 Abstract | Artificial and natural instances of networks are ubiquitous, and many problems of
practical interest may be formulated as questions about networks. Determining
the optimal topology of a network is pertinent to many domains. Evolutionary algorithms
constitute a well-established optimisation method, but they scale poorly
if applied to the combinatorial explosion of possible network topologies. Generative
representation schemes aim to overcome this by facilitating the discovery
and reuse of design dependencies and allowing for adaptable exploration strategies.
Biological embryogenesis is a strong inspiration for many such schemes, but
the associated complexities of modelling lead to impractical simulation times and
poor conceptual understanding. Existing research also predominantly focuses on
specific design domains such as neural networks.
This thesis seeks to define a simple yet universally applicable and scalable
method for evolving graphs and networks. A number of contributions are made
in this regard. We establish the notion of directly evolving a graph grammar
from which a population of networks can be derived. Compact cellular productions
that form a hypergraph grammar are optimised by a novel multi-objective
evolutionary design system called G/GRADE. A series of empirical investigations
are then carried out to gain a better understanding of graph grammar evolution.
G/GRADE is applied to four domains: symbolic regression, circuit design, neural
networks, and telecommunications. We compare different strategies for composing
graphs from randomly mutated productions and examine the relationship
between graph grammar diversity and fitness, presenting both the use of phenotypic
diversity objectives and an island model to improve this. Additionally, we
address the issue of bloat and demonstrate how concepts from swarm intelligence
can be applied to production selection and mutation to improve grammatical
convergence. The results of this thesis are relevant to evolutionary research into
networks and grammars, and the wide applicability and potential of graph grammar
evolution is expected to inspire further study. |
