Engineering Optimization

2Optimization Application Diversity and Complexity

2.1 Optimization

Optimization is a procedure that seeks the best and is relevant to a wide range of applications, but uses a common statement:

(2.1)

However, there is a wide diversity of applications presenting a variety of characteristics that should be considered when choosing an optimizer.

Many algorithms have a common approach to determining the DV* values: Set the derivative of the OF w.r.t. each DV equal to zero, and solve the set of equations for the DV* value. However, characteristics of the OF and DV often create difficulties (multiple solutions, nonlinear nature, no analytic methods to get derivatives, discrete values) that make this approach impossible to implement.

This chapter provides an overview of the diversity of applications and reveals the unique issues and difficulties associated with them.

2.2 Nonlinearity

Consider the simple example of determining the dimensions of rectangular box to meet a desired volume while minimizing surface area. If the sides have dimensions of height, width, and length, but no thickness, and if the sides can be constructed from ideal planes, then the volume is and the surface area is . Since choosing two dimensions constrains the third to meet the volume constraint, the optimization ...