Using Cooperative Coevolution for Data Mining of Bayesian Networks - Advanced Techniques in Knowledge Discovery and Data Mining - page 168

one-point or two-point crossover, we devise a modified crossover operator.
Because we have a limit k on the size of the parent set, many of the bit-
string are 0s. As an illustration, suppose that the number of all possible
parents of a node is 30 and that k equals 5, the bit-string will contain many
0s and a few 1s. As a result, one-point or two-point crossover will be likely
to exchange segments of 0s and create nothing new.
To circumvent this problem, we use an approach similar to uniform
crossover [6.36]. For the two bit-strings that take part in crossover, we create
two different masks for each of them. As an illustration, Fig. 6.9 shows the
mask defined and the bit-strings. Here, suppose the number of all possible
parents of a node is six and hence the bit-strings are six bits long. A mask
of equal length is created for each bit-string. In a position where the original
string is 0, the mask is undefined. In a position where the original string is
1, the mask has a value of either 1 or 0. Consider the upper bit string in
Fig. 6.9, it has 1s only at the second, fourth, and sixth bits. Hence, the mask
value is undefined for the first, third, and fifth bits. If the mask value is 0,
the corresponding bit is copied to its offspring. Otherwise, if the mask value
is 1, the corresponding bit is copied to the offspring of the other partner. Re-
ferring to Fig. 6.9, the upper mask has the value 1 in the fourth bit position,
thus the corresponding bit is copied to the offspring of the other partner. The
action is indicated by the arrow in the figure.
With this crossover operator, we hope to have a uniform combination of
two given parent sets. From our experience, this modified crossover operator
indeed improves over the two-point crossover operator.
Update of . After the new population is created and evaluated at each

species population, an individual that has a better score than its correspon-
dent in

S

. If a better parent set is found for node
N i , then it will replace the parent set of node N i

S will be used to update S

. However, due to the
relaxation of the ordering constraint, such substitution may create an edge

in S

0 1 0 mask

000 1 1 1

first chromosome

0 10 1 0 1

offspring of the first chromosome

0 11 0 0 0

offspring of the second chromosome

0 1 1 0 0 0

second chromosome

0 1 mask

Fig. 6.9. The modified crossover operator.