An Improved Multioperator-Based Constrained Differential Evolution for Optimal Power Allocation in WSNs

. 2021 Sep 18;21(18):6271. doi: 10.3390/s21186271

Algorithm 1 Pseudo-code of IMO-CADE

Input: Algorithm parameters:

N p, μ_{C r}, μ_{F}, c, p_{min}, α, N F E s_{max}

; WSN parameters:

K, ϵ, ρ, γ_{0}

Output: The best solution

x^{best} = {G_{1}^{best}, \dots, G_{K}^{best}}

1:
Initialize the population $P$ with $N p$ solutions;
2:
Evaluate the population $P$ and set $N F E s = N p$ ;
3:
For each operator, set $q_{o} = 0$ and $p_{o}^{'} = 1 / 2$ ;
4:
Set $A = Φ$ ;
5:
while $N F E s < N F E s_{max}$ do
6:
Set $S_{C r} = Φ$ , $S_{F} = Φ$ ;
7:
Sort the solutions in $P$ based on the feasibility rules from the best to the worst;
8:
For each solution in $P$ , set $p_{o, i}^{″}$ according to Equation (21);
9:
For each solution, calculate $p_{o, i}$ based on Equation (22);
10:
for $i = 1$ to $N p$ do
11:
Select the operator $o^{i}$ based on the selection probability;
12:
Calculate $C r^{i}$ and $F^{i}$ based on Equations (23) and (24), respectively;
13:
Generate $u^{i}$ and deal with the violated variables based on Equation (13);
14:
Evaluate $u^{i}$ , $N F E s = N F E s + 1$ , and $C \leftarrow u^{i}$ ;
15:
end for
16:
$M \leftarrow P \cup C$ ;
17:
For each solution $x$ in $M$ , calculate $F (x)$ under the current situation;
18:
for $i = 1$ to $N p$ do
19:
if $F (u^{i}) \leq F (x^{i})$ then
20:
$A \leftarrow x^{i}$ ;
21:
Calculate ${\hat{F}}^{i}$ based on Equation (17) and save it into $S_{o} (i)$ ;
22:
$S_{C r} \leftarrow C r^{i}$ and $S_{F} \leftarrow F^{i}$ ;
23:
Replace $x^{i}$ with $u^{i}$ ;
24:
else
25:
Set ${\hat{F}}^{i} = 0$ and save it into $S_{o} (i)$ ;
26:
end if
27:
end for
28:
Update $μ_{C r}$ and $μ_{F}$ ;
29:
for $o = 1$ to 2 do
30:
Calculate $R_{o}$ based on Equation (18);
31:
Update $p_{o}^{'}$ based on Equation (20);
32:
end for
33:
end while