Firefly-inspired algorithm for discrete optimization problems: An application to manufacturing cell formation

The canonical firefly algorithm is basically developed for continuous optimization problems. However, lots of practical problems are formulated as discrete optimization problems. The main purpose of this paper is to present the discrete firefly algorithm (DFA) to solve discrete optimization problems. In the DFA, we define a firefly's position in terms of changes of probabilities that will be in one state or the other. Then by using this metaheuristic algorithm, the manufacturing cell formation problem is solved. To illustrate the behavior of the proposed model and verify the performance of the algorithm, we introduce a number of numerical examples to illustrate the use of the foregoing algorithm. The performance evaluation shows the effectiveness of the DFA. The proposed metaheuristic algorithm should thus be useful to both researchers and practitioners.