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which the EER is defined. They used two diversity functions for adjustment
purposes.
The dynamic GA presented by Li
et al.
operates in the following three stages:
x in the
initial stage
, in which the diversity measures follow the initial
conditions and the initial parameter values of GA
x in the
search stage
, in which the dynamic GA varies its parameters to
enable a broad search and improved exploitation
x in the
refinement stage
, in which the balance is adapted to manage the
search process more efficiently, while the best chromosome is already
close to the optimum problem solution in the search space.
Srinivas and Patnaik (1994) also used the manipulation of crossover and mutation
probabilities to retain the population diversity and still to support the convergence
capability of the algorithm. In order to vary the crossover, mutation and
reproduction probabilities,
i.e.
to vary
p
(
c
),
p
(
m
) and
p
(
r
) adaptively with the
objective of preventing the premature convergence of the GA to a local optimum,
they first tried to identify whether the GA is converging to a local or to a global
optimum at all. For this, they recommended the observation of the relation between
the average fitness value
f
across the population and the maximum fitness value
max
f
within the population (
i.e.
the fitness of the best chromosome in the
population). The value of the difference
avg
f f
is likely to be less for a
population that has converged to an optimum solution than that of the population
scattered in the solution space. The same property has been observed in
experiments with the GA. This is obvious, because convergence of the GA means
that the majority of the population has a similar high fitness value. This
alternatively implies that the average fitness of the population is high and is most
possibly close to the maximum fitness of the population. Therefore, this justifies
the difference
(
)
max
avg
being used here as the measure of convergence of the
f
f
max
avg
GA.
Usually in the adaptive GA experiments, the probability values
p
(
c
),
p
(
m
), and
p
(
r
) are varied, depending on the difference value
f f
,
i.e.
on search
results (Palit and Popovic, 2000). Since the probability values of
p
(
c
) and
p
(
m
)
have to be increased (in order to bring more genetic diversity into the population)
when the GA converges to the local optimum,
i.e.
when the difference
max
avg
f
f
max
avg
decreases, both
p
(
c
) and
p
(
m
) have to be varied inversely with
(
f
f
).
max
avg
Therefore, the same expression can be written mathematically as follows:
pr
()
(9.1)
f
f
k
rep
max
avg
pm
()
(9.2)
f
f
k
mu
max
avg
pc
()
(9.3)
k
f
f
cross
max
avg
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