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. 2023 Mar 25;25(4):561. doi: 10.3390/e25040561

Algorithm 1: Update of

P O P

Input: population

P O P

; convergence-related decision variables

C V

;
diversity-related decision variables

D V

Output: updated population

n e w

_POP

1.
Select the parent population from POP by the tournament selection method according to the nondominated ranks of the individuals in POP;

2.
Obtain offspring population Q by performing the crossover and mutation operators only on the CV of the parent population;

3.
$C a n d i d a t e s \leftarrow P O P \cup$ Q, obtain the nondominated ranks of the members in $C a n d i d a t e s$ .

4.
Select $N$ individuals with the better nondominated ranks from $C a n d i d a t e s$ as POP1 and N is the size of POP;

5.
Select the parent population from POP1 randomly;

6.
Obtain offspring population Q by performing the crossover and mutation operators only on the DV of the parent population;

7.
$C a n d i d a t e s \leftarrow P O P \cup$ Q, obtain the nondominated ranks of the members in $C a n d i d a t e s$ .

8.
$n e w_$ POP = ${x | x \in C a n d i d a t e s and n o n d o m i n a t e_r a n k (x) = 1}$ . If | $n e w_$ POP| > N, then delete members from $n e w_$ POP randomly until | $n e w_$ POP| = N.

9.
R = 2;

10.
While | $n e w_$ POP| < N

11.
P contains the members from $C a n d i d a t e s$ whose nondominated ranks is R;

12.
If $| n e w_$ POP| $+$ |P| > N

13.
While | $n e w_$ POP| < N

14.
$n e w_$ POP $\leftarrow n e w_P O P \cup {argmax}_{x \in P} (\min_{y \in n e w_P O P} angle (x, y))$ ;

15.
Delete x from P;

16.
EndWhile

17.
Else

18.
$n e w_$ POP $\leftarrow n e w_P O P \cup$ P

19.
EndIf

20.
R = R + 1;

21.
EndWhile