Chapter 2 - Optimum Design Problem Formulation

Abstract

A key step in the solution process is the formulation of a given problem as an optimization problem. This process is described in five well-defined steps. At the end of this process, a well-defined optimization problem is obtained that has three main ingredients: optimization (design) variables that describe design of the system, an objective (cost) function that measures worth of the system, and a set of performance constraints that the system must meet. This five-step procedure is developed and discussed using an example problem. The five-step procedure is demonstrated by formulating several design optimization problems from different areas. Some problems can be formulated in several different ways depending on the definition of design variables. This is demonstrated in some example problems. Then a general design optimization model is defined as minimizing a cost function subject to equality constraints and inequality constraints expressed in the “less than or equal to” form. Active, inactive and violated constraints, feasible set, and some other terms used in the optimization process are defined. Types of optimization problems encountered in practice are discussed. The numerical process needed to develop a proper optimization formulation for a practical design problem is explained.