Firefly Algorithm

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 $\mathbf_i$ and $\mathbf_j$ is
:: \mathbf_i^=\mathbf_i^t + \beta \exp \gamma r_^2(\mathbf_j^t - \mathbf_i^t) +\alpha_t \boldsymbol_t
where $\alpha_t$ is a parameter controlling the step size, while $\boldsymbol_t$ 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.

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).

{{collective animal behaviour

Nature-inspired metaheuristics