A Simple Modularity Measure for Search Spaces based on Information Theory

Within the context of Artificial Life the question about the role of modularity has turned out to be crucial, especially with regard to the problem of evolvability. In order to be able to observe the development of modular structure, appropriate modularity measures are important. We introduce a continuous measure based on information theory which can characterize the coupling among subsystems in a search problem. In order to illustrate the concepts developed, they are applied to a very simple and intuitive set of combinatorial problems similar to scenarios used in the seminal work by Simon (1969). It is shown that this measure is closely related to the classification of search problems in terms of Separability, Non-Decomposability and Modular Interdependency as introduced in (Watson and Pollack, 2005).