Evolutionary Computation - Computational Intelligence in Time Series Forecasting - page 208

which are capable of communicating with the automatically defined branches, and
result-producing branches , and are also capable of calling the automatically
defined functions. Koza (1994) has shown that genetic programming with
automatically defined functions is scalable, enabling genetic programming to
determine the size and the shape of the problem solution automatically ( i.e . of the
program tree).
However, when multipart programs and automatically defined functions are
integrated, the problem arises as to how to tailor the architecture of the evolved
programs. This problem has been solved through dynamic evolutionary selection
of the architecture of the overall program while running the genetic programming.
5.3.5 Applications
Application examples of genetic programming are numerous. Apart from abundant
mathematical applications, such as applications in symbolic regression, many
practical applications have been reported in engineering, particularly in pattern
classification, vehicle control, robotics, etc . For the reader, of direct interest is
genetic programming application in time series prediction (Santini and Tettamanzi,
2001), where two problem solution strategies have mostly been applied:
x a neural network model has been optimally tuned by genetic programming
(Zang et al. , 1997)
x appropriate programs have been evolved using genetic programming for
computing the future values of a given time series, given its last values
(Yoshichra et al., 2000 ).
The first strategy belongs to the category of evolving neural networks using
evolutionary computation in general, which will be treated in detail in Part 3 of the
topic. In the following, our attention will be focused on the strategy used by Santini
and Tettamanzi (2001), mainly achieved by
x evolving the individuals made up of some different expressions, one for
each prediction step
x developing of special crossover and mutation operators adapted to the
generated individuals of population
x calculating the fitness based on given time series data.
Mulloy et al. (1996) used the genetic programming approach in the prediction of
chaotic time series.
5.4 Evolutionary Strategies
Evolutionary approaches that are very similar to genetic algorithms are the
evolutionary strategies developed by Rechenberg and Schwefel (Rechenberg,
1973) while working on the design of an optimal jet nozzle that produces the most
powerful propulsion at the lowest fuel consumption. They came to the idea of
developing a new solution concept that starts with commercially available jet