Water Resources Research Report - Western Engineering ...

Individual
1
Table 1. An illustrative example
Population Size NP = 6 (user defined), D = 3
Individual
2
Individual
3
Individual
4
Individual
5
Individual
6
x 1 0.68 0.92 0.22 0.12 0.40 0.94
x 2 0.89 0.92 0.14 0.09 0.81 0.63
x 3 0.04 0.33 0.40 0.05 0.83 0.13
f (x)
1.61 2.17 0.76 0.26 2.04 1.70
Table 2. Calculation of the weighted difference vector for the illustrative example
Individual
2
Individual
4
Difference
Vector
Weighted
Difference
Vector
x 1 0.92 0.12 = 0.80 = 0.64
x 2 0.92 - 0.09 = 0.83
× F
(F = 0.80)
= 0.66
0.05 = 0.28
= 0.22
x 3 0.33
Table 3. Calculation of the noisy random vector for the illustrative example
Weighted
Difference
Vector
Individual
6
Noisy
Random
Vector
x 1 0.64 0.94 = 1.58
x 0.66 + 0.63 = 1.29
2
x 3 0.22
0.13 = 0.35
The noisy random vector does a crossover with the target vector to generate the trial
vector as shown in Table 4. This is carried out by (1) generating random numbers equal
to the dimension of the problem (2) for each of the dimensions: if random number > CR;
copy the value from the target vector, else copy the value from the noisy random vector
into the trial vector. In this example, the crossover constant CR is chosen as 0.50.
8