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In-Depth Information
the dynamic correlations between rules. This kind of measure can be used to
assist clustering rules.
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Fig. 13.10
.
Control structure of RUDI (Picture from Grefenstette, 1988)
Grefenstette had proposed a method to modify intensity, called profit-sharing
plan(PSP). In this method, problem solving plan is divided into a series of plots,
which are differentiated based on received exterior reward. If a plot wins in
bidding competition, related rule is considered to be active in this plot. In the plot
t, PSP can modify the intensity
S
i
(
t
) of each active rule:
S
i
(
t
+ 1) =
S
i
(
t
) -b
S
i
(
t
) +b
p
(
t
)
(13.26)
where
) is the obtained exterior reward when the plot is finished; that is, when
exterior reward is obtained, each active rule collects the bids and offers a part of
exterior reward. PSP's influence on a given rule R
i
can be calculated by the
following equation:
p
(
t
t
Ã
(i-b)
t-i
p
(i-1)
) = (1-b)
t
S
i
(
t
S
i
(0) + b
(13.27)
i
=
1
where t is a plot in which rule
R
i
is active, namely,
S
i
(
t
) is basically the average of
exterior reward; (1 -
b
) is exponential attenuation factor. If
b
is small enough,
S
(
t
)
is equal to the average of
p
(
t
). If exterior reward
p
(
t
) is a constant
p
*
,
S
i
will
*
:
converge to an equilibrium value
S
i
t
Ã
(
i
-
b
)
t-i
p
*
] =
p
*
i
*
= lim
t
ŗ¯
[(1-
)
t
S
b
S
i
(0)+
b
(13.28)
i
=
1
Under the case of constant profit, it is in accord with equation (13.27), and the
error
E
i
(
t
) =
p
* -
S
i
(
t
) is reduced by the following rate
E
i
(
t
) =
p
* -
S
i
(
t
):
