APPLICATION: FLOOD FORECASTING MODEL FOR KLODZKO CATCHMENT (POLAND) - Modelling Uncertainty in Flood Forecasting Systems - page 96

A combination of jump and creep mutation is used. In jump mutation the chromosome
is chosen for mutation randomly. In creep mutation, on the other hand, the child will
have a chromosome set which is different from one of its parents by only a small
increment or decrement. As also applied by Carroll (1996) an equal probability was
assigned for both jump and creep mutations. Elitism is used to guarantee that the
chromosome set of the best parent (generated so far) is preserved. After the population is
generated, the GA checks if the best parent has been replicated; if not, a random
individual is chosen and the chromosome set of the best parent is mapped into that
individual. The present GA also uses the operation called niching (sharing). Niching
describes a process of identifying when individuals are converging on distinct optima
and taking action to allow all the potential peaks to develop adequately. Goldberg and
Richardson (1987) showed niching as an effective GA technique for multimodal
problems. A sharing scheme by Goldberg and Richardson (1987) with a triangular
sharing function was used.
The micro-GA (Krishnakumar, 1989) is used with tournament selection, uniform
crossover, two children per pair of parents, elitism and niching. No mutation operation is
used in this case. A micro-GA starts with a very small random population, which evolves
in a normal GA fashion and converges in a few generations (typically 4 to 5). From this a
new random population is created while keeping the best individual from the previously
converged generation and restarting the evolution process (Yang et al., 1998).
A flowchart (Fig. 5.8) is presented here to illustrate the methodology presented in
Subsection 5.2.3 combined with a conventional or normal GA. The Steps 1 to 7 in the
flowchart are same as those in Subsection 5.2.3. In Step 2, the value of k is either n or
n !1, depending on the type of the method used for the generation of coefficients b i,j (see
Subsection 4.1.6). Also in the figure, UB and LB represent upper and lower bounds
respectively. In Step 9, the lower and upper bounds of the output discharges correspond
to the minimum and maximum of the model outputs, respectively, which depends on the
type of fitness function (Eq. (5.15)) used in Step 6.