Evolutionary Computation - Computational Intelligence in Time Series Forecasting - page 207

during which the functions and terminals are randomly picked from their sets, until
all branches end in terminals.

5.3.2 Execution of Algorithm

Once the initial population is obtained, the execution of the kernel algorithm
procedure starts with the execution of all programs of the initial population
generated, assigning the fitness values according to the fitness measures.
Thereafter, a new population of programs is created through

x reproduction of existing programs and by their copying into a new

population
x crossover of new programs generated from existing programs by genetic
recombination of their randomly chosen parts, and by executing the
crossover operation on two recombined programs
x mutation of a randomly chosen part of the program created from an
existing program.

After the run of genetic programming the best computer program in the population
is, for the time being, considered as the best, or nearly best one for the problem
solution. The program run can be finished or continued in order to check whether a
still better program can be found.
However, it should also be mentioned here that, like in genetic algorithms, the
mutation operation is very sparingly used.

5.3.3 Fitness Measure

So far, we have not considered one of the most principal issues in genetic
programming applications, i.e . the fitness measure . It is a tool that helps calculate
how well the individual programs of the population contribute to the evolutionary
progress of finding the problem solution. In practice, the fitness measure is
determined subjectively, so that it is viewed as a more obscure action than as an
exact definition. Also, formulation of the fitness measure is strongly problem
dependent. For the majority of problems it is understood as the error delivered by
the programs after their execution. This is true for every program run, so that it is
expected that the initial programs will most probably produce the lowest fitness
value, but some among them could have higher values than the rest of the
population. This triggers the evolutionary process. The offspring population, after
undergoing treatment through genetic operational steps, could replace the parent
population and undergoes a fitness check that is the basis for the next evolutionary
step. This continues until the best solution of the problem is found.

5.3.4 Improved Genetic Versions

Koza (1994) reported about a second, amended version of genetic programming
capable of evolving multipart programs by integrating the reusable, parameterized
subprograms into the main program. The subprograms are termed automatically
defined functions . Each such program can contain function defining branches ,