Kouli_etal_2008_Groundwater modelling_BOOK.pdf - Pantelis ...

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K.L. Katsifarakis
fields with very regular shape. Even in the most sophisticated numerical models, though, field
boundaries are smoothed to successive linear segments. Moreover it should be kept in mind
that impermeable boundaries are actually inferred from geological maps, supported,
sometimes, by geophysical exploration. A certain degree of inaccuracy enters the definition of
constant head boundaries, too, although they are visible, since inclined coasts should be
considered as vertical in two-dimensional flow models. In some cases, the scope of the study
plays a role in the final judgement of the researcher. If, for instance, it is checked whether a
pumping scheme results in excessive water level drawdown, placing an impermeable
boundary relatively closer to pumped wells, leads to increased safety factor.
As computers become more and more efficient, one is tempted to use the most
complicated available model, since the importance of computational volume and computer
memory requirements become less and less important. But, as already implied in the previous
paragraphs, this might not be the best choice. Detailed models produce better results, only if
they are fed with accurate and adequate field data. Moreover, the implicit error, which is due
to the numerical procedure, might go undetected, as the users of complicated numerical
models tend to be too confident of their results.
3. The Role of the Optimization Model
In groundwater resources management, models for flow simulation are very often combined
with optimization ones. In the last few years, evolutionary methods, such as genetic
algorithms, become more and more popular as optimization tools, e.g. McKinney and Min-
Der Lin (1994), Ouazar and Cheng (2000). Use of these methods requires that the flow
simulation model is run many times. Thus, the total computational volume may become the
limiting factor and the balance between accuracy and computational efficiency should be
reconsidered. To clarify this point, genetic algorithms, the most common evolutionary
method, is briefly outlined.
3.1. Outline of the Method of Genetic Algorithms
Genetic algorithms (G.A.), initially introduced by Holland (1975), are a mathematical tool
with a wide range of applications. They are particularly efficient in optimization problems,
especially when the respective objective functions exhibit many local optima or discontinuous
derivatives.
There are already extensive books, e.g. Goldberg (1989), Michalewicz (1996), Reeves
and Rowe (2003), which deal with the theoretical background, the perspectives, the
computational details and the applications of genetic algorithms (and other evolutionary
techniques). Their main concepts are briefly described in the following paragraphs.
As their name implies, genetic algorithms are essentially a mathematical imitation of the
biological process of evolution of species. They start with a number of random, potential
solutions of the investigated problem. These solutions, which are called chromosomes,
constitute the population of the first generation. In binary genetic algorithms, each
chromosome is essentially a binary string. The number of its characters, which are called
genes, is usually predetermined.