Algorithm 2: IDE in MOEA/D-HH Framework

Input:$\mathrm{Setting} \mathrm{solution} \mathrm{to} X={B(i‘)}^g\cup {\mathrm{A}\left(i\right)}^g$.

Step 1: Sorting and Partitioning:

Step 1.1:$\mathrm{Sorting} X$ using fitness value of scalarising function.  Step 1.2:$\mathrm{Superior} \mathrm{group} S\leftarrow \mathrm{top} 30\% \mathrm{of} X$. Step 2: $\mathrm{Generation} \mathrm{of} \mathrm{mutation} \mathrm{vector}.$

$\hspace{1em}\mathrm{Randomly} \mathrm{select} {X_S}^g \mathrm{and} {X_I}^g \mathrm{from} \mathrm{groups} S \mathrm{and} I, \mathrm{respectively}.$

$\hspace{1em}\mathrm{Generate} \mathrm{new} \mathrm{mutation} \mathrm{vector} \mathrm{as} {V_{i‘}}^g={X_{i‘}}^g+F·({X_S}^g-{X_I}^g)$.

Step 3:$\mathrm{Crossover} \mathrm{as}:$

$u_{i‘,j}^g=\left\{\begin{array}{c}{v}_{i‘,j}^g, if (rand\left(\mathrm{0,1}\right)\le CR, or j=j_{rand})\\ x_{i‘,j}^g\end{array}\right.$

$\hspace{1em}\mathrm{where} u_{i‘,j}^g$ denotes the trial vector, $F \mathrm{denotes} \mathrm{the} \mathrm{mutation} \mathrm{factor}, \mathrm{and} CR$ denotes the crossover probability.

Step 4:$\mathrm{Updating}: \mathrm{If} fit\left(U_{i‘}^g\right)\le fit\left(X_{i‘}^g\right)$$, \mathrm{then} X_{i‘}^{g+1}=U_{i‘}^g$.

Output: $X_{i‘}^{g+1}$.