Algorithm 4. The pseudocode of the EJSARO

Inputs: number of search agents ($N$), number of iterations ($m_i$), problem dimension ($d$), and lower ($LB$) and upper ($UB$) boundaries of search space

Outputs: the best search agent ($X_B$) and its fitness ($F_B$)

//Initialization

$i=1$;    $c_i= 1$;

while ($i\le N$)

Initialize $X_i$ by Equation (39)

Calculate $F_i$ using PMSE formulated by Equation (42)

${ct}_i=0$;    $i=i+1$;

end for

Find $X_B$ and $F_B$

//Optimization

while ($c_i\le m_i$)

$i=1$

while ($i\le N$)

$j=randint\left(N\right)$;

if $rand\left(\mathrm{0,1}\right)<0.5$

//Modified Detour foraging (ARO)

Calculate R, Z, and L using Equations (20), (21), and (23), respectively

${newX}_i=X_B+R.(X_i-X_j)+Z$

else

//Modified Random hiding (JS)

Compute $step$ using Equation (15)

${newX}_i = X_B + r_5.step$

end if

//Check and rectify the new solution

Calculate $\phi$ using Equation (46)

$new{X}_i$ = $\phi .\left[r_{13} \times (UB-LB)+LB\right] \times + \left[{newX}_i \times \overline{\phi }\right]$

//Elitism (greedy selection)

Compute ${newF}_i$ using Equation (42)

if $({newF}_i< F_i)$

$X_i= {newX}_i$;    $F_i={newF}_i$;    ${ct}_i=0$;

else

${ct}_i= {ct}_i+1$

end

if $({newF}_i< F_B)$

$X_B= {newX}_i$;    $F_B={newF}_i$;

end

//Levy flight-based motion

Calculate ${Lv}_i$ using Equation (48)

${newX}_i=X_i+{Lv}_i$

//Check and rectify the new solution

$new{X}_i$ = $\phi .\left[r_{13} \times (UB-LB)+LB\right] \times + \left[{newX}_i \times \overline{\phi }\right]$

//Elitism (greedy selection)

Compute ${newF}_i$ using Equation (43)

if $({newF}_i< F_i)$

$X_i= {newX}_i$;    $F_i={newF}_i$;    ${ct}_i=0$;

else

${ct}_i= {ct}_i+1$

end

if $({newF}_i< F_B)$

$X_B= {newX}_i$;    $F_B={newF}_i$;

end

//Local departure mechanism

if $({ct}_i\ge Th)$

Reset${ct}_i$ and reinitialize $X_i$ using Equation (39)

end

$i=i+1$

end for

//Proposed local search procedure

Improve $X_B$ using Equation (52) and the proposed local search

$c_i= c_i+ 1$

end while

Return $X_B$ and $F_B$