and this procedure for evaluation and reproduction of all chromosomes
was repeated until the stopping criterion is satisfied. The basis
of GA is the continual improvement of the fitness of the
population by means of genetic operators, as individuals are passed
from one generation to the next. In this way, the ANN weights and
thresholds are initialized as chromosome of best fitness population
member. This procedure is completed by applying a BP algorithm
on the GA established initial connection weights and thresholds.
If the BP stopping condition is false, the weights and thresholds
are updated; otherwise, they are saved and provided for future prediction
of the flow.
3. Application case
Data used in this paper are from the Ourika basin, located in
semi-arid region of Marrakech and is the most important subcatchment
of Tensift basin drainage. The basin area is 503 km2,
and its mean annual rainfall is approximately 800 mm. The rainfall
and runoff daily data at the average of Aghbalou, Oukaimeden and
Arghbar stations were used for model investigation. The data contains
information for a period of four years (2000–2003). Furthermore,
data from 2000 to 2002 constitute the training set and the
365 remaining data is used in the testing phase.
The input vector is represented by rainfall and runoff values for
the preceding 4 days (i.e., t 1, t 2, t 3, t 4). Accordingly, the
output vector represents the expected runoff value for day tðbQ
tÞ.
In this study data, the best ANN architecture was: 4–5–1 (4 input
units, 5 hidden neurons, 1 output neuron). Before training and testing
all source data are normalized into the range between 1 and
1, by using the maximum and minimum values of the variable over
the whole data sets.
4. Results and discussion
Fig. 3 shows the comparison between predicted and measured
runoff values at training and testing phases by hybrid GA–ANN
model using the daily data from the Ourika catchment. The GA–
ANN algorithm was run with a population size of 100, uniform
crossover probability was set to 0.9 and uniform mutation probability
was set to 0.1. GA–ANN was trained by 80 generations, followed
by a BP training procedure. The value of learning
coefficient 0.01 and momentum correction factor 0.08 were used
for the back-propagation training algorithm.
In Fig. 3 the output of the model, simulated with test data,
shows a good agreement with the target. The simulation performance
of the GA–ANN model was evaluated on the basis of root
mean square error (RMSE) and efficiency coefficient R2 (Nash &
Sutcliffe, 1970). The parameters RMSE = 0.162 and R2 = 0.91 suggest
a very good performance. In general, a R2 value greater than
0.9 indicates a very satisfactory model performance, while a R2 value
in the range 0.8–0.9 signifies a good performance and values
less than 0.8 indicate an unsatisfactory model performance (Coulibaly
& Baldwin, 2005).
In order to evaluate the performance of the genetic algorithmbased
neural network, back-propagation neural network was applied
with the same data sets used in the GA–ANN model. Fig. 4
shows the extent of the match between the measured and predicted
daily flow values by GA–BP and BP neural networks in term