Principles of Optimal Design Modeling and Computation

Designing is a complex human process that has resisted comprehensive description and understanding. All artifacts surrounding us are the results of designing. Creating these artifacts involves making a great many decisions, which suggests that designing can be viewed as a decision-making process. In the decision-making paradigm of the design process we examine the intended artifact in order to identify possible alternatives and select the most suitable one. An abstract description of the artifact using mathematical expressions of relevant natural laws, experience, collected data, and geometry is the mathematical model of the artifact. This mathematical model may contain many alternative designs, and so criteria for comparing these alternatives must be introduced in the model. Within the limitations of such a model, the best, or optimum, design can be identified with the aid of mathematical methods.

In this first chapter we define the design optimization problem and describe most of the properties and issues that occupy the rest of the book.We outline the limitations of our approach and caution that an “optimum” design should be perceived as such only within the scope of the mathematical model describing it and the inevitable subjective judgment of the modeler.

Mathematical Modeling

Although this book is concerned with design, almost all the concepts and results described can be generalized by replacing theword design by theword system. We will then start by discussing mathematical models for general systems.

The System Concept

A system may be defined as a collection of entities that perform a specified set of tasks. For example, an automobile is a system that transports passengers. It follows that a system performs a function, or process, which results in an output. It is implicit that a system operates under causality; that is, the specified set of tasks is performed because of some stimulation, or input.