Analysis of objectives relationships in multiobjective problems using trade-off region maps

Understanding the relationships between objectives in many-objective optimisation problems is desirable in order to develop more effective algorithms. We propose a techniquefor 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

Multi-Objective Combinatorial Optimization: Problematic and Context

International audienceThe present chapter aims to serve as a brief introduction for the rest of the chapters in this volume. The main goal is to provide a general overview of multi-objective combinatorial optimization, including its main basic definitions and some notions regarding the incorporation of user's preferences. Additionally, we also present short descriptions of some of the most popular multi-objective evolutionary algorithms in current use. Since performance assessment is a critical task in multi-objective optimization, we also present some performance indicators, as well as some discussion on statistical validation in a multi-objective optimization context. The aim of this chapter is not to be comprehensive, but simply to touch on the main fundamental topics that are required to understand the material that is presented in the rest of the book