Algorithm 3 ABC

Input: the parameters M, N,$\delta$,$F$, $Limit$ Begin S1: initialize M individuals $x_i\left(t\right)$ randomly by Equation (2), and appoint $\frac{M}{2}$ bees to the employed foragers, iterative times t = 1; S2: compute $f\left(i\right), 0<i\le M$, update $p_g\left(t\right)$; if it satisfies (t > N or precision$\le \delta$), then go to step S4; otherwise, go to step S3; S3: employed foragers search new food sources by Equation (3) and compute$f\left(i\right)$; update the food sources if the new one is better than the old one; onlookers choose food sources of employed foragers according to Equations (4) and (5), and generate new food sources by Equation (3); update the food sources if the new one is better than the old one; if there are some food sources which need to be given up (cannot be optimized after$Limit$ times searches); the corresponding bees become the scouts, and generate new sources by Equation (2); increase times t = t + 1, go to step S2; S4: output the optimized results. End