Algorithm 2 Generation t of NSGA-III procedure [36].

$$\begin{gathered} \mathbf{Input}:H\mathrm{structured}\mathrm{reference}\mathrm{points}{Z}^s\mathrm{or}\mathrm{supplied}\mathrm{aspiration}\mathrm{points}{Z}^a,\mathrm{parent} \\ \mathrm{population}{P}_t \end{gathered}$$

$\mathbf{Output}:P_{t+1 }$

$1: S_{t }=\varnothing , i=1$

$2: Q_{t }= \mathrm{Recombination}+\mathrm{mutation} (P_{t })$

$3: R_t=P_{t }\cup Q_{t }$

$4: (F_{1 },F_{2 },\dots )=$ $\mathrm{Non}-\mathrm{dominated}-\mathrm{sort} (R_{t })$

$5: \mathbf{Repeat}$

$6:\hspace{1em}{S}_{t }=S_t\cup F_i and i=i+1$

$7: \mathbf{Until} \left|S_t\right|\ge N$

$8: \mathrm{Last} \mathrm{front} \mathrm{to} \mathrm{be} \mathrm{included}: F_{l }=F_i$

$9: \mathbf{If} \left|S_t\right|=N \mathbf{then}$

$10:\hspace{1em}{P}_{t+1 }=S_t\mathrm{break}$

$\mathrm{11}:\mathbf{Else}$

$12:\hspace{1em}{P}_{t+1} ={\cup }_{j=1}^{i-1}{F}_j$

$13:\hspace{1em}\mathrm{Points} \mathrm{to} \mathrm{be} \mathrm{chosen} \mathrm{from} F_{l }:K=N-\left|P_{t+1}\right|$

$14:\hspace{1em}\mathrm{Normalize} \mathrm{objectives} \mathrm{and} \mathrm{create} \mathrm{reference} \mathrm{set} Z^r:Normalize \left(f^n, S_t,Z^r,Z^s,Z^a\right)$

$15:\hspace{1em}\mathrm{Associate} \mathrm{each} \mathrm{member} \mathrm{s} \mathrm{of} S_t\mathrm{with}a\mathrm{reference}\mathrm{point}:$

$\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left[\pi \left(s\right), d\left(s\right)\right]=Associate\left(S_t,Z^r\right) \% \pi \left(s\right):closest reference point,$

$\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}d:distance between s and \pi \left(s\right)$

$16: \mathrm{Computer} \mathrm{niche} \mathrm{count} \mathrm{of} \mathrm{reference} \mathrm{point} j ϵ Z^r:{\rho }_j=$

$\hspace{1em}\hspace{1em}{\displaystyle \sum }_{s\epsilon S_t/F_l}\left(\left(\pi \left(s\right)=j\right)?1:0\right)$

$17:\hspace{1em}\mathrm{Choose} \mathrm{K} \mathrm{members} \mathrm{one} \mathrm{at} \mathrm{a} \mathrm{time} \mathrm{from} F_l\mathrm{to}\mathrm{construct}$

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

$18\mathbf{End}\mathbf{if}$