In this paper we propose the Graduated NonConvexity and Graduated Concavity Procedure (GNCGCP) as a general optimization framework to approximately solve the combinatorial optimization problems on the set of partial permutation matrices. GNCGCP comprises two sub-procedures, graduated nonconvexity (GNC) which realizes a convex relaxation and graduated concavity (GC) which realizes a concave rela...

The generalized quadratic assignment problem (GQAP) is a generalization of the NP-hard quadratic assignment problem (QAP) that allows multiple facilities to be assigned to a single location as long as the capacity of the location allows. The GQAP has numerous applications, including facility design, scheduling, and network design. In this paper, we propose several GRASP with path-relinking heur...

Particle Swarm Optimization (PSO) algorithm has exhibited good performance across a wide range of application problems. But research on the Quadratic Assignment Problem (QAP) has not much been investigated. In this paper, we introduce a novel approach based on PSO for QAPs. The representations of the position and velocity of the particles in the conventional PSO is extended from the real vector...

We present an integer linear formulation that uses the so-called “distance variables” to solve the quadratic assignment problem (QAP). The model involves O(n) variables. Valid equalities and inequalities are additionally proposed. We further improved the model by using metric properties as well as an algebraic characterization of the Manhattan distance matrices that Mittelman and Peng [28] rece...

This paper is concerned with automated tuning of parameters in local-search based meta-heuristics. Several generic approaches have been introduced in the literature that returns a ”one-size-fits-all” parameter configuration for all instances. This is unsatisfactory since different instances may require the algorithm to use very different parameter configurations in order to find good solutions....

We apply the level-3 Reformulation Linearization Technique (RLT3) to the Quadratic Assignment Problem (QAP). We then present our experience in calculating lower bounds using an essentially new algorithm, based on this RLT3 formulation. This algorithm is not guaranteed to calculate the RLT3 lower bound exactly, but approximates it very closely and reaches it in some instances. For Nugent problem...

The problem of designing new keyboards layouts able to improve the typ-ing speed of an average message has been widely considered in the literature ofthe Ergonomics domain. Empirical tests with users and simple optimizationcriteria have been used to propose new solutions. On the contrary, very fewpapers in Operations Research have addressed this optimization problem. Inthis ...

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...

The application of the Reformulation Linearization Technique (RLT) to the Quadratic Assignment Problem (QAP) leads to a tight linear relaxation with huge dimensions that is hard to solve. Previous works found in the literature show that these relaxations combined with branch-and-bound algorithms belong to the state-of-the-art of exact methods for the QAP. For the level 3 RLT (RLT3), using this ...

The quadratic assignment problem (QAP) is among the hardest combinatorial optimization problems. Some instances of size n = 30 have remained unsolved for decades. The solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful computational platforms. In this article we describe a novel approach to solve QAPs using a state-of-the-...