Genetic and Evolutionary Algorithms for PSP - Digital Signal Processing in Power System Protection and Control - page 276

Parent 1 Parent 2

0 000 110011 10 0 011 000010 11

0000 000010 10 0011 110011 11

Descendant 1 Descendant 2

Fig. 13.5 An example of two-point crossover

of the same individual is limited and can happen only when the section for an
individual is wider than the distance between the pointers.

13.1.2 Emerging of the Next Generation

The bunch of selected individuals is further used to produce the population of the
next generation. The descendants/offsprings are created from their parents in the
process of crossover, mutation and recombination, whereas the chromosomes of
descendants are a result of chromosome material changes of two (or just one)
parent individuals. The genetic operations mentioned should be understood as

• Crossover—exchange of some parts of chromosome information of two selected
parent individuals, Fig. 13.5.
• Mutation—small change of the chromosome information (usually at one or two
positions of the chromosome string), Fig. 13.6 .
• Recombination—creating of new individuals by finding their ''location'' along a
line or at line crossings (discrete or real-valued recombination), Fig. 13.7 .

The crossover on two strings of genes can be single-point (when the chromo-
somes are cut at single point, the same for both individuals), multi-point (with
multiple cutting points, in Fig. 13.5 —two-point cutting) or uniform operation
(when bits are randomly copied from the first or from the second parent).
It should be mentioned that the individuals to take part in given genetic
operation are selected from the intermediate population randomly. The probabil-
ities of genetic operations should be defined at the beginning of optimization
procedure, being constant numbers or values changing with the generation number
(with time). It can happen that not all individuals are subjected to genetic oper-
ations, some of them can pass to the next generation without any change. It is usual
practice that the population of next generation contains the same number of
individuals as the preceding one, which simplifies automation of the GA

procedure.
Summarizing, one can enumerate the following steps of GA implementation:
• Specify the problem, define constraints and optimality criteria,
• Chose the way of encoding (binary, permutation, value, tree …),