. We show that this special case, which we call the Wiener maximum quadratic assignment problem, is NP-hard in the ordinary sense and solvable in pseudo-polynomial time. Our approach also yields a polynomial time...