An Efficient Implementation of the Robust Tabu Search Heuristic for Sparse Quadratic Assignment Problems

We propose and develop an efficient implementation of the robust tabu search heuristic for sparse quadratic assignment problems. The traditional implementation of the heuristic applicable to all quadratic assignment problems is of O(N^2) complexity per iteration for problems of size N. Using multiple priority queues to determine the next best move instead of scanning all possible moves, and using adjacency lists to minimize the operations needed to determine the cost of moves, we reduce the asymptotic complexity per iteration to O(N log N ). For practical sized problems, the complexity is O(N)

РОЗВ’ЯЗУВАННЯ КВАДРАТИЧНОЇ ЗАДАЧІ ПРО ПРИЗНАЧЕННЯ

Стаття присвячена проблемі розв’язання квадратичної задачі про призначення (QAP) з використанням сучасних методів оптимізації. В статті розглянуто декілька різних методів дослідження QAP, але вони не знаходять найкращі розв’язки та потребують багато часу. В роботі використано метод Франка-Вулфа, який потребує досить мало часу, навіть при розв’язуванні задач великої розмірності. Далі для розв’язування задачі QAP використано точну квадратичну регуляризацію. Це дозволяє отримувати найкращі розв’язки в задачі QAP навіть для задач великої розмірності. Проведені порівняльні числові експерименти підтверджують ефективність методу точної квадратичної регуляризації при розв’язуванні задач QAP.

Hybrid Algorithm for Solving the Quadratic Assignment Problem

The Quadratic Assignment Problem (QAP) is a combinatorial optimization problem; it belongs to the class of NP-hard problems. This problem is applied in various fields such as hospital layout, scheduling parallel production lines and analyzing chemical reactions for organic compounds. In this paper we propose an application of Golden Ball algorithm mixed with Simulated Annealing (GBSA) to solve QAP. This algorithm is based on different concepts of football. The simulated annealing search can be blocked in a local optimum due to the unacceptable movements; our proposed strategy guides the simulated annealing search to escape from the local optima and to explore in an efficient way the search space. To validate the proposed approach, numerous simulations were conducted on 64 instances of QAPLIB to compare GBSA with existing algorithms in the literature of QAP. The obtained numerical results show that the GBSA produces optimal solutions in reasonable time; it has the better computational time. This work demonstrates that our proposed adaptation is effective in solving the quadratic assignment problem

Solving the Quadratic Assignment Problem by a Hybrid Algorithm

This paper presents a hybrid algorithm to solve the Quadratic Assignment Problem (QAP). The proposed algorithm involves using the Greedy Randomized Adaptive Search Procedure (GRASP) to obtain an initial solution, and then using a combined Simulated Annealing (SA) and Tabu Search (TS) algorithm to improve the solution. Experimental results  indicate that the hybrid algorithm is able to obtain good quality solutions for QAPLIB test problems within reasonable computation time

A Sule’s Method initiated genetic algorithm for solving QAP formulation in facility layout design: A real world application

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 applications. Hence, in this work, we propose the use of Sule’s Method and genetic algorithms, for a QAP (stated as a facility Layout Problem) in a real industry application in Colombia so that the total cost to move the required material between the facilities is minimized. As far as we know, this is the first work in which Sule’s Method and genetic algorithms are used simultaneously for this combinatorial optimization problem. Additionally the proposed approach was tested using well-known datasets from the literature in order to assure its efficiency

Solving the quadratic assignment problem by a Hybrid Algorithm

This paper presents a hybrid algorithm to solve the Quadratic Assignment Problem (QAP). The proposed algorithm involves using the Greedy Randomized Adaptive Search Procedure (GRASP) to obtain an initial solution, and then using a combined Simulated Annealing (SA) and Tabu Search (TS) algorithm to improve the solution. Experimental results  indicate that the hybrid algorithm is able to obtain good quality solutions for QAPLIB test problems within reasonable computation time

Solving the teacher assignment problem by two Metaheuristics

International Journal of Information and Management Sciences22173-86IIMS

Hybridization of modified sine cosine algorithm with tabu search for solving quadratic assignment problem

Sine Cosine Algorithm (SCA) is a population-based metaheuristic method that widely used to solve various optimization problem due to its ability in stabilizing between exploration and exploitation. However, SCA is rarely used to solve discrete optimization problem such as Quadratic Assignment Problem (QAP) due to the nature of its solution which produce continuous values and makes it challenging in solving discrete optimization problem. The SCA is also found to be trapped in local optima since its lacking in memorizing the moves. Besides, local search strategy is required in attaining superior results and it is usually designed based on the problem under study. Hence, this study aims to develop a hybrid modified SCA with Tabu Search (MSCA-TS) model to solve QAP. In QAP, a set of facilities is assigned to a set of locations to form a one-to-one assignment with minimum assignment cost. Firstly, the modified SCA (MSCA) model with cost-based local search strategy is developed. Then, the MSCA is hybridized with TS to prohibit revisiting the previous solutions. Finally, both designated models (MSCA and MSCA-TS) were tested on 60 QAP instances from QAPLIB. A sensitivity analysis is also performed to identify suitable parameter settings for both models. Comparison of results shows that MSCA-TS performs better than MSCA. The percentage of error and standard deviation for MSCA-TS are lower than the MSCA which are 2.4574 and 0.2968 respectively. The computational results also shows that the MSCA-TS is an effective and superior method in solving QAP when compared to the best-known solutions presented in the literature. The developed models may assist decision makers in searching the most suitable assignment for facilities and locations while minimizing cost