Procedure of JADE with Archive as in [11] and [14]

Start

Initialize:

${\mu }_{CR}=0.5$ ; ${\mu }_F=0.5$ ; $A=\varnothing$ ; and create a random initial population $\left\{X_{i,0}:i=1:NP\right\}$

For $g=1:G$ ; Generation loop

$S_F=\varnothing$ ; $S_{CR}=\varnothing$ ;

For $i=1:NP$ ; Population size loop

Generate:

$C{R}_i=\text{randni}\left({\mu }_{CR}\mathrm{,0.1}\right)$ , $F_i=\text{randci}\left({\mu }_F\mathrm{,0.1}\right)$ .

Randomly choose:

$X_{best\mathrm{,}g}^p$ as one of the 100p% best vectors, $X_{r\mathrm{1,}g}\ne X_{i\mathrm{,}g}$ from current population $P$ ,

and ${\tilde{X}}_{r\mathrm{2,}g}\ne X_{r\mathrm{1,}g}\ne X_{i\mathrm{,}g}$ from $P\cup A$ .

Compute

$V_{i\mathrm{,}g}=X_{i\mathrm{,}g}+F_i\ast \left(X_{best\mathrm{,}g}^p-X_{i\mathrm{,}g}\right)+F_i\ast \left(X_{r\mathrm{1,}g}-{\tilde{X}}_{r\mathrm{2,}g}\right)$

Generate:

$j_{rand}=\text{randint}\left(\mathrm{1,}D\right)$

For $j=1:D$ Dimension loop

If $j=j_{rand}$ or $\text{rand}\left(\mathrm{0,1}\right)<C{R}_i$ then $u_{j,i,g}=v_{j,i,g}$ Else $u_{j,i,g}=x_{j,i,g}$ . End If

End for Dimension loop

If $E\left(X_{i\mathrm{,}g}\right)\le E\left(U_{i\mathrm{,}g}\right)$ then $X_{i,g+1}=X_{i,g}$ Else $X_{i,g+1}=U_{i,g}$ ; $X_{i\mathrm{,}g}\to A$ ; $C{R}_i\to S_{CR}$ , $F_i\to S_F$ .

End If

End for Population size loop

Randomly remove solutions from $A$ so that the cardinal of $A$ is less or equal to NP

${\mu }_{CR}=\left(1-c\right)\ast {\mu }_{CR}+c\ast {\text{mean}}_A\left(S_{CR}\right)$

${\mu }_F=\left(1-c\right)\ast {\mu }_F+c\ast {\text{mean}}_L\left(S_F\right)$

End for Generation loop

End