Chapter 18 - Multi-objective Optimum Design Concepts and Methods

Abstract

There are numerous applications where one would like to optimize multiple conflicting objective functions simultaneously. Methods to solve such multi-objective optimization problems are presented. First, some basic concepts and terminology associated with the problem are explained. These include criterion space, design space, utility and preference functions, and Pareto optimal set. It is noted that the multi-objective optimization problem does not have a unique optimum solution. There are actually infinite solutions depending on the preferences for various objective functions. These solutions constitute a set known as the Pareto optimal set. Various multi-objective optimization methods are presented and discussed. These include genetic algorithms, the weighted sum method, the weighted min–max method, the weighted global criterion method, the lexicographic method, the bounded objective function method, and goal programming. Criteria to select a method are discussed and presented in a table.