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Advances in Operations Research
Volume 2014, Article ID 215182, 12 pages
Research Article

Heuristic-Based Firefly Algorithm for Bound Constrained Nonlinear Binary Optimization

1Department of Mathematics and Applications, Centre of Mathematics, University of Minho, 4710-057 Braga, Portugal
2Algoritmi Research Centre, University of Minho, 4710-057 Braga, Portugal

Received 30 May 2014; Accepted 20 September 2014; Published 8 October 2014

Academic Editor: Imed Kacem

Copyright © 2014 M. Fernanda P. Costa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Firefly algorithm (FA) is a metaheuristic for global optimization. In this paper, we address the practical testing of a heuristic-based FA (HBFA) for computing optima of discrete nonlinear optimization problems, where the discrete variables are of binary type. An important issue in FA is the formulation of attractiveness of each firefly which in turn affects its movement in the search space. Dynamic updating schemes are proposed for two parameters, one from the attractiveness term and the other from the randomization term. Three simple heuristics capable of transforming real continuous variables into binary ones are analyzed. A new sigmoid “erf” function is proposed. In the context of FA, three different implementations to incorporate the heuristics for binary variables into the algorithm are proposed. Based on a set of benchmark problems, a comparison is carried out with other binary dealing metaheuristics. The results demonstrate that the proposed HBFA is efficient and outperforms binary versions of differential evolution (DE) and particle swarm optimization (PSO). The HBFA also compares very favorably with angle modulated version of DE and PSO. It is shown that the variant of HBFA based on the sigmoid “erf” function with “movements in continuous space” is the best, in terms of both computational requirements and accuracy.