Information Measure for Modularity in Engineering Design

Modular structures are common in complex natural and artificial systems, and the terms “modular” or “modularity” are used throughout the engineering design literature. However, formal ways to measure or quantify modularity are still needed. This paper introduces an information-based approach to measure modularity, built on the relationship between complexity and modularity. In this information-based measure, a modular structure is encoded as a message describing information contained in the modular structure; the shorter the message, the higher the modularity of the structure. The information measure is dependent on the modeling and representation of the system. Following this basic idea, an approximate expression for the information measure of abstract graph structures is introduced. Since function structures in engineering design are typically represented as abstract graphs, this approach can be used to synthesize favorable modularity in parallel with the design of new systems. Using a genetic algorithm approach, with the reciprocal of the approximate measure as the fitness function, modular configurations are found in abstract graphs.