Algorithm 1. Shows the Pseudo Code of AMG-QUATRE Algorithm.

// Initialization phase

Initialize the searching space V, dimension D, Set the generation counter Gen=1, randomly initialize the population $X$ with $ps$ individuals, and evaluate fitness values of all individuals, set initial ${\mu }_F=0.5$, ${\sigma }_F=0.1$.

// Main loop

1: while stopping criterion is not satisfied do

2:  Randomly partition the population into three groups, $group1$, $group2$ and $group3$

3:  Generate matrices $M_{group1}$ and ${\overline{M}}_{group1}$, $M_{group2}$ and ${\overline{M}}_{group2}$, $M_{group3}$ and ${\overline{M}}_{group3}$, using Equation (3).

4:  Calculate mutation matrix $B_{group1}$ using QUATRE/target-to-best/1, $B_{group2}$ using QUATRE/rand/1, $B_{group3}$ using QUATRE/best/1.

5:  Evolve individuals in each group using Equation (1).

6:  Evaluate fitness values of all individuals.

7:   for $i=1;i\le ps;i++$ do

8:    if $f({\mathrm{X}}_i)\le f({\mathrm{X}}_{pbest,i})$ then

9:     $X_{pbest,i}=X_i$

10:    end if

11:   end for

12:  $X=X_{pbest}$, $X_{gbest}=opt\left\{X_{pbest}\right\}$.

13:  Update scale factor F according to Equation (12).

14:  $Gen=Gen+1$

15: end while

Output: The global optimum $X_{gbest}$, global best fitness value $f({\mathrm{X}}_{pbset})$.