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150 Biomimetics: Biologically Inspired Technologies

10% (bandgap size). It is interesting to note that similar skewed-hexagonal pattern also appears in
nature for the same purpose (Figure 4.10c). The number of domains where open-ended synthesis
algorithms are producing human-competitive designs is growing rapidly (Koza, 2003).

4.7 FUTURE CHALLENGES

Parametric evolutionary optimization has been successfully applied in almost every engineering
domain (e.g., Gen and Cheng, 1999; Zalzala and Fleming, 1999; Jamshidi et al., 2002; Karr and
Freeman, 1998; Mazumder and Rudnick, 1998), but the use of evolution for open-ended design will
likely have an even higher impact. It is also one of the most poorly understood areas of evolutionary
computation. We are seeking to understand what underlies the complexity limits of what can be
designed automatically, and what allows natural systems to evolve systems so much more advanced
than what we can evolve artificially. Is it simply a matter of computational power — that nature is
performing an immeasurable number of evaluations every second? Or is there something more
fundamental about the evolutionary process that we have failed to capture? What are the implica-
tions of physical embodiment and self-replication that we often bypass in our simulations? What
are the implications of external fitness measures that we impose on the system, and of arbitrary
inductive biases we introduce thorough our choices of atomic building blocks and representations?
Does complexity require complex ecosystem with coevolution, symbiosis, competition, and co-
operation? Can we outperform natural evolution by using analytical shortcuts through its weak
statistical processes?
These are long standing problems that are not unique to evolutionary computation. The question
of how complex systems are synthesized is fundamental from three perspectives: AI research
interested in automating discovery processes, engineering research in understanding the design
process, and biology research interested in the origin of complexity. These perspectives are
captured well in the following statments:
One may wonder, [ ...] how complex organisms evolve at all. They seem to have so many genes, so
many multiple or pleiotropic effects of any one gene, so many possibilities for lethal mutations in early
development, and all sorts of problems due to their long development.
(Bonner, J. T., (1988) The Evolution of Complexity, p. 173.)

Today more and more design problems are reaching insoluble levels of complexity... these problems
have a background of needs and activities which is becoming too complex to grasp intuitively ...The
intuitive resolution of contemporary design problems simply lies beyond a single individual’s integra-
tive grasp.
(Alexander, C. A., Notes on the Synthesis of Form, 1964, pp. 3–5.)
I believe that scalability of open-ended evolutionary processes depends on their ability to exploit
functional modularity, structural regularity, and hierarchy (Lipson, 2004). Functional modularity
creates a separation of function into structural units, thereby reducing the amount of coupling
between internal and external behavior on those units and allowing evolution to reuse them as
higher-level building blocks. Structural regularity is the correlation of patterns within an individual.
Examples of regularity are repetition of units, symmetries, self-similarities, smoothness, and any
other form of reduced information content. Regularity allows evolution to specify increasingly
extensive structures while maintaining short description lengths. Hierarchy is the recursive com-
position of function and structure into increasingly larger and adapted units, allowing evolution to
search efficiently increasingly complex spaces.
The existence of modular, regular, and hierarchical architectures in naturally evolved systems
is well established (Wagner and Altenberg, 1996; Hartwell et al., 1999). Though evolutionary
processes have been studied predominantly in biological contexts, they exist in many other