Multidisciplinary Design Optimization Supported by Knowledge Based Engineering

6Optimizing Multiobjective Function Problems

6.1 Introduction

Chapters 3 and 4 focused on the problem of optimizing a single-term objective function; unfortunately, this is not the normal situation confronting a real-world team, when designing a major artifact such as an airplane, an automobile, or a ship. In these situations, the problem usually involves a number of objective functions that often conflict with each other. An engineer designing a new car will be confronted with the need to create a design that is fuel economic, has adequate acceleration for overtaking, is comfortable, does not cost too much, and has customer appeal. The reader will note that some of these design criteria require minimizing a function such as fuel consumption and purchase price, while other criteria require maximizing, such as the rate of acceleration. To bring all the objective function to the same standard mode “smaller is better” introduced previously in the book, we minimize the negative of those functions that require maximizing.

Formally speaking, the standard single-objective constrained minimization becomes in a multiobjective optimization case

(6.1)

The “q” objective functions in (6.1) may be of different type—one being manufacturing cost, another structural mass, etc.—and if the vector of design variables x has n components, that is, x_i = 1, …, n, then some of the objective functions may ...