This paper presents a history of a difficult facility layout problem that falls into the category of the Koopmans-Beckmann variant of the Quadratic Assignment Problem (QAP), wherein 30 facilities are to be assigned to 30 locations. The problem arose in 1972 as part of the design of a German university hospital, Klinikum Regensburg. This problem, known as the Krarup30a upon its inclusion in the ...

By the use of the GRIBB software for distributed computing across the Internet, we are investigating the obstacles and the potential for efficient parallelization of Branch and Bound algorithms. Experiments have been carried out using two different applications, i.e. the Quadratic Assignment Problem (QAP) and the Traveling Salesman Problem (TSP). The results confirm the potential of the approac...

In this paper, we introduce a new combinatorial optimization problem entitled the color mix (CMP), which is more general case of grey pattern quadratic assignment (GP-QAP). Also, propose an original hybrid genetic-iterated tabu search algorithm for heuristically solving CMP. addition, present both analytical solutions and graphical visualizations obtained solutions, clearly demonstrate excellen...

In this paper, an efficient hybrid genetic algorithm (HGA) and its variants for the wellknown combinatorial optimization problem, the quadratic assignment problem (QAP) are discussed. In particular, we tested our algorithms on a special type of QAPs, the structured quadratic assignment problems. The results from the computational experiments on this class of problems demonstrate that HGAs allow...

This paper considers the Quadratic Assignment Problem (QAP) as one of the most important issues in optimization. This NP-hard problem has been largely studied in the scientific literature, and exact and approximate (heuristic and meta-heuristic) approaches have been used mainly to optimize one or more objectives. However, most of these studies do not consider or are not tested in real applicati...

The Quadratic Assignment Problem, QAP, is a classic combinatorial optimization problem, classified as NP-hard and widely studied. This problem consists in assigning N facilities to N locations obeying the relation of 1 to 1, aiming to minimize costs of the displacement between the facilities. The application of Reformulation and Linearization Technique, RLT, to the QAP leads to a tight linear r...

This paper aims to highlight the motivations for investigating genetic algorithms (GAs) solve DNA Fragment Assembly (DNAFA) problem. DNAFA problem is an optimization that attempts reconstruct original sequence by finding shortest from a given set of fragments. continuation our previous research in which existence polynomial-time reduction into Traveling Salesman Problem (TSP) and Quadratic Assi...

This paper presents an improved as well as a completely new version of a mixed integer linear programming (MILP) formulation for solving the quadratic assignment problem (QAP) to global optimum. Both formulations work especially well on instances where at least one of the matrices is sparse. Modification schemes, to decrease the number of unique elements per row in symmetric instances, are pres...

We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans-Beckman form QAP(A,B), by showing that the identity permutation is optimal when A and B are respectively a Robinson similarity and dissimilarity matrix and one of A or B is a Toeplitz matrix. A Robinson (dis)similarity matrix is a symmetric matrix whose entries (increase) decrease monotonically along row...

In this paper, we show how an Extended Guided Local Search can be applied to the Quadratic Assignment Problem and show the extensions can improve its performance. GLS is a general, penalty-based meta-heuristic, which sits on top of local search algorithms, to help guide them out of local minima. GLS has been shown to be successful in solving a number of practical real life problems, such as the...