Information Technology Reference
In-Depth Information
For a multidimensional optimization task, multigenic chromosomes are
obviously used. Consider, for instance, the chromosome below composed of
three genes (the Dc's are shown in bold):
010101
?
2
?
4
?
1
(8.2)
and respective arrays of random numerical constants:
C
1
= {-1.777252, -0.281341, -1.666779, -1.060455, 1.65213},
C
2
= {1.340088, -0.242614, -0.592712, 0.729187, -1.63266},
C
3
= {-0.113372, -0.763123, 0.138122, 1.322388, -1.060913}.
Its expression results in three different parameter values:
p
1
= -1.666779,
p
2
= -1.63266,
p
3
= -0.763123.
These parameters are then used to find the maximum (or minimum) of a
function. For instance, for the function below:
f
(
p
,
p
,
p
)
2
.
sin
p
2
1
p
2
2
1
02
sin(
4
p
)
(8.3)
1
2
3
3
they give:
f
(-1.666779, -1.63266, -0.763123) = 3.1324168397
which is the output or value returned by function (8.3) for that particular set
of parameter values.
So, each chromosome in a parameter optimization task encodes a particu-
lar set of parameter values. And for each set of parameter values, the evalu-
ation of the function at hand returns a corresponding output. And this output
is what will be used as basis for evaluating the fitness of the individual. But
since the value returned by a particular set of parameters can be anywhere in
the real line, something must be done about negative or zero fitnesses. To
solve this problem, for each generation, the worse-of-generation fitness
f
min
is evaluated and, if
f
min
is zero or negative, the absolute value of
f
min
plus 1 is
added to the fitness of all individuals. This way one guarantees that all the
individuals will have positive fitness, with the less fit having fitness equal to
one. This transformed fitness can now be used to select individuals to repro-
duce with modification and will be used in all the problems of this chapter.
