Biomedical Engineering Reference
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randomly selected individuals. For this analysis, 80,000 individuals were selected uniformly from
16 runs and over 100 generations using a generative representation. Each point represents a
particular fitness change (positive or negative) associated with a particular mutation size. The
points on the left plot of Figure 4.6e were carried out on the nongenerative representation generated
by the generative representation and serve as the control set. For these points, 1 to 6 mutations
were applied so as to approximate mutations of similar phenotypic-size as those on the generative
representation. Each mutation could modify or swap a sequence of characters. The points on
the right of Figure 4.6e were also carried out randomly but on the generative representations
of the same randomly selected individuals. Only a single mutation was applied to the generative
representation, and consisted of modifying or swapping a single keyword or parameter. Mutation
size was measured in both cases as the number of modified commands in the final construction
sequences.
The two distributions in Figure 4.6e have distinct features. The data points separate into two
distinguishable clusters, with some overlap. Mutations generated on the generative representations
clearly correlate with both positive fitness and negative fitness changes, whereas most mutations on
the nongenerative representation result in fitness decrease. Statistics of both systems, averaged over
8 runs each, reveal that the two means are different with at least 95% confidence. Cross-correlation
showed that in 40% of the instances where a nongenerative mutation was successful, a generative
mutation was also successful, whereas in only 20% of the instances where a generative mutation
was successful, was a nongenerative mutation successful too. In both cases smaller mutations are
significantly more successful than larger mutations. However, large mutations (
>
100) were an
order of magnitude more likely to be successful in the generative case than in the nongenerative
case. All these measures indicate that the generative representation is more efficient in exploiting
useful search paths in the design space.
4.4.3
Regulatory Network Representations
The way that morphologies of organisms develop in biology is not only dependent on their
genotype; many other environmental effects play an important role. The ontology of an organism
depends on chains of productions that trigger other genes in a complex regulatory network. Some of
these triggers are intracellular, such as one set of gene products resulting in expression of another
group of genes, while other products may inhibit certain expressions creating feedback loops and
several tiers of regulation. Some signaling pathways transduce extracellular signals that allow the
morphology to develop in response to particular properties of its extracellular environment. This
is in contrast to the representations discussed earlier, where the phenotype was completely defined
by the genotype. Through these regulatory pathways, a genotype may encode a phenotype with
variations that can compensate, exploit, and be more adaptive to its target environment.
Bongard and Pfeifer (2003) explored a regulatory network representation for evolving both a
body and a brain of a robot. The machines were composed of spherical cells, which could each
contain several angular actuators, touch sensors, and angular sensor, as seen in Figure 4.7a. The
actuators and sensors were connected through a neural network as in Figure 4.1b, but the specific
connectivity of the network was determined by an evolved regulatory network. The regulatory
network contained genes which could sprout new connections and create new spherical cells, as
well as express or inhibit ''chemical'' signals that would propagate through the structure. These
chemical signals could also trigger the expression of other genes, giving rise to complex signaling
and feedback pathways. Some machines evolved in response to a fitness rewarding the ability to
push a block forward are shown in Figure 4.7b. These machines grow until they reach the block and
have a firm grasp of the ground; their regulatory nature would allow them to attain a slightly dif-
ferent morphology if they would be growing in the presence of a slightly differently shaped block.
It is interesting to note that an analysis of the regulation pattern (who regulates who, Figure 4.7c)
shows that genes that regulate growth of neurons (colored red) and genes that regulate growth if new
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