A Simple Modularity Measure For Search Spaces Based On Information Theory

Daniel Polani, Principal Lecturer, Computer Science, University of Hertfordshire, United Kingdom

In striving to understand of how complex systems can consistently arise from simpler ones (e.g. evolvability), a number of central motifs are increasingly coming into focus: the need for a unified language in which complex phenomena can be described, analysed and ultimately constructed, and the insight that a systematically sustained drive for increasing global complexity requires control of local complexities. For the first, information theory is a natural candidate, the second emphasizes the importance of modularity in many complex systems.

We present a measure to quantify modularity in a classical simple, but instructive search space scenario. For this purpose, the scenario is translated into the language of information theory. It turns out that, while successful as universal language for dynamical processes, information theory requires some unexpectedly subtle treatment in this static context. Among other, the measure provides a handle for studying the connection between search space complexity and evolvability.