Algorithm 2. MOC for Multiple shell Scheme Design:

Input: ${\{{\theta }_s\}}_{s=0}^S$, ${\{K_s\}}_{s=1}^S$

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

Initialize coverage sets ${\{{\text{CS}}_s\}}_{s=0}^S$ as S + 1 empty sets, and initialize Ns = 0, ∀s ∈ [1, S];

for n = 1 to ${\sum }_{s=1}^S{K}_s$ do

if n == 1 then choose any point as u1,1, s ← 1, i ← 1;

if 1 < n ≤ S then s ← n, i ← 1, choose us,i in (𝕊2 – CS0) such that the set

C(us,i, θ0) ⋂ CS0 has the largest area ;

if n > S then

Set V as an empty set;

for s′ = 1 to S do

if Ns′, < Ks′, and (𝕊2 – (CSs′ ⋃ CS0)) is not empty then

choose vs′ in (𝕊2 – (CSs′ ⋃ CS0)) such that the overlap set

C(vs′,, θs′) ⋂ (CSs′ ⋃ CS0) has the largest area denoted as As′;

V ← V ⋃ {vs′};

end

end

if V is empty then

IsSatisfied = False; return

else

choose s and vs ∈ V such that their corresponding area As is the largest one among ${\{A_{s\prime }\}}_{s\prime =1}^S$;

i ← Ns + 1, us,i ← vs;

end

end

CSs ← CSs ⋃ C(us,i, θs); CS0 ← CS0 ⋃ C(us,i, θ0); Ns ← Ns + 1;

end

IsSatisfied=True; return;