Firefly algorithm
Introduction In mathematical optimization, the '''firefly algorithm''' is a metaheuristic proposed by Xin-She Yang and inspired by the flashing behavior of fireflies.
Algorithm In pseudocode the algorithm can be stated as: '''Begin'''     1) Objective function:      2) Generate an initial population of fireflies      3) Formulate light intensity  so that it is associated with         (for example, for maximization problems,      4) Define absorption coefficient       '''while''' (t < MaxGeneration)         '''for''' i = 1 : n (all n fireflies)             '''for''' j = 1 : i (n fireflies)                                      Vary attractiveness with distance r via                      move firefly i towards j;                                     Evaluate new solutions and update light intensity;                 '''end if'''              '''end for''' j         '''end for''' i         Rank fireflies and find the current best;     '''end while''' '''end'''Note that the number of objective function evaluations per loop is one evaluation per firefly, even though the above pseudocode suggests it is ''n''×''n''. (Based on Yang's MATLAB code.) Thus the total number of objective function evaluations is (number of generations) × (number of fireflies).The main update formula for any pair of two fireflies  and  is:: where  is a parameter controlling the step size, while  is a vector drawn from a Gaussian or otherdistribution.zaeIt can be shown that the limiting case  corresponds to the standard Particle Swarm Optimization (PSO). In fact, if the inner loop (for j) is removed and the brightness  is replaced by the current global best , then FA essentially becomes the standard PSO.
Criticism Nature-inspired metaheuristics in general have attracted criticism in the research community for hiding their lack of novelty behind metaphors. The firefly algorithm has been criticized as differing from the well-established particle swarm optimization only in a negligible way.
See also * Swarm intelligence
References
External links *  Files of the Matlab programs included in the book: Xin-She Yang, Nature-Inspired Metaheuristic Algorithms, Second Edition, Luniver Press, (2010).