{
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  "slug": "firefly-algorithm",
  "title": "Firefly algorithm",
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  "lead": "In mathematical optimization, the firefly algorithm is a metaheuristic proposed by Xin-She Yang and inspired by the flashing behavior of fireflies.",
  "body": "In mathematical optimization, the firefly algorithm is a metaheuristic proposed by Xin-She Yang and inspired by the flashing behavior of fireflies. 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 \\mathbf{x}_i and \\mathbf{x}_j is \\mathbf{x}_i^{t+1}=\\mathbf{x}_i^t + \\beta \\exp[-\\gamma r_{ij}^2] (\\mathbf{x}_j^t - \\mathbf{x}_i^t) +\\alpha_t \\boldsymbol{\\epsilon}_t where \\alpha_t is a parameter controlling the step size, while \\boldsymbol{\\epsilon}_t is a vector drawn from a Gaussian or other distribution. It can be shown that the limiting case \\gamma \\rightarrow 0 corresponds to the standard particle swarm optimization (PSO). In fact, if the inner loop (for j) is removed and the brightness I_j is replaced by the current global best g^* , then FA essentially becomes the standard PSO. ==See also== Swarm intelligence ==External links== [https://www.mathworks.com/matlabcentral/fileexchange/29693-firefly-algorithm] Files of the Matlab programs included in the book: Xin-She Yang, Nature-Inspired Metaheuristic Algorithms, Second Edition, Luniver Press, (2010).",
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    "title": "Firefly algorithm",
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    "publisher": "Anticloud FZ LLE",
    "publisher-place": "Dubai, United Arab Emirates",
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