On the performance of parallel hybrid algorithms for the solution of the quadratic assignment problem

Abstract

The quadratic assignment problem (QAP) is a combinatorial optimization problem, which is computationally demanding, and considered to be NP-hard. Therefore, the problem cannot be solved in polynomial time. The known sequential algorithms can solve small problem instances within long computational times; moreover, parallelization may provide only a linear speed-up. Near-optimal solutions can be obtained in feasible times using heuristics like genetic algorithms and tabu search. The QAP algorithms can be modified to solve various problems like the travelling salesman problem, the data allocation problem, and the file allocation problem. In this paper, a parallel hybrid algorithm (PHA) with three stages was proposed. In the first stage, a genetic algorithm was used to obtain a high quality seed. Later, a diversification phase was run on the initial seed. Finally, a robust tabu search was run on the intermediate solution to find a near-optimal result. Parallel computing was used to increase the seed quality, and a considerable speed-up was obtained in the diversification phase of the tabu search. The QAPLIB benchmark instances were used to conduct the experiments. The PHA is quite competitive with respect to the best-performing algorithms in the literature in terms of solution quality and execution time. It achieves results on average within 0.05% of the best solutions given in the QAPLIB. The PHA was able to solve even the largest problem instance size of 256 within 11h, and with a higher accuracy than the best-known solutions. It was also observed that the solution quality improved considerably especially for larger instances, when the degree of parallelism increased.