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crossover. We use
T
and
T
as expressions of these trees, respectively. In each
parental individual, we define a set
′
()
A
as the set of agents that refers to the
selected tree
T
. When we perform a crossover operation on trees
T
and
T
′ ,
the following three cases may arise:
z
Type a. If the relation between the sets is
() ()
′
, the structure of each
A
T
=
A
T
individual is unchanged.
z
Type b. If the relation between the sets is
() ()
, the division of groups
takes place in the individual with
T
, so that the only tree referred to by the
agents in
′
A
T
⊃
A
T
() ()
can be used for crossover. The individual that
maintains
T
′ is unchanged.
z
Type c. If the relation between the sets is
′
A
T
∩
A
T
() ()
() ()
⊄
′
,
the unification of groups takes place in both individuals so that the agents in
() ()
′
A
T
⊄
A
T
and
A
T
A
T
′
A
T
∪
A
T
can refer to an identical tree.
We expect that this method will make the search efficient and an adequate
group structure will be acquired. At the same time, the acquired group structure
becomes a clue for understanding the cooperative behavior and the necessary
division of labor.
7.3.3 Extraction of Rules by ADG
Each agent group represents experts that have a tree structural program as the
approximate formula for describing the data. For the training data, each group
calculates the predicted value from input
x
. The results acquired from respective
groups become candidates for the output
o
. The value closest to the answer
y
i
is adopted as the output
o
from the set of candidates.
Suppose that the
k
th agent belongs to a certain group,
g
. We define the load
of the agent
w
as follows:
k
(
) (
)
(7.10)
In the training data, each group calculates the predicted value from input data.
The calculation results acquired from respective groups become candidates for the
output. The value closest to the answer is adopted as the output. If there are
multiple groups, which have the closest value to the answer, the group with more
agents is adopted. Adopted frequencies of respective groups are defined as the
number of adoptions for all data. In experiments for hepatobiliary disorder, the
adopted frequency of each group is counted when the rule successfully returns true
for each data of the target disorder.
We calculate the variance of the load in all agents,
V
. From the point of
view of minimization of prediction error and load balancing, the fitness
f
is
defined as in Eq. (7.11). We minimize
w
k
=
adopted
frequency
of
/
Number
of
agents
that
belong
to
.
g
g
f
by evolution:
(
)
2
∑
f
=
y
−
o
+
α
V
.
(7.11)
i
i
a
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