GOGG: Graph of Graphs Generator
Nested structures to support Hierarchical Genetic Evolution
Cameron Lamir, Undergraduate Research Student

VAIL Undergraduate Research Group - ROLLINS COLLEGE
Dr. Jennifer Seitzer, Director
jseitzer@rollins.edu
407-646-2303


This work describes a system that serves as a generative as well as an evaluative tool to represent nested chromosomes as well as measure them using dual fitness functions: one of the atomic and one of the structural, to enable the work of HGAs modeling CAESs. We have implemented HGAs in two other systems [Calvo2011] and [Wei2011] and are now engaged in applying this work to the modeling and evolution of CAESs using this tool, Graph-of-graphs Generator.

The driving motivation for developing system GOGG lay in both deductive and inductive applications. In the inductive domain, GOGG is being used to measure nested chromosomes in the simultaneous evolution of a solution at two different abstraction layers – providing a mechanism for fitness evaluation of nested chromosomes used in hierarchical genetic algorithms. In the deductive realm, plans are being made for system GOGG to provide a repository of hierarchical knowledge.

Application o HGA

A Hierarchical Genetic Algorithm (HGA) is an algorithmic technique of artificial intelligence that converges on a solution at both the atomic and structural levels. Complex adaptive and emergent systems (CAESs) are ubiquitous in our world— appearing as beehives, to social systems, to the brains in our heads that contemplate them. The modeling techniques used for understanding and predicting behavior of these systems in the past been ordinary differential equations, cellular automata, evolutionary game theory, agent based models, and networks [Ahmed2005]. Because of their implicit nested structure, self-organizing and iterative nature, however, we contend that HGAs show great promise to provide an alternative method of modeling CAESs.



Graph Theory and HGAs

One genre of problems that allow us to study CAESs using HGAs are graph theory problems. The undirected graph is a fundamental, widely used formalism for problem representation [Gross1999]. Moreover, cellular automata, which are based on one graph, have been successfully used to model CAESs [Fryer2004]. Our interest in expanding the consideration of graph theory to HGAs and CAESs is that many graph theory algorithms require both local and global attention. This ‘zooming in’ at each vertex and ‘zooming out’ to consider the whole graph as a structural entity is precisely the interaction of an HGA system as it vacillates between the atomic and structural levels.

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