On February 17, 2026, Dr. Lennart Schäpermeier successfully defended his PhD thesis “Opening the Black-box of Continuous Multi-objective Optimization: Problem Visualization, Performance Assessment and Benchmarking”. The doctoral thesis was awarded summa cum laude. Congratulations!

Background and Motivation

In many optimization problems, you need to be balancing multiple goals. For example, when you travel from Germany to Spain, you want to travel there (1) quickly and (2) for little money. Thus, you want to identify all trade-offs between these goals, as most likely the fastest connection is not simultaneously the cheapest. In this example, one would like to find all options between the cheapest long-distance bus, a fast high speed rail connection and a private charter flight. However, any slow and expensive connection would not be of interest. In his research, Dr. Lennart Schäpermeier studies properties of such multi-objective optimization problems.

Optimization often uses the picture of an “optimization landscape” – hills and valleys that represent good and bad solutions with a slope leading you to the nearest hill, or local optimum. For multi-objective problems, similar helpful analogies or intuitions do not exist. Therefore, the thesis revolves around describing these challenges and advancing related tools. It also investigates how we can leverage a deeper understanding of multi-objective problem landscapes to build better optimization heuristics.

Methodology

The foundation lays in a visualization technique that was developed to illustrate the optimization landscape for the studied multi-objective problems – the so-called Plot of the Landscape with Optimal Trade-offs (PLOT). PLOTs for problems studied by other researchers gave surprising insights about the search dynamics in these multi-objective problems, as well as an insight into under- and overrepresented challenges in widespread problem collections. The thesis built on theoretical insights from the community and transferred them to empirical research in multi-objective optimization. For example, Dr. Lennart Schäpermeier created an interpretable benchmark for multi-objective optimizers building on simple, well-understood problems. For the large benchmarking experiments, he utilized the HPC resources provided by ScaDS.AI Dresden/Leipzig and the Center for Information Services and High Performance Computing (ZIH) at TU Dresden.

Results

The newly developed visualization technique helps researchers to get a better understanding of multi-objective problems. Furthermore, many tools were built around insights that were derived from that, including:

• an optimization heuristic that exploits “tunnels” between local optima (that would conventionally be considered dead ends),
• improvements in performance assessment (to tell which heuristic is suited to solve which kinds of problems), and
• a diverse set of test problems with controllable optimization challenges.

Together, these advances contribute to a better understanding of multi-objective optimization problems – including the challenges and opportunities their “landscapes” present to the algorithms and heuristics operating thereon – and how to find optimal trade-offs in complex systems with multiple, conflicting optimization goals.

Outlook

Many decisions in practice are taken by solving some kind of optimization problem. This includes examples such as ticket pricing, delivery routing, or training machine learning models. While there often are conflicting interests to consider, these are then reduced to a single-objective problem. A better grasp on multi-objective problems can help us consider additional objectives more effectively. For example, this could include emissions in addition to costs for package delivery or fairness in addition to raw accuracy in machine learning.

The thesis has shown that the right visualization method allows for a much better understanding of the optimization domain. It addresses some open but also poses many new research questions. The optimization community can already apply the results to better understand the inner workings of multi-objective optimization heuristics. From an industry-oriented perspective, well-understood test problems can stand in as surrogates for real-world optimization problems. They allow to cheaply test an optimization procedure before applying it in a potentially very cost-intensive, but structurally similar, environment – as in related single-objective optimization domains.

Further Information and Resources

Visualizations

• R package
• Visualization dashboard

Performance Assessment / Benchmarking

• https://github.com/schaepermeier/2023-emo-mpm2
• https://github.com/schaepermeier/r2-revisited
• https://github.com/schaepermeier/bonobench
• https://zenodo.org/records/18403177

Papers in the Cumulative Dissertation

• Lennart Schäpermeier, Christian Grimme, Pascal Kerschke (2022). Plotting Impossible? Surveying Visualization Methods for Continuous Multi-Objective Benchmark Problems. IEEE Transactions on Evolutionary Computation. Vol. 26 (6), pp. 1306-1320, IEEE. DOI: 10.1109/TEVC.2022.3214894
• Lennart Schäpermeier, Christian Grimme, Pascal Kerschke (2022). MOLE: Digging Tunnels Through Multimodal Multi-Objective Landscapes. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2022). pp. 592-600, ACM. DOI: 10.1145/3512290.3528793
• Angel E. Rodriguez-Fernandez, Lennart Schäpermeier, Carlos Hernández, Pascal Kerschke, Heike Trautmann, Oliver Schütze (2025). Finding ϵ-Locally Optimal Solutions for Multiobjective Multimodal Optimization. IEEE Transactions on Evolutionary Computation. Vol. 29 (5), pp. 2019-2031, IEEE. DOI: 10.1109/TEVC.2024.3458855
• Lennart Schäpermeier, Pascal Kerschke (2024). Reinvestigating the R2 Indicator: Achieving Pareto Compliance by Integration. Proceedings of the 18th International Conference on Parallel Problem Solving From Nature (PPSN XVIII). pp. 202-216, Springer. DOI: 10.1007/978-3-031-70085-9_13
• Lennart Schäpermeier, Pascal Kerschke (2025). R2 v2: The Pareto-Compliant R2 Indicator for Better Benchmarking in Bi-Objective Optimization. Evolutionary Computation. pp. 1-17, MIT Press. DOI: 10.1162/EVCO.a.366
• Lennart Schäpermeier, Pascal Kerschke, Christian Grimme, Heike Trautmann (2023). Peak-A-Boo! Generating Multi-Objective Multiple Peaks Benchmark Problems with Precise Pareto Sets. Proceedings of the 12th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2023). pp. 291-304, Springer. DOI: 10.1007/978-3-031-27250-9_21
• Lennart Schäpermeier, Pascal Kerschke (2025). BONO-Bench: A Comprehensive Test Suite for Bi-Objective Numerical Optimization with Traceable Pareto Sets. ACM Transactions on Evolutionary Learning. ACM (Just Accepted). DOI: 10.1145/3795775

Awards

One publication included in the thesis called “Reinvestigating the R2 Indicator: Achieving Pareto Compliance by Integration.” won the “Best Paper Award” out of 101 accepted publications at the PPSN 2024 conference (CORE ranking: A).

Dr. Lennart Schäpermeier

Dr. Lennart Schäpermeier learned about multi-objective optimization, and some of the open research questions he eventually tackled in his PhD, while working as a student assistant under the supervision of Prof. Pascal Kerschke (“Friedrich List” Faculty of Transport and Traffic Sciences and principal investigator at ScaDS.AI Dresden/Leipzig), who would later become his PhD supervisor. He was fascinated by the search dynamics in these problems, and the opportunities presented by studying them more closely. This curiosity fueled a lot of his PhD studies. Dr. Lennart Schäpermeier will continue his academic journey as a PostDoc at the University of Münster. He has joined the research group “Computational Social Science and Systems Analysis” lead by Prof. Christian Grimme. We wish him all the best for the next step in his academic career!