Page 97 - Data Science Algorithms in a Week

Evolutionary Optimization of Support Vector Machines … 81

n
Other types include -point crossover or uniform crossover. In uniform crossover, a
mask determines which parent will provide each bit. For instance, one child could be
formed by selecting the bit from parent1 if the corresponding bit in the mask is a 1 and
selecting the bit from parent 2 if the bit in the mask is a 0. Another child could be formed
by doing the inverse (Figure 5).

Figure 5. Uniform crossover.

There is no clear “best crossover” and the performance of the GA usually depends on
the problem and the other parameters as well.
Crossover is not limited to two parents, though. There have been experimental results
pointing out that multiparent crossover, e.g., six parent diagonal crossover, have better
performance than the one-point crossover (see Eiben, 2002 and references therein).
In the one-child version of the diagonal crossover, if there are n parents, there will
be n  1 crossover points and one child (see Figure 6).

In GAs, crossover is the main operator of variation, while mutation plays a reduced
role. The simplest type of mutation is flipping a bit at each gene position with a
predefined probability. Some studies have shown that varying the mutation rate can
improve significantly the performance rate when compared with fixed mutation rates (see
Thierens, 2002).

Figure 6. Diagonal crossover with one child.

There are three main approaches to varying the mutation rate (Thierens, 2002):
dynamic parameter control, in which the mutation rate is a function of the generations.