Firefly algorithm

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Metaheuristic proposed by Xin-She Yang

title: "Firefly algorithm" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["nature-inspired-metaheuristics"] description: "Metaheuristic proposed by Xin-She Yang" topic_path: "general/nature-inspired-metaheuristics" source: "https://en.wikipedia.org/wiki/Firefly_algorithm" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Metaheuristic proposed by Xin-She Yang ::

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 I so that it is associated with f(\mathbf{x}) (for example, for maximization problems,
  4. Define absorption coefficient γ

while (t for i = 1 : n (all n fireflies) for j = 1 : i (n fireflies) if (I_jI_i ), Vary attractiveness with distance r via \exp(-\gamma ; r) ; 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.

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.

References

References

  1. Yang, X. S.. (2008). "Nature-Inspired Metaheuristic Algorithms". [[Luniver Press]].
  2. (2016). "A new fuzzy membership assignment and model selection approach based on dynamic class centers for fuzzy SVM family using the firefly algorithm". Turkish Journal of Electrical Engineering & Computer Sciences.
  3. Lones, Michael A.. (2014). "Proceedings of the Companion Publication of the 2014 Annual Conference on Genetic and Evolutionary Computation".
  4. Weyland, Dennis. (2015). "A critical analysis of the harmony search algorithm—How not to solve sudoku". Operations Research Perspectives.
  5. Ariyaratne MKA, Pemarathne WPJ (2015) A review of recent advancements of firefly algorithm: a modern nature inspired algorithm. In: Proceedings of the 8th international research conference, 61–66, KDU, Published November 2015, http://ir.kdu.ac.lk/bitstream/handle/345/1038/com-047.pdf?sequence=1&isAllowed=y

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