Digital Signal Processing Reference
In-Depth Information
to select a particular value of
η
from the meme pool
{
η
1
,η
2
,...,η
10
}
using the
Q(S
i
,η
j
),j
1
,
2
,...,
10 for the individual member located at state
S
i
.
The adaptation of
Q(S
i
,η
j
)
is done through the reward/penalty mechanism of
classical TDQL. If a member of the population at state
S
i
on selecting
η
=
η
j
moves
to a new state
S
k
causing an improvement in its fitness measure, then
Q(S
i
,η
j
)
is
given a positive reward following the TDQL algorithm. Otherwise a penalty is given
to
Q(S
i
,η
j
)
by introducing a decrease in
Q
-value.
The basic algorithm is outlined in the following sections.
=
8.5.1 Initialization
The algorithm employs a population of
NP D
-dimensional parameter vectors rep-
resenting the candidate solutions. Thus the
j
th component of the
i
th population
member is initialized according to (
8.21
) as mentioned in Sect.
8.3
. The entries for
the
Q
-table are initialized as small values. For instance, if the maximum
Q
-value
attainable is 100, then we initialize the
Q
-values of all entries in the
Q
-table as 1.
8.5.2 Adaptive Selection of Memes
The proper choice of the Reinforcement Learning Scheme facilitates the adaptive
selection of memes from the meme pool. We employ Fitness Proportional selec-
tion, also known as the Roulette-Wheel selection, for the selection of potentially
useful memes. A basic advantage of this selection mechanism is that diversity of
the meme population can be maintained. Although fitter memes would enjoy much
higher probability of selection, the memes with poorer fitness do manage to survive
and may contribute some components as evolution continues. Mathematically, the
selection commences by the selection of a random number in the range
for
each population member. Let us consider the selection from the
η
meme pool for a
member of state
S
i
. The next step involves the selection of
η
j
such that the cumula-
tive probability of selection of
η
[
0
,
1
]
=
η
1
through
η
j
−
1
is greater than
r
. Symbolically,
j
−
1
10
p(S
i
,η
=
η
m
)<r<
p(S
i
,η
=
η
m
).
(8.27)
m
=
1
m
=
j
The probability of selection of
η
=
η
j
from the meme pool
{
η
1
,η
2
,...,η
10
}
is
given by
Q(S
i
,η
j
)
10
k
=
=
=
p(S
i
,η
η
j
)
.
(8.28)
1
Q(S
i
,η
k
)
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