APPLICATION: FLOOD FORECASTING MODEL FOR KLODZKO CATCHMENT (POLAND) - Modelling Uncertainty in Flood Forecasting Systems - page 93

5.2.4 Simplification of the methodology

An obvious drawback of the above methodology is that as the number of subbasins
and subperiods increases, the search space becomes very large, which significantly re-
duces the performance of the genetic algorithm or any other algorithms used for the

determination of the maximum and minimum. In an attempt to reduce the search space it
was checked in several cases and it was found that the minimum and maximum of the
model outputs ( Q min and Q max ) actually correspond to the lower bound and the

upper bound values (for the given ! -cut), respectively, of the precipitation
determined in Step 2 of the algorithm. Therefore, instead of looking for all possible
values of precipitations between LB and UB, is used to evaluate Q min and is
used to evaluate Q max . This means that the model function is assumed to be monotonic
with respect to the quantity of the accumulated precipitation of the forecast period. This
simplification reduces the number of parameters for the GA (N p ) from nm to ( n !1) m .
This is viewed as an important issue because it helps to reduce the computational effort
especially working with a big catchment consisting of many subbasins.

5.3 Genetic algorithms for minimum and maximum determination

Due to the widespread nature of the optimization problem for determining the minimum (or
maximum) of a function, this has been one of the major fields of operational and mathematical
research for decades. Algorithms for solving optimization problems range from linear,
nonlinear to global. The suitability of the applications of these algorithms depends on the nature
of the problem among other things. The global optimization algorithms (GOAs) have a
particular advantage in solving problems in which other optimization techniques have
difficulties when there exist multiple extrema and/or difficulties in defining
functions analytically. Since GO algorithms do not require computation of
derivatives, they can be a good alternative in solving optimization problems using
off-the-shelf (black-box) software, where the details of the underlying algorithms may
not be known. Successful applications of various GOAs are reported elsewhere,
including Maskey et al. (2000a, b & 2002b). One of the most famous GOAs with wide-
spread application is genetic algorithms (GAs). A comprehensive evaluation of
optimization algorithms is not the intent of this study. However, the successful and ex-
tensive use of genetic algorithms (GAs) in various fields of engineering, including water
related problems, inspired the author to choose a GA scheme as an optimizer.

5.3.1 Principles of genetic algorithms

Genetic algorithms, developed by Holland (1975), are search algorithms based on the
mechanics of natural selection and natural genetics (Goldberg, 1989). A simple GA consists of