A Mathematical Theory of Design : Foundations, Algorithms, and Applications

Abstract

The complexity of a design process or a design artifact substantially influences their performance. When evaluation of terms such as "design complexity" and its "quality" is addressed in studies, it is often performed in an ad hoc manner. This chapter attempts to remedy this situation by articulating two definitions of design complexity (structural complexity versus funcitonal complexity), their associated value measures, and the relationships between them. The structural definition states that a design complexity is a function of its representation. Defining design complexity in the structural way provides quantitative techniques for evaluating vague terms such as 'abstraction level', 'design form's size', and 'designing effort'. the functional definition states that a design complexity is a function of its probability of successfully achieving the required specifications (functional requirements and constraints). The proposed measurable metrics provide a proper basis for evaluating each step of the design process, and accordingly recommends the direction to follow for design modification and enhancement. It also provides a framework for comparing competing artifacts (the output of a design process). Detailed examples of complexity valuation using the measures are described. The chapter concludes by discussing the scope of the measures.