Algorithm 1. IMOC for Multiple shell Scheme Design:

Input: number of samples for S shells: ${\{K_s\}}_{s=1}^S$

Output: ${\{{\mathbf{u}}_{s,i}\}}_{i=1}^{K_s}$.

// binary search {θs} from {(0, ${\theta }_s^{\text{ub}}$)}. ${\{{\theta }_s^{\text{ub}}\}}_{s=0}^S$ are the upper bounds of the covering radii;

${\theta }_s^0=0$, ${\theta }_s^1={\theta }_s^{\text{ub}}$, ∀s = 0, 1, …, S;

repeat

${\theta }_s=({\theta }_s^0+{\theta }_s^1)/2$, ∀s = 0, 1, …, S;

$[\text{IsSatisfied},\{{\mathbf{u}}_{s,i}\}]=\mathbf{\text{MOC}}({\{{\theta }_s\}}_{s=0}^S,{\{K_s\}}_{s=1}^S);$

if IsSatisfied then ${\theta }_s^0={\theta }_s$, ∀s = 0, 1, …, S;

else ${\theta }_s^1={\theta }_s$, ∀s = 0, 1, …, S;

until θs does not change, ∀s = 0, 1, …, S;