Chapter 17 - Multi-objective Optimum Design Concepts and Methods

Abstract

This chapter describes basic terminology, concepts, and solution methods for multiobjective optimization problems. There are many practical applications where the designer may want to optimize two or more objective functions simultaneously. These are called multiobjective, multicriteria, or vector optimization problems; which is referred as multiobjective optimization problems. From a classical standpoint, optimizing a single function simply entails determining a set of stationary points, identifying a local maximum or minimum, and possibly finding the global optimum. In contrast, the process of determining a solution for a multiobjective optimization problem is slightly more complex and less definite than that for a single-objective problem. The predominant solution concept in defining solutions for multiobjective optimization problems is that of Pareto optimality. A key characteristic of multiobjective optimization methods is the nature of the solutions that they provide. Some methods always yield Pareto optimal solutions but may skip certain points in the Pareto optimal set. Other methods are able to capture all of the points in the Pareto optimal set, but may also provide non-Pareto optimal points. The former quality is beneficial when we are interested in using a method to obtain just one solution point. The latter quality is useful when the complete Pareto optimal set needs to be generated.