Optimization Methods

Abstract

Optimization problems discussed in this chapter can be formulated in the general form presented in Sect. 1.3.4, where the objective function and the constraints are nonlinear functions of the variables. The solution methods commonly used for obtaining the optimal design may be divided into several categories. One classification of solution methods considers specific versus general methods. Specific optimality criteria methods, used exclusively in structural optimization, will be presented in Sect. 4.3. In this chapter general-purpose mathematical programming (MP) methods, which are commonly applied to optimization problems in several fields, will be discussed. These methods have the advantage of wider applicability and base of resources. As a result, efficient and reliable algorithms are continually developed. Applying MP methods to structural design, a wide variety of problems can be considered, including:

• a. Complex structural systems subject to different failure modes in each of several load conditions.

• b. General design variables representing cross-sectional dimensions, the geometry or the topology of the structure.

• c. Various constraints on the structural behavior and on the design variables.

• d. A general objective function representing the cost or the weight of the structure.