Algorithm 6 FA

Input: the parameters M, N,$\delta$, $I_0$, ${\beta }_0$ and $step$ Begin S1: initialize M individuals $x_i\left(t\right)$randomly,$0<i\le M$, iterative times t = 1; S2: compute $f\left(i\right),0<i\le M$, if t > 1 and the new position is better than the old one, update $x_i\left(t\right)$ and $p_g\left(t\right)$; if it satisfies (t > N or precision$\le \delta$), then go to step S4; otherwise, go to step S3; S3: for the ith firefly $x_i\left(t\right)$, FA searches another firefly (suppose the jth firefly $x_j\left(t\right)$, and $i\ne j$) in the population that has the luminance calculated with Equation (14). If the luminance of $x_j\left(t\right)$ is larger than that of $x_i\left(t\right)$, $x_i\left(t\right)$ moves toward $x_j\left(t\right)$ by Equation (17), iterative times t = t + 1; go to step S2; S4: output the optimized results. End