Algorithm 3: GA for the Placement Scheme

Input: $M$, $N$

Output: $O$, $F_{pro}$

$n_a\leftarrow 0$, $G_{n_{gene}\times n}=\varnothing$ ${G_{n_{gene}\times n}}^{\prime }=\varnothing$

While $n_{gene}<N_p$

Initial $G_{n_{gene}}$

$G_{n_{gene}\times n}\leftarrow G_{n_{gene}\times n}\cup G_{n_{gene}}$

$n_{gene}\leftarrow n_{gene}+1$

End

While $t<N_r$

Sort $G_{n_{gene}\times n}(t)$ by $F_{pro}(t)$

While parents $<N_r{P}_c$ do

Select parents $G_{n_0}(t)$ &$G_{n_1}(t)$ by $p_r$

Apply crossing to get offspring $G_{n_0}(t+1)$ &$G_{n_1}(t+1)$

Apply mutation to $G_{n_0}(t+1)$ &$G_{n_1}(t+1)$

$G_{n_{gene}\times n}(t+1)\leftarrow G_{n_{gene}\times n}(t+1)\cup G_{n_0}(t+1)\cup G_{n_1}(t+1)$

$\mathrm{parents}\leftarrow \mathrm{parents}+2$

End

Sort $G_{n_{gene}\times n}(t)$ for finding $G_{N_r(1-P_c)}(t)$

$G_{n_{gene}\times n}(t+1)\leftarrow G_{n_{gene}\times n}(t+1)\cup G_{N_r(1-P_c)}(t)$

$G_{n_{gene}\times n}\leftarrow G_{n_{gene}\times n}(t+1)$

$t\leftarrow t+1$

End

Find $O_{ij}$ by $G_{n_{gene}\times n}$

Calculate $F_{pro}$