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 ...

In this paper we define a class of edge-weighted graphs having nonnegatively valued bisections. We show experimentally that complete such graphs with more than three vertices and also some special graphs with only positive edges can be applied to improve the existing lower bounds for a version of the quadratic assignment problem, namely with a matrix composed of rectilinear distances between po...

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 is at the core of several real-life applications. Finding an optimal assignment is computationally very difficult, for many useful instances. The best results are obtained with hybrid heuristics, which result in complex solvers. We propose an alternate solution where hybridization is obtain by means of parallelism and cooperation between simple single-heuristic ...

In this article we provide an exact expression for computing the autocorrelation coefficient ξ and the autocorrelation length ℓ of any arbitrary instance of the Quadratic Assignment Problem (QAP) in polynomial time using its elementary landscape decomposition. We also provide empirical evidence of the autocorrelation length conjecture in QAP and compute the parameters ξ and ℓ for the 137 instan...

The paper presents a new heuristic method for the quadratic assignment problem. This method is based on an artificial ant system, hybridized with a fast local search. The method is easy to implement and numerical results show that it is fast and efficient for structured problems.

Program libraries are one way to make the cooperation between specialists from various fields successful: the separation of application-specific knowledge from applicationindependent tasks ensures portability, maintenance, extensibility, and flexibility. This paper demonstrates the success in combining problem-specific knowledge for the quadratic assignment problem (QAP) with the raw computing ...

The previously proposed cunning ant system (cAS), a variant of the ACO algorithm, worked well on the TSP and the results showed that the cAS could be one of the most promising ACO algorithms. In this paper, we apply cAS to solving QAP. We focus our main attention on the effects of applying local search and parallelization of the cAS. Results show promising performance of cAS on QAP.