Analysis of Objectives Relationships in Multiobjective Problems Using Trade-Off Region Maps

Abstract

Understanding the relationships between objectives in many-objective optimisation problems is desirable in order to develop more effective algorithms. We propose a technique for the analysis and visualisation of complex relationships between many (three or more) objectives. This technique looks at conflicting, harmonious and independent objectives relationships from different perspectives. To do that, it uses correlation, trade-off regions maps and scatter-plots in a four step approach. We apply the proposed technique to a set of instances of the well-known multiobjective multidimensional knapsack problem. The experimental results show that with the proposed technique we can identify local and complex relationships between objectives, trade-offs not derived from pairwise relationships, gaps in the fitness landscape, and regions of interest. Such information can be used to tailor the development of algorithms.