Geoscience Reference
In-Depth Information
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Cut point
(a)
(b)
FIGURE 7. 2
Two examples of recombination on bitstrings: (a) single-point crossover and (b) uniform
crossover.
7.4.4 r
ecoMBination
/c
roSSoVer
Recombination is the process by which new individuals (offspring) are created through combining
information from both parents. The resulting offspring inherits components from both parents. This
allows the EA to explore new areas of solutions in the search space. Without recombination, the
offspring are simply duplicates of the parents. This does not give any opportunity for improving the
fitness of the population.
Figure 7.2 shows the classic operators that are used in GA: single-point crossover and uniform
crossover. It is important to note that the choice of operator must match the representation of the
solution chosen. For example, representation in GAs is often binary, and hence operators such as
single-point and uniform crossover should be used. This would not be appropriate for GP where
representation is through trees.
7.4.5 M
utation
The main challenge in finding the global solution lies with the presence of multiple local minima,
that is, there are potentially many different solutions available for the problem. Graphically, this
can be represented by a series of mountains and valleys (see Figure 7.3). Finding the lowest point in
a particular valley is relatively easy; a simple progression down the slope will often give the local
minimum. However, locating the global minimum is a more challenging problem; there is no cer-
tain way of knowing which valley it is located within, or even how many valleys there are, without
fully searching the whole of the parameter space.
B
C
A
D
E
F
FIGURE 7. 3
Example of a function containing multiple maxima and minima to demonstrate the difference
between local and global extrema. A and C represent local maxima; D and E are two of four local minima; F
is the global minimum.
