Firefly algorithm

Firefly Algorithm

Firefly Algorithm (FA) was 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. Yang formulated this firefly algorithm by assuming 1) All fireflies are unisex, so that one firefly will be attract to all other fireflies; 2) Attractiveness is proportional to their brightness, and for any two fireflies, the less brighter one will attract (and thus move) to the brighter one; however, the brightness can decrease as their distance increases; 3) If there are no fireflies brighter than a given firefly, it will move randomly. The brightness should be associated with the objective function.

The pseudo code can be summarized as

Begin

1) Objective function: $f(\mathbf {x} ),\quad \mathbf {x} =(x_{1},x_{2},...,x_{d})$;
2) Generating initial population of fireflies $\mathbf {x} _{i}\quad (i=1,2,...,n)$;
3) Light intensity $I_{i}$ is associate with $f(\mathbf {x} _{i})$;
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;
         end if 
      Vary attractiveness with distance r via $exp(-\gamma r)$;
      Evaluate new solutions and update light intensity;
      end for j
   end for i
   Rank fireflies and find the current best;
end while
Post-processing the results and visualization;

end

It can be shown that the limiting case $\gamma \rightarrow 0$ corresponds to the standard Particle Swarm Optimization (PSO).

Recent studies shows that the firefly algorithm is very efficient, and could outperform other metaheuristic algorithms including PSO.