Genetic and Evolutionary Algorithms for PSP - Digital Signal Processing in Power System Protection and Control - page 273

1 2 1 1 A B

1 1 H

1 1 C

2 1 E

2 2 2 2 D G

1 1 F

Initial Pop. Intermediate Pop. Next Pop.

(1 = good, 2 = bad)

Fig. 13.1 Basic scheme of the genetic-optimization process

In the field of genetic optimization the concepts and definitions borrowed from
genetics are exploited, such as

• Population—a set of individuals of selected number (living in the same envi-
ronment and competing with each other).
• Individuals—representatives of the prospective problem solutions given in a
coded form (treated also as points in the search universe).
• Chromosomes (coding chains or sequences)—ordered sequences (vectors) of
genes, encoding all the information about an individual.
• Gene—single element of the genotype, and in particular of the chromosome.
• Genotype (i.e., words-structure)—a set of chromosomes of given individual.
• Phenotype—a set of values corresponding to given genotype, i.e., its decoded
structure (the ''outward, physical manifestation'' of the organism, the organism
itself).

Natural principles according to the theory of Darwin, such as heredity, cross-
over, mutation, and selection, are used over several generations to develop and
improve the characteristics of the individuals. An important role in GA plays the
idea of adaptation function, which is also called matching function or goal func-
tion. The adaptation function allows assessing the adaptation grade of each indi-
vidual in the population, which forms the base for selection of the best individuals,
according to the general rule that ''only the strongest can survive''.
The general scheme of the basic genetic procedure is presented in Fig. 13.1 .
The algorithm starts from creating of the initial population, which can be under-
stood as a random choice of individuals that are represented by vectors of their
encoded parameters (chromosomes). In each iteration of GA the adaptation grade
of each individual is assessed, basing on which the intermediate population is
established with the best individuals from previous stage being represented more
frequently. The members of intermediate population are then subjected to further
genetic modifications and as a result the next population of individuals is created.
Consecutive iterations of GA are called generations, while the new individuals
can be treated as offspring (descendants) of elder population. The GA usually runs
in a closed loop with the interruption conditions defined according to the specific
requirements of the problem to be solved. In optimization analyses the algorithm