Algorithm 1: Framework of RGEA

Input:

H structured reference ponits $Z^s$ or supplied aspiration ponits $Z^a$

P: population

N: population size

maxGen: maximum number of iterations

N uniformly distributed weight vectors: ${\lambda }^1,\dots ,{\lambda }^N$

div: the size of grid division

$\alpha$: the interval for calculating the entropy value

Initialization:

t = 1

$P_t$ = Initialize(P)

Compute maximum entropy: MaxEntropy;

Optimization:

while t < maxGen do

1: $S_t=\varnothing$, $i=1$,

2: $Q_t$ = Genetic Recombination and Mutation($P_t$)

3: $R_t=P_t\bigcup Q_t$

4: $\left(F_1,F_2,\dots \right)$ = Non-dominated Sorting$\left(R_t\right)$

5: while $\left|S_t\right|<N$ do

6:   $S_t=S_t\bigcup F_i$

7:   $i=i+1$

8: Final Front to Incorporate: $F_l=F_i$

9: if $\left|S_t\right|=N$ then

10:   $P_{t+1}=S_t$

11: else

12:  $P_{t+1}={\bigcup }_{j=1}^{l-1}{F}_j$

13:  Points Selected From $F_l:K=N-\left|P_{t+1}\right|$

14: if kind = 1

15:   Normalize Objectives and Establish Reference Set $Z^r$:$normalize\left(f^n,S_t,Z^r,Z^s,Z^a\right)$

16:   Associate each member of with a reference point: $\left[\pi \left(s\right),d\left(s\right)\right]=Associate\left(S_t,Z^r\right)$

17:   Compute niche count of reference point $j\in Z^r:{\rho }_j={\sum }_{s\in S_t/F_l}\left(\left(\pi \left(s\right)=j\right)?1:0\right)$

18:   Choose members one at a time from $F_l$ to construct

$P_{t+1}$:$Niching\left(K,{\rho }_j,\pi ,d,Z^r,F_l,P_{t+1}\right)$

19: else

20:   $Gri{d}_{-}setting\left(S_t\right)$

21:   $Fitnes{s}_{-}assignment\left(S_t\right)$

22:   $P_{t+1}=Environmenta{l}_{-}selection\left(S_t\right)$

23: end if

24: if $t\%\alpha ==0$

25:   Calculate CurrentEntropy: $CurrentEntropy$

26:   if MaxEntropy - CurrentEntropy <= 0, then

27:     kind = 2

28: end if

29: end if

30: end if

31: $t=t+1$

32: end

Output:

P