Evolutionary Computation - Computational Intelligence in Time Series Forecasting - page 197

5.2.1.4 Crossover
Crossover is a recombination operator that combines subparts of two parent
chromosomes to produce offspring that contain some parts of both parents' genetic
material. A crossover probability term P ( C ) is set to determine the operation rate.
Many GA practitioners consider the crossover operator to be the determining factor
that distinguishes the GA from all other optimization algorithms.
The power of a GA arises from crossover, which causes a structured, yet
randomized exchange of genetic materials between solutions, with the possibility
that “good” solutions can generate the “better” ones. In the crossover process, two
individuals called parent 1 and parent 2 are required. A crossover operation
between parent 1 and parent 2 takes place with respect to a particular bit location
(called the crossover point ) selected randomly and the portions of the
chromosomes beyond this point are exchanged to form offspring. Hence, a
crossover generates two new individuals of the next generation.
In our experiment, the best individual or chromosome from all generations is
always selected as parent 1. Parent 2 is selected through the RW selection
procedure from the mating pool. The crossover operation between two individuals
takes place if a certain condition is satisfied. For example, two individuals undergo
a crossover operation if a random number generated is greater than the probability
of crossover (a small number). Otherwise, both individuals remain unaffected. If
two new individuals are generated through crossover, then the population counter
is incremented by 2, starting with

0.5 N u . Otherwise the population counter
remains the same. In our case, using the crossover operator, only 50% of the
population is created for the next generation (see Figure 5.1).

pop

5.2.2 Auxiliary Genetic Operators

In addition to the above standard genetic operators , the following operators are
also used in the GA experiment.

5.2.2.1 Fitness Windowing or Scaling
Regulation of the number of copies of superfit or extraordinary individuals is
especially important in small-population GAs. At the beginning of the GA runs it is
common to have a few extraordinary individuals in a population of mediocre
colleagues. However, if left to the normal proportionate selection rule, say to the
RW, the extraordinary individuals would take over a significant proportion of the
finite population in a single generation, and this is undesirable, as it leads to
premature convergence. This is because without the fitness scaling during the
matured run of the GA most of the individuals may converge and maintain a small
diversity, giving rise to a small difference between their fitness value even though
the GA run may not have located the desired global optimum. Therefore, the
crossover operation in this case produces new offspring practically without much
improvement in their fitness value during the matured run of the GA. Only the
mutation operator tries to maintain a small diversity and explores the new region
randomly. As a remedy for this premature convergence, fitness scaling or fitness
windowing can generally be applied. This prevents any super-fit individual from
always taking over and suppressing the lower fitness individual during the RW