Dimo Brockhoff, Tea Tusar “Benchmarking Multiobjective Optimizers 2.0”
Benchmarking is an important part of algorithm design, selection and recommendation. In this tutorial, we will discuss the past and future of benchmarking multiobjective optimizers. In particular, we will discuss the benchmarking of multiobjective algorithms by falling back on single-objective (quality indicator values) comparisons and thus how we are able to use all methodologies and tools from the single-objective domain such as empirical distributions of runtimes. We will also discuss the advantages and drawbacks of some widely used multiobjective test suites, that we all have become familiar with over the years, and explain how we can do better: by going back to the roots of what a multiobjective problem is in practice, namely the simultaneous optimization of multiple objective functions. Finally, we discuss recent advances in the visualization of (multiobjective) problem landscapes and compare the previous and newly proposed benchmark problems in the context of those landscape visualizations.
Amiram Moshaiov “Evolutionary Multi-Concept Optimization”
Multi-Concept Optimization (MCO) was originally motivated by the desire to computationally support the selection of a conceptual solution in the early stage of the engineering design process. Over the years MCO has evolved into a multi-facet category of search problems, which is not restricted to engineering design. Among such problem types are: concept selection, multi-modal optimization, and design/decision space exploration. In MCO problems, the term conceptual solution, or in short concept, refers to a pre-defined subset of the feasible solutions, which is meaningful to the decision-makers. In such problems, the predefined meaningful subsets of particular solutions are explored to reach some informative results at the conceptual and the particular design/decision levels. Research on techniques to solve MCO problems has focused primarily on unique EMO techniques for MCO (EMCO). This tutorial will provide insight to the unique features of EMCO and to its potential real-life applications. It aims to introduce the EMO community of researchers and practitioners to past and current research on EMCO and to provide an overview about potential future research directions concerning EMCO.
Erella Eisenstadt-Matalon, Amiram Moshaiov, Kalyan Deb “Multi-Objective Games”
Game theoretic studies commonly deal with scalar games. Yet, there are many situations in which each of the intertwined decision problems involves conflicting objectives of the player. Multi-Objective Games (MOGs), which are also known as multi-payoff games, vector-payoff games, and multi-criteria games, aim to model and solve such situations. Research on MOGs has grown exponentially since its emergence during the 50s; yet, most studies on MOGs remain theoretical and have rarely been accompanied with developments of associated numerical methods to solve such games. The possible applications include trustworthy security system design, arms race problems and other coevolutionary competitive and cooperative systems. The main difference between MOGs and Multi-Objective Optimization (MOO) is that MOO commonly involves just one decision process whereas MOG involves intertwined decision problems. This is reflected by the fact that in a MOO problem each solution is commonly associated with one performance vector, whereas in a MOG each strategy is associated with a set of such vectors. This tutorial aims to provide the EMO community with some background on MOGs and their solution by evolutionary computation. It also aims to shed some light about the relationships between MOGs, robust multi-objective optimization, bi-level multi-objective optimization, and multi-objective coevolutionary games. Finally, this tutorial is expected to motivate EMO, MCDM, and Games researchers to collaborate and make the ideas more computationally attractive and practically applicable.
Kalyan Deb, Dhish Saxena, Erik Goodman “Machine Learning Assisted Evolutionary Multi-Objective Optimization”
Evolutionary multi- and many-objective optimization algorithms (EMaOAs) iteratively evolve a set of solutions, towards a good Pareto Front approximation. The availability of multiple solution sets over successive generations, makes EMaOAs amenable to application of machine learning (ML), for different pursuits. This tutorial will begin by highlighting the existing studies on ML-based enhancements for EMaOAs, before focusing on the recently proposed innovized progress operators within the gamut of reference vector (RV) based EMaOAs. This will include a detailed discussion on how the convergence and diversity capabilities of RV-EMaOAs can be simultaneously enhanced, by learning efficient search directions through a judicious mapping of inter- and intra-generational solutions, respectively. Results on hard-to-solve test problems will demonstrate the utility of the above approach, in light of convergence-diversity balance, ML-based risk-reward tradeoff, and avoidance of extra solution evaluations. This tutorial will conclude by proposing a list of ML-based enhancements that could be explored in future.
Christian Grimme, Lennart Schaepermeier, Pascal Kerschke “Continuous Multimodal Multi-Objective Optimization”
In the context of optimization, multimodality describes the existence of several (local or global) optimal solutions. On the one hand, additional (locally) optimal solutions can be attractive as they provide potential alternatives for practical realizations. On the other hand, local solutions can represent traps for many optimization approaches and lead to delayed or premature convergence. Multimodality also plays an important role in multi-objective optimization. However, a lack of formal definitions of multimodality in MO problems and a lack of intuitive approaches for visualizing landscapes curbed the development of this relatively new research field for a long time. This tutorial provides a comprehensive overview of the challenges and interpretations of multimodality in MO problems, highlights the theoretical fundamentals of multimodality in MO, and details visualization approaches, algorithms, benchmarks, as well as measures that address specific aspects of multimodality. The tutorial is suited for beginners and experts in EMO.