Enhanced firefly algorithm for constrained numerical optimization

Firefly algorithm is one of the recent and very promising swarm intelligence metaheuristics for tackling hard optimization problems. While firefly algorithm has been proven on various numerical and engineering optimization problems as a robust metaheuristic, it was not properly tested on a wide set of constrained benchmark functions. We performed testing of the original firefly algorithm on a set of standard 13 benchmark functions for constrained problems and it exhibited certain deficiencies, primarily insufficient exploration during early stage of the search. In this paper we propose enhanced firefly algorithm where main improvements are correlated to the hybridization with the exploration mechanism from another swarm intelligence algorithm, introduction of new exploitation mechanism and parameter-based tuning of the exploration-exploitation balance. We tested our approach on the same standard benchmark functions and showed that it not only overcame weaknesses of the original firefly algorithm, but also outperformed other state-of-the-art swarm intelligence algorithms.