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In mathematical optimization, the firefly algorithm is a metaheuristic proposed by Xin-She Yang and inspired by the flashing behavior of fireflies.
f(𝐱),𝐱=(x1,x2,...,xd); 2) Generate an initial population of fireflies \\mathbf{x}_i \\quad (i=1,2,\\dots,n)</math>;."}},"i":0}}]}'>f(𝐱) (for example, for maximization problems, I \\propto f(\\mathbf{x})</math> or simply <math>I=f(\\mathbf{x})</math>;)"}},"i":0}}]}'>γ while (t < MaxGeneration) for i = 1 : n (all n fireflies) for j = 1 : i (n fireflies) I_j>I_i </math>),"}},"i":0}}]}'>if (I_i "}}'>Ij>Ii), Vary attractiveness with distance r via \\exp(-\\gamma \\; r) </math>;"}},"i":0}}]}'>𝐱j is 𝝐t is a vector drawn from a Gaussian or other distribution.It can be shown that the limiting case g∗, then FA essentially becomes the standard PSO.
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.
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