Chapter 16 - Pareto Boundary Maps

Abstract

This chapter discusses the Pareto boundary maps. Rather than a single method, Pareto boundary maps refer to a whole class of methods that first aggregate a problem's multiple objective functions into a single objective, and then systematically vary the parameters of scalarization while optimizing the resulting functions to generate a series of candidate solutions. Such methods can be thought of as exploring the non-inferior set in objective function space by parameterizing it using a mapping. The reason for resorting to the parameterization is that the characteristic irregularity of the non-inferior set makes it difficult to explore directly. With an appropriate parameterization, this obstacle is circumvented. The non-inferior set is explored indirectly by navigating around the much more amenable structure of the parameterization. While any number of parameterizations will work, the chosen one must satisfy some requirements if it is to successfully perform its navigational function. The parameter set must have a simple, a priori visible structure. Moreover, there must be a one-to-one mapping between parameter values and corresponding non-inferior values.