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Firefly algorithm
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Firefly algorithm : ウィキペディア英語版
Firefly algorithm
The firefly algorithm (FA) is a metaheuristic algorithm, inspired by the flashing behaviour of fireflies. The primary purpose for a firefly's flash is to act as a signal system to attract other fireflies. Xin-She Yang formulated this firefly algorithm by assuming:
#All fireflies are unisexual, so that any individual firefly will be attracted to all other fireflies;
#Attractiveness is proportional to their brightness, and for any two fireflies, the less bright one will be attracted by (and thus move towards) the brighter one; however, the intensity (apparent brightness) decrease as their mutual distance increases;
#If there are no fireflies brighter than a given firefly, it will move randomly.
The brightness should be associated with the objective function.
Firefly algorithm is a nature-inspired metaheuristic optimization algorithm.
== Algorithm description ==
The pseudo code can be summarized as:
Begin
1) Objective function: f(\mathbf), \quad \mathbf=(x_1,x_2,...,x_d) ;
2) Generate an initial population of fireflies \mathbf_i \quad (i=1,2,\dots,n);.
3) Formulate light intensity I so that it is associated with f(\mathbf)
(for example, for maximization problems, I \propto f(\mathbf) or simply I=f(\mathbf);
4) Define absorption coefficient \gamma

While (t < MaxGeneration)
for i = 1 : n (all n fireflies)
for j = 1 : n (n fireflies)
if (I_j>I_i ),
move firefly i towards j;
Vary attractiveness with distance r via \exp(-\gamma \; r) ;
Evaluate new solutions and update light intensity;
end if
end for j
end for i
Rank fireflies and find the current best;
end while

Post-processing the results and visualization;

end
The main update formula for any pair of two fireflies \mathbf_i and \mathbf_j is
:: \mathbf_i^=\mathbf_i^t + \beta \exp(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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Firefly algorithm」の詳細全文を読む



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