Page 135 - Control Theory in Biomedical Engineering

120 Control theory in biomedical engineering

Random
initial population

Evaluate fitness function

Yes
Stopping criteria
No
Selection New population
Result
Crossover

Mutation
Fig. 12 Genetic algorithm process.

until the stopping criteria (the maximum generation number, the maximum
number of iteration, etc.) are reached. At the end, the solution with the low-
est RMSE is selected as the best one and its optimized parameters are
returned.
In our case, as it is shown in Fig. 13, an example of a binary chromosome
is illustrated. The chromosome represents the Gaussian parameters (μ and δ)
and the number of fuzzy rules. The elitism selection is used to select which
solutions are retained for further reproduction. The n-point crossover is
selected to obtain new solutions from existing ones. The binary mutation
is applied as introducing diversity into the solution pool by means of ran-
domly swapping or turning off solution bits.
In our study, the GA is applied for the configured FLC with three and
two Gaussian fuzzy sets. Table 6 reports the obtained performances, where
MF is the membership function, Num-fuzzy_set is the number of fuzzy sets
and Num_R is the number of fuzzy rules. Bold values indicate the adopted
FLC performances after genetic optimization.
Table 6 shows that the minimal RMSE between the FLC outputs and
their corresponding targets (RMSE¼0.619) is obtained by using three
Gaussian fuzzy sets and applying 62 fuzzy rules. Accordingly, the distribution

1 1 1 0 0 0 1 0 1 0 1 0
m and d Number of fuzzy rules
Fig. 13 Example of a chromosome solution.