Firefly algorithm: Difference between revisions

Revision as of 20:09, 5 January 2024

Latest revision as of 01:16, 9 February 2025

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The main update formula for any pair of two fireflies <math>\mathbf{x}_i </math> and <math>\mathbf{x}_j </math> is

:: <math display="block">\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 </math>

where <math>\alpha_t </math> is a parameter controlling the step size, while <math>\boldsymbol{\epsilon}_t </math> is a vector drawn from a Gaussian or other

distribution.zae

It can be shown that the limiting case <math>\gamma \rightarrow 0 </math> corresponds to the standard [[Particleparticle Swarmswarm Optimizationoptimization]] (PSO). In fact, if the inner loop (for j) is removed and the brightness <math>I_j</math> is replaced by the current global best <math>g^*</math>, then FA essentially becomes the standard PSO.

== Criticism ==