Tutorial on Evolutionary Multiobjective Optimization

Abstract

Many optimization problems are multiobjective in nature in the sense that multiple, conflicting criteria need to be optimized simultaneously. Due to the conflict between objectives, usually, no single optimal solution exists. Instead, the optimum corresponds to a set of so-called Pareto-optimal solutions for which no other solution has better function values in all objectives. Evolutionary Multiobjective Optimization (EMO) algorithms are widely used in practice for solving multiobjective optimization problems due to several reasons. As randomized blackbox algorithms, EMO approaches allow to tackle problems with nonlinear, nondifferentiable, or noisy objective functions. As set-based algorithms, they allow to compute or approximate the full set of Pareto-optimal solutions in one algorithm runeopposed to classical solution-based techniques from the multicriteria decision making (MCDM) field. Using EMO approaches in practice has two other advantages: they allow to learn about a problem formulation, for example, by automatically revealing common design principles among (Pareto-optimal) solutions (innovization) and it has been shown that certain single-objective problems become easier to solve with randomized search heuristics if the problem is reformulated as a multiobjective one (multiobjectivization). This tutorial aims at giving a broad introduction to the EMO field and at presenting some of its recent research results in more detail. More specifically, we are going to (i) introduce the basic principles of EMO algorithms in comparison to classical solution-based approaches, (ii) show a few practical examples which motivate the use of EMO in terms of the mentioned innovization and multiobjectivization principles, and (iii) present a general overview of state-of-the-art algorithms and techniques. Moreover, we will present some of the most important research results in areas such as indicator-based EMO, preference articulation, surrogate-assisted EMO, and performance assessment. Though classified as introductory, this tutorial is intended for both novices and regular users of EMO. Those without any knowledge will learn about the foundations of multiobjective optimization and the basic working principles of state-of-the-art EMO algorithms. Open questions, presented throughout the tutorial, can serve for all participants as a starting point for future research and/or discussions during the conference.