About

In the context of optimization, multimodality describes the existence of multiple locally (or globally) optimal solutions. Multimodality is often one of the main challenges associated with optimizing a given problem and thus one of the main properties that is considered when developing optimization algorithms and designing benchmark sets to evaluate and compare state-of-the-art methods. Additionally, decision makers are often interested in more than one (best) solution to a given optimization problem, and want to be offered a variety of good alternative solutions with different characteristics. Sometimes, especially in practical applications, near-optimal solutions with specific properties are considered interesting as well, justifying the need for finding and characterizing locally optimal solutions as well.

While multimodality is extensively studied for single-objective problems (Preuss 2015; Li, Engelbrecht, and Epitropakis 2013), it is only beginning to be understood in the domain of multi-objective (MO) optimization, where optimal trade-offs between multiple, conflicting objectives are sought. Formal descriptions of multimodal multi-objective (MMO) problems have only recently been developed (Grimme et al. 2021), and there still exist different viewpoints on the subject within the evolutionary computation community (Cosson et al. 2022; Tanabe and Ishibuchi 2020; Schütze and Hernández 2021; Schütze et al. 2024). MMO problems prove to give rise to new challenges in problem formulation and optimizer convergence, but also new opportunities: It turns out that what is thought to be local search traps can often serve as a guide to further exploration of the search space, leading to dominating solutions (Grimme, Kerschke, and Trautmann 2019; Schäpermeier, Grimme, and Kerschke 2022).

In our workshop, we strive to discuss perspectives from different MMO communities and try to foster collaborations and the exchange of challenges, solution approaches and tools to study MMO landscapes in different problem domains. We invite presentations covering various optimization problem domains (continuous/numeric, discrete/combinatorial) as well as presentations in the realm of machine learning (ML) and algorithm configuration, where configuration landscapes are oftentimes multi-objective and multimodal simultaneously.

References

Cosson, Raphaël, Roberto Santana, Bilel Derbel, and Arnaud Liefooghe. 2022. “Multi-Objective NK Landscapes with Heterogeneous Objectives.” In Proceedings of the Genetic and Evolutionary Computation Conference, 502–10. GECCO ’22. New York, NY, USA: Association for Computing Machinery. https://doi.org/10.1145/3512290.3528858.

Grimme, Christian, Pascal Kerschke, Pelin Aspar, Heike Trautmann, Mike Preuss, André H. Deutz, Hao Wang, and Michael Emmerich. 2021. “Peeking Beyond Peaks: Challenges and Research Potentials of Continuous Multimodal Multi-Objective Optimization.” Computers & Operations Research 136: 105489. https://doi.org/https://doi.org/10.1016/j.cor.2021.105489.

Grimme, Christian, Pascal Kerschke, and Heike Trautmann. 2019. “Multimodality in Multi-Objective Optimization - More Boon Than Bane?” In Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, East Lansing, MI, USA, March 10-13, 2019, Proceedings, edited by Kalyanmoy Deb, Erik D. Goodman, Carlos A. Coello Coello, Kathrin Klamroth, Kaisa Miettinen, Sanaz Mostaghim, and Patrick M. Reed, 11411:126–38. Lecture Notes in Computer Science. Springer. https://doi.org/10.1007/978-3-030-12598-1_11.

Li, Xiaodong, Andries Petrus Engelbrecht, and Michael G. Epitropakis. 2013. “Benchmark Functions for CEC’2013 Special Session and Competition on Niching Methods for Multimodal Function Optimization.” RMIT Univ., Australia: Evolutionary Computation; Machine Learning Group.

Preuss, Mike. 2015. Multimodal Optimization by Means of Evolutionary Algorithms. Springer. https://doi.org/10.1007/978-3-319-07407-8.

Schäpermeier, Lennart, Christian Grimme, and Pascal Kerschke. 2022. “MOLE: Digging Tunnels Through Multimodal Multi-Objective Landscapes.” In Proceedings of the Genetic and Evolutionary Computation Conference. GECCO ’22. New York, NY, USA: Association for Computing Machinery. https://doi.org/10.1145/3512290.3528793.

Schütze, Oliver, and Carlos Hernández. 2021. Archiving Strategies for Evolutionary Multi-Objective Optimization Algorithms. Springer. https://doi.org/10.1007/978-3-030-63773-6.

Schütze, Oliver, Angel E. Rodríguez-Fernández, Carlos Segura, and Carlos Hernández. 2024. “Finding the Set of Nearly Optimal Solutions of a Multi-Objective Optimization Problem.” IEEE Transactions on Evolutionary Computation, 1–1. https://doi.org/10.1109/TEVC.2024.3353546.

Tanabe, Ryoji, and Hisao Ishibuchi. 2020. “A Review of Evolutionary Multi-Modal Multi-Objective Optimization.” IEEE Transactions on Evolutionary Computation (TEVC) 24 (1): 193–200. https://doi.org/10.1109/TEVC.2019.2909744.