An improved firefly algorithm for numerical optimization problems and it's application in constrained optimization

Metaheuristic algorithms are successful methods of optimization. The firefly algorithm is one of the known metaheuristic algorithms used in a variety of applications. Recently, a new and efficient version of this algorithm was introduced as NEFA, which indicated a good performance in solving optimization problems. However, the introduced attraction model in this algorithm may not provide good coverage of the search space and thus trap the algorithm in a local optimum. In this paper, a new and efficient improved firefly algorithm called INEFA is proposed to improve the performance of NEFA. In INEFA, a new model of attraction is introduced in which each firefly can be attracted to brighter fireflies located in different areas of the search space, using the clustering concept to classify fireflies. To evaluate the performance of INEFA, it was used to optimize several known benchmark functions. The results were compared with the results of the firefly algorithm and some of its known improvements. The comparison of results indicated the significant power of INEFA compared to the algorithms. It was used to evaluate its application in solving a constrained optimization problem. The comparison results showed that INEFA performs better than most of the compared algorithms.