4Direct Search Methods for Locating the Optimum of a Design Problem with a Single-Objective Function

4.1 Introduction

At the core of any MDO system, there is a set of algorithms which optimizes an objective function subject to a range of constraints that are derived from the design requirements. It is, therefore, important for the engineer to know the capabilities of these algorithms and the demands they make on the rest of the software modules in an MDO system configured for a specific application. This requires having a basic understanding of the algorithms strengths and limitations. It is important to know what specific algorithms require from other modules in the system which may be complex discipline-based modules, so that an appropriate choice can be made. For example, some optimization algorithms require gradient information, and if this is not available, they cannot be directly employed.

The chapter is intended to supply the reader with sufficient information to understand what the various mono-optimization methods and algorithms require in terms of gradients, update formulae, etc. With this information, an engineer can make rational choices on the selection of appropriate optimization tools for use in a practical MDO design system. However, we are not attempting to provide a comprehensive set of methods covering the entire range of such software. The reader wanting to obtain a comprehensive description of the methods touched on should consult the references found within ...

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