Algorithm 4 BA

Input: the parameters M, N,$\delta$,$Freq$,$A$, $\alpha$ and $\gamma$ Begin S1: initialize M individuals $x_i\left(t\right)$randomly,$0<i\le M$, iterative times t = 1; S2: compute $f\left(i\right), 0<i\le M$, 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: update $Freq$,$x_i\left(t\right)$ and $v_i\left(t\right)$ by Equation (6), generate a random number $ran{d}_1$, if $ran{d}_1>r$, the bat with the global optimum generates a new solution by Equation (7). Bats generate new solutions randomly, and BA generates a random number$ran{d}_2$; if $ran{d}_2<A$ and the new solution is better than the old one, BA updates the corresponding position by Equation (7), and updates $A_{i }$and $r_{i }$ by Equations (8) and (9); iterative times t = t + 1, go to step S2; S4: output the optimized results. End