Multidisciplinary Design Optimization Supported by Knowledge Based Engineering

3Constrained Design Space Search

3.1 Introduction

At the heart of any MDO system are the algorithms that guide the design process to an optimizing point, but before looking at them, we need to discuss and elaborate some of the characteristics and properties of the space within which an optimizing point lies. Some concepts and notations need to be reviewed together with a description of the optimality criteria which allow us (or some algorithm) to recognize an optimum when it has been located. This chapter covers this broad topic area and can be considered as a precursor to Chapters 5 and 7 which discuss optimizing strategies. The material presented, however, is not intended to be comprehensive as there are numerous books (Avriel, 1976; Nocedal & Wright, 1995; Sundaram, 1996) which discuss the fundamentals of nonlinear programming in detail; our intention is to provide an aide-memoire. Readers familiar with the foundations of nonlinear optimization and optimization theory may wish to move directly to latter chapters.

In Chapter 2, the concept of design variables is introduced, and we saw that these serve as coordinates of the design space in which the objective function(s) and constraints appear as functions of the design variables. That part of the design space which lies within the constraints is known as the feasible region, and any set of design variables that define a design point lying within the feasible region is known as a feasible design. If we are dealing with a single-objective ...