Information Technology Reference
In-Depth Information
However, the use of multigenic chromosomes is more appropriate to evolve
solutions to complex problems, for they permit the modular construction of
more complex, hierarchical structures, where each gene codes for a smaller
building block (see the section Testing the Building Blocks Hypothesis in
chapter 12). These small building blocks are separated from each other and,
therefore, can evolve with a certain degree of independence.
And now consider another chromosome, this time encoding three Boolean
sub-ETs, linked by a three-argument function (the tails are shown in bold):
012345678901234501234567890123450123456789012345
IOaIA
cbaaacaacac
AOcaI
ccabcbccbac
IONAA
bbbbacbcbbc
(2.15)
As you can see in Figure 2.6, at least three genes are required to link the sub-
ETs with the IF(
a
,
b
,
c
) function. Note also that if more sub-ETs were needed,
the simplest organization would require at least nine sub-ETs so that they
could be linked properly by the three-argument function. Again, the multi-
subunit ET encoded in chromosome (2.15) could be linearized, forming the
following K-expression:
0123456789012345678901234567890
IIAIOaIOcONAAcbaaaIAbbbbacccaac
(2.16)
In summary, to express fully a chromosome, the information concerning
the kind of interaction between the sub-ETs must also be provided. There-
fore, for each problem, the type of linking function or type of interaction
between sub-ETs is chosen a priori. We can start with addition for algebraic
expressions or OR for Boolean rules but, in some cases, another linking func-
tion might be more appropriate (like multiplication or AND, for instance).
The idea, of course, is to find a good solution, and different linking functions
can be used to explore different recesses of the fitness landscape, increasing
the odds of finding Mount Everest. Notwithstanding, the basic gene expres-
sion algorithm can be easily modified to enable the evolution of linking func-
tions. And an elegant and interesting way of solving this problem consists in
the creation of homeotic genes that encode a developmental program or cell
in which different combinations of sub-ETs are brought together by follow-
ing the linking interactions operating in that particular cell (see how this is
achieved in the next section).
