Overview

In Part I of this book, we reviewed preparatory knowledge needed to start learning optimization: Matlab, and elementary mathematics. In Part II, we were exposed to the world of optimization and its potentially powerful role in our lives as engineers or professionals in quantitative fields. We then delved into the specific activities of analysis, design, and optimization, their links and distinctions. In the previous chapter, we then began addressing the fundamental aspects of computational optimization. These included single objective optimization, and the different approaches to optimization (analytical, numerical, experimental, and graphical). This was followed by a discussion of software options.

In this chapter, we study one of the most important aspects of optimization in practice, the notion of multiobjective optimization. Stated simply, Multiobjective optimization is the art and science of formulating how to optimize a set of competing objectives, which is almost always the case in practice. A detailed presentation of the pertinent methods is provided in such a way as to allow you to be readily productive and effective in practical design.

The Multiobjective Problem Definition

The identification of the right design objectives plays a crucial role in the design of any system. More often than not, in real-life design, you will find that your optimization problem contains more than one design objective. For example, wouldn't it be nice if your car dealer would tell you that the car you like happens to feature more miles per gallon and also costs less than a competitor's car? As an engineer, you would think twice before making a decision based on his interesting comments. If he were right, the other car company would probably not stay in business for very long. The point here is that while designing any product or system, you will almost always have to consider several competing design objectives. As a car designer, you would like the car to provide the most miles per gallon possible, while taking care that the car does not cost a million dollars.