Complexity and Modularity Within Evolved Robotic Control Systems
John T. Loree, Vassar College ’16, Evan Altiero, Vassar College ’16, Joshua Ridley, Vassar College ’17, Jessica Ng, Vassar College’16 and Joshua Bongard, Ken Livingston, Nick Livingston, John Long, Jodi Schwarz and Marc Smith
Evolutionary robotics seeks to find principles that explain how autonomous agents respond to selection and, in some cases, become more complex over generational time. To begin to find these principles, we test the hypothesis that modularity of bodies and genetic systems is key to permitting the evolution of complex behaviors. Testing involves experiments in which we create robots (see poster by Ridley et al.), test them in selection trials, and analyze the outcomes of those trials. Hypothesis testing in this contexts depends crucially on an appropriate measure of modularity. We employ the measure Q as developed by Newman (2008) to capture the degree of independence of subunits within a complex system.
We examine the behavior of Q across the spectrum of networks and complexities that will be investigated in this project (see poster by Altiero et al.). Previously Q has been calculated as a simple sum and found using search algorithms which surveyed the entire space of possible network divisions. As an alternative, Newman (2008) calculated Q via an eigenvector optimization of a connection matrix representative of the size and structure of the network in question. We used this formulation and found a composite computer code to efficiently analyze networks, both with and without the real constraints present in our evolved control system. In addition, an algorithm and code was written in MatLab to create matrices and analyze the data generated. The results of this analysis will allow us to establish the changes in modularity that occur as our populations of robots evolve over generations and thus contribute to our understanding of one of the basic principles that affect the evolution of complexity.