Basic Concepts of Multi-objective Optimization

Abstract

Basic important concepts of multiobjective optimization was originated from Edgeworth and Pareto from the late of nineteenth century to the beginning of twentieth century, while a mathematical development was made by Cantor at almost the same ages. Today, we usually refer a solution of multiobjective optimization to as a Pareto solution. Scalarization techniques for multiple objective functions are already presented in Edgeworth’s book more than one hundred years ago. Several mathematical properties from a viewpoint of mathematical programming was developed by Kuhn and Tucker in the middle of twentieth century. This chapter describes some essential topics of mathematical foundations in multiobjective optimization which will be used in the following chapters.