Engineering Optimization

30Perspective

30.1 Introduction

This chapter contains diverse points of information, which can be clarifying or of interest. It is a step back to gain perspective of the forest. I often sense that the sequence of details on one topic can obscure its relation to other topics. Many have been presented. This chapter seeks to connect diverse topics so that the reader can understand the choices and interactions.

30.2 Classifications

Optimizers can be classified as to their algorithms. Additionally, applications can be classified as to the issues that they present. And convergence criteria can be classified as to their basis. Often the name of the category of one is misapplied to describe the other.

1. Optimizers can be classified by their methodology:
   1. Analytical—Use calculus to exactly solve for the solution. This may provide an explicit solution, or it may result in iterative root finding on the equations.
   2. Direct search—Only use function values. Guide the next trial solution with human heuristic rules.
   3. Region elimination—A methodology applied to univariate direct searches to eliminate a DV range that probably does not contain the optimum.
   4. Gradient based—Use local surface slopes (sensitivity of OF to DV) to direct the search.
   5. Second‐order techniques—Use a quadratic model of the OF response to DVs to direct the next TS.
   6. Surrogate model based—Generate an approximating model of the OF response to DVs, and then use its optimum to direct the next TS. SQ uses a quadratic model as a surrogate ...