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 matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in practice, but such SDPs typically scale badly, involving matrix variables of dimension n where n is the number of nodes. To achieve a speed up, we propose a ...

We consider three known bounds for the quadratic assignment problem (QAP): an eigenvalue, a convex programming (CQP), and semidefinite (SDP) bound. Since last two were not compared directly before, we prove that SDP bound is stronger than CQP then apply these to improve on discrete energy minimization problem, reformulated as QAP, which aims minimize potential between repulsive particles toric ...

| One of the most notorious network design problems is the Quadratic Assignment Problem (QAP). We develop an heuristic algorithm for QAPs along with an M/G/C/C state dependent queueing model for capturing congestion in the tra c system interconnecting the nodes in the network. Computational results are also presented.

3 Why Use SDP? 5 3.1 Tractable Relaxations of Max-Cut . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1.1 Simple Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.2 Trust Region Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.3 Box Constraint Relaxation . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.4 Eigenvalue Bound . . . . . . . . . . . . ...

Ant Colonies optimization take inspiration from the behavior of real ant colonies to solve optimization problems. This paper presents a parallel model for ant colonies to solve the quadratic assignment problem (QAP). The cooperation between simulated ants is provided by a pheromone matrix that plays the role of a global memory. The exploration of the search space is guided by the evolution of p...

The Quadratic Assignment Problem (QAP) has remained one of the great challenges in combinatorial optimization. It is still considered a computationally nontrivial task to solve modest size problems, say of size n = 20: The QAPLIB was rst published in 1991, in order to provide a uni ed testbed for QAP, accessible to the scienti c community. It consisted of virtually all QAP instances that were a...

This paper is concerned with automated tuning of parameters of algorithms to handle heterogeneous and large instances. We propose an automated parameter tuning framework with the capability to provide instance-specific parameter configurations. We report preliminary results on the Quadratic Assignment Problem (QAP) and show that our framework provides a significant improvement on solutions qual...

The quadratic assignment problem (QAP) is one of the most studied NPhard problems with various practical applications. In this work, we propose a powerful population-based memetic algorithm (called BMA) for QAP. BMA integrates an effective local optimization algorithm called Breakout Local Search (BLS) within the evolutionary computing framework which itself is based on a uniform crossover, a f...