Formulating Design Problems as Optimization Problems

Abstract

Abstract Proper formulation of a design problem as an optimization problem is an important step in the solution process. A procedure used to formulate optimization problems is described, discussed, and illustrated. The mathematical definition of an optimization problem has three basic elements: design variables, an objective function, and constraints. These terms have been defined and discussed in this chapter. Examples are used to illustrate the process of transcribing a design problem into an optimization problem. Then a general model that can represent many different types of design optimization problems is defined and discussed. Various concepts and terms associated with the solution of an optimization problem are explained. Many engineering design problems require numerical methods to simulate their response to the inputs. Formulation of such optimization problems involves implicit functions of the design variables. Such formulations are also presented and discussed. In addition, there are formulations that use the design variables, the analysis variables, and other intermediate variables simultaneously as unknowns of the optimization problem. These are known as alternative formulations and are also described. Practical optimization problems require numerical methods to solve them. Many good programs are available that incorporate modern computational algorithms to solve these problems once they have been formulated properly. Excel is one such program that is widely available. Its use is demonstrated by solving some of the example problems.