Engineering Optimization, 5th Edition

15 Practical Aspects of Optimization

15.1 Introduction

Although the mathematical techniques described earlier, particularly Chapters 3-13, can be used to solve different types of engineering optimization problems, the use of engineering judgment and approximations help in reducing the computational effort involved. In this chapter we consider several types of approximation techniques that can speed up the analysis time without introducing too much error [1]. The approximation methods include the reduction of size of an optimization problem, fast reanalysis techniques, and use of derivatives of static displacements and stresses, eigenvalues and eigenvectors, and transient response of mechanical and structural systems in gradient evaluations, and also in predicting the response in the neighborhood of a base design. These techniques are especially useful in finite element analysis‐based optimization procedures. This chapter presents several types of approximation methods that can be used in practical computation, and also the use of derivatives of different structural/mechanical system response quantities to speed up the optimization process.

15.2 Reduction of Size of an Optimization Problem

15.2.1 Reduced Basis Technique

In the optimum design of certain practical systems involving a large number of (n) design variables, some feasible design vectors X ₁, X ₂, …, X _r may be available to start with. These design vectors may have been suggested by experienced designers ...