Algorithm 2: Mating Selection

Input: $P$

Output: $M P$

1: $P_{1}, P_{2} \in P$

2: if $P_{1} ≺ P_{2}$ or $P_{1} ≺_{G r i d} P_{2}$ then

3: return $P_{1}$

4: else if $P_{2} ≺ P_{1}$ or $P_{2} ≺_{G r i d} P_{1}$ then

5: return $P_{2}$

6:else if $G C D (P_{1}) ≺ G C D (P_{2})$ then

7: return $P_{1}$

8: else if $G C D (P_{2}) ≺ G C D (P_{1})$ then

9: return $P_{2}$

10: else if $r a n d o m (0, 1) < 0.5$ then

11: return $P_{1}$

12: else

13: return $P_{2}$

14: end if