Page 342 - Decision Making Applications in Modern Power Systems

304 Decision Making Applications in Modern Power Systems

Each individual is a point in a search space and a possible solution. The indi-
viduals of the population are made to go through a process of evolution.
GAs are based on analogy with the genetic structure and behavior of chro-
mosomes within a population of individuals using the following bases [8]:

The individuals in a population compete for resources and mates.
The most successful individuals in each “competition” will produce more
offspring than those who have a poor performance.
The genes of individuals “good” spread throughout the population so that two
good parents sometimes produce offspring that are better than either parent.
Thus each succeeding generation becomes more suitable to their
environment.
The simplest form of GA has the following three types of operators [10]:
Selecting and playing: This operator drains chromosomes among the pop-
ulation to make the play. The more capable is the chromosome, the more
often will be selected to reproduce.
Crossing: This is an operator who has to choose a place of function and
change the sequences before and after that position between two chromo-
somes, to create a new offspring (e.g., 10,010,011 and 11,111,010 chains can
cross after the third place to produce offspring 10011010 and 11110011),
and mimics the biological recombination between the haploid organisms.
Mutation: This operator produces random variations in a chromosome
(e.g., the chain can exchange 00011100 its second position for the current
01,011,100). The mutation can take place in each position of a bit in a
string, with a probability typically very small (e.g., 0.001). As can be
seen, the GAs are different from traditional methods of search and opti-
mization in four key areas.
They seek a population of points, not a single point. Maintaining a popu-
lation of well-adapted sampling points, the probability of falling into a
false peak is reduced.
Employing the objective function and it doesn’t need derivatives or other
information complementary, because sometimes they are very hard to be
achieved. Thus they gain in efficiency and generality.
They use stochastic transition rules, not deterministic. The GAs use ran-
dom operators to guide the search to the best spots; it may seem strange,
but the nature is full of precedents in this regard.

12.2.3 Nondominated sorting genetic algorithm II
For the development the multiobjective algorithms require mathematical
methods optimization on a population of solutions because the NSGA-II was
chosen as proposed, due to its diversity and reliability characteristics.
However, an overview should be maintained to enable the use of other pro-
cedures, such as ant colonies, simulated annealing, and the particle swarm.