On Handling a Large Number of Objectives A Posteriori and During Optimization

Dimensionality reduction methods are used routinely in statistics, pattern recognition, data mining, and machine learning to cope with high-dimensional spaces. Also in the case of high-dimensional multiobjective optimization problems, a reduction of the objective space can be beneficial both for search and decision making. New questions arise in this context, e.g., how to select a subset of objectives while preserving most of the problem structure. In this chapter, two different approaches to the task of objective reduction are developed, one based on assessing explicit conflicts, the other based on principal component analysis (PCA). Although both methods use different principles and preserve different properties of the underlying optimization problems, they can be effectively utilized either in an a posteriori scenario or during search. Here, we demonstrate the usability of the conflict-based approach in a decision-making scenario after the search and show how the principal-component-based approach can be integrated into an evolutionary multicriterion optimization (EMO) procedure.