Firefly algorithm is a swarm-based search algorithm, in which fireflies interact with each other to look for the optimal solution to a given optimization problem in a provided search space. Even though the firefly algorithm has been shown good performance, researchers have not adequately explained how it works and effects of its control coefficients in terms of theory. Further, classical variants of the algorithm have unexpected parameter settings and limited update laws, notably the homogeneous rule needs to be improved in order to do more search in dealing with various problems. This study analyzes trajectory of a single firefly in both traditional algorithm and an adaptive variant based on our previous study, respectively. Accordingly, these analyses lead to a general model of the algorithms including a set of boundary conditions for selections of the control parameters guaranteeing the convergence tendencies of all individuals. The numerical experiments on twelve well-suited benchmark functions show the implementation of the proposed adaptive algorithm, which is derived from the analyses, can enhance the search ability of each individual in looking for the optima.
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Figure 1. The comparison of different strategies for the randomization parameter α.
Figure 2. Comparison of different algorithms (mean values of best-so-far) on the benchmark functions.