Peak-A-Boo! Generating Multi-objective Multiple Peaks Benchmark Problems with Precise Pareto Sets

Research output: Contribution to book/conference proceedings/anthology/reportConference contributionContributedpeer-review



The design and choice of benchmark suites are ongoing topics of discussion in the multi-objective optimization community. Some suites provide a good understanding of their Pareto sets and fronts, such as the well-known DTLZ and ZDT problems. However, they lack diversity in their landscape properties and do not provide a mechanism for creating multiple distinct problem instances. Other suites, like bi-objective BBOB, possess diverse and challenging landscape properties, but their optima are not well understood and can only be approximated empirically without any guarantees. This work proposes a methodology for creating complex continuous problem landscapes by concatenating single-objective functions from version 2 of the multiple peaks model (MPM2) generator. For the resulting problems, we can determine the distribution of optimal points with arbitrary precision w.r.t. a measure such as the dominated hypervolume. We show how the properties of the MPM2 generator influence the multi-objective problem landscapes and present an experimental proof-of-concept study demonstrating how our approach can drive well-founded benchmarking of MO algorithms.


Original languageEnglish
Title of host publicationEvolutionary Multi-Criterion Optimization - 12th International Conference, EMO 2023, Proceedings
EditorsMichael Emmerich, André Deutz, Hao Wang, Anna V. Kononova, Boris Naujoks, Ke Li, Kaisa Miettinen, Iryna Yevseyeva
Number of pages14
Publication statusPublished - 2023

External IDs

Scopus 85151045717
Mendeley aebef3d5-fbc2-3944-b9f0-1c8df33aa68e
ORCID /0000-0003-3929-7465/work/142241484



  • Numeric optimization, Problem generator, Benchmarking, Multi-objective optimization, Multimodal optimization