Engineering Optimization

1Optimization: Introduction and Concepts

1.1 Optimization and Terminology

Optimization is a procedure for seeking the best choices, and there are essential elements to the procedure. First, there must be criteria for rating choices. This can be alternately stated as a method for determining the value of a metric of goodness, the assessment value of how a person balances desirables and undesirables. One must have this assessable or quantifiable metric of desirability to be able to choose the best. Also, there must be a relation between choices and the evaluation of the outcome. This relation can be either a model or an experiment. The procedure (equation, algorithm, experimental method) for determining the value of the desirability metric is called the objective function (OF). The choices that you can change to improve the OF value are called the decision variables (DVs).

You might want to minimize (costs, expenses, risk, etc.) or maximize (profit, reliability, probability of success, etc.). Optimization will seek DV values that lead to the optimum, either minimum or maximum.

A trial solution (TS) is a particular DV choice. It might not be the optimum. The optimum is denoted as DV*. For simple, idealized applications, one can determine the exact value of DV*; but, for most applications, this is an ideal concept, like the value of π. You’ll get close enough to the true value for a particular need and call the close enough TS the DV*.

There are usually several opposing concepts ...