Mechanical Engineering Design Complexity Metrics: Size, Coupling, and Solvability

Developing objective measures for evaluating and measuring the complexity of design would facilitate (1) empirical studies that require the use of equivalent but different design problems, (2) the development of design curriculums, and (3) the comparison of computer aided design automation tools. This paper surveys and evaluates different approaches to defining complexity in design for the design problem, process, and product. Three fundamental aspects to complexity are identified, size, coupling, and solvability, and expanded with respect to the three elements of design, problem, process, and product. Alternative methods for measuring these characteristics of the design are based on computational, information, and traditional design views of complexity. A method of measuring size as it relates to complexity is proposed for measuring the information content of design. A second method is proposed for decomposing a graph-based representation of design that provides a measure of the interconnectedness as it relates to complexity. Finally, two methods are proposed for determining the solvability complexity of design based on the effort involved and the degree of freedom of design. These measures are developed specifically for parametric and geometric problems as found in the embodiment design, but these principles may be applied beyond this.