Engineering Optimization

33Evaluating Optimizers

33.1 Introduction

An optimizer is a procedure for determining the optimum. A classic statement is to determine the value of the decision variable to maximize desirables and minimize undesirables:

(33.1)

The optimization algorithms presented in prior chapters included the analytical method, Newton’s, Golden Section, heuristic direct, Hooke–Jeeves, leapfrogging, etc. The question here is not “What is the result when an optimizer is used?” but “Which is the best optimizer?” Here the DV is not a variable in an engineering model, but the choice of the optimizer, a class variable. The statement is

(33.2)

In order to evaluate an optimizer, we must define the desirables and undesirables, define metrics to assess them, and define a way to either combine them in a single OF or to alternately use a Pareto analysis.

As well as class variables for the DVs, each optimizer has coefficient values (such as the number of players, an acceleration/temper factor, initial step sizes, or thresholds for logic switching or convergence). These may be continuum valued or discrete. Further, there are other diverse category choices and other class variables, such as forward or central difference, surrogate model type, and local exploration pattern. Accordingly, the DV list should include ...