Algorithm 2: $Searchoptimal\left(P\right)$

Input:

$p_{opt}$: optimal solution in P

$p_i$: the i-th solution P

Optimization:

1: $p_{opt}⟵p_1$

2: for $i=2$ to $\left|P\right|$ do

3:   if $GR\left(p_i\right)<GR\left(p_{opt}\right)$ then

4:     $p_{opt}⟵p_i$

5:   else if $GR\left(p_i\right)=GR\left(p_{opt}\right)$ then

6:     if $GCD\left(p_i\right)<GCD\left(p_{opt}\right)$ then

7:       $p_{opt}⟵p_i$

8:     else if $GCD\left(p_i\right)=GCD\left(p_{opt}\right)$ then

9:       if $GCPD\left(p_i\right)<GCPD\left(p_{opt}\right)$ then

10:          $p_{opt}⟵p_i$

11:       end if

12:     end if

13:   end if

14: end for

Output:

$p_{opt}$