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.
%0 Conference Paper
%1 schapermeier2023peakaboo
%A Schäpermeier, Lennart
%A Kerschke, Pascal
%A Grimme, Christian
%A Trautmann, Heike
%B Evolutionary Multi-Criterion Optimization
%C Germany
%D 2023
%E Emmerich, Michael
%E Deutz, André
%E Wang, Hao
%E Kononova, Anna V.
%E Naujoks, Boris
%E Li, Ke
%E Miettinen, Kaisa
%E Yevseyeva, Iryna
%I Springer
%K topic_engineering Benchmarking Multi-objective_optimization Multimodal_optimization Numeric_optimization Problem_generator n/a_OA_procedure
%P 291--304
%R 10.1007/978-3-031-27250-9_21
%T Peak-A-Boo! Generating Multi-objective Multiple Peaks Benchmark Problems with Precise Pareto Sets
%X 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.
%@ 978-3-031-27249-3
@inproceedings{schapermeier2023peakaboo,
abstract = {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.},
added-at = {2024-10-02T13:52:45.000+0200},
address = {Germany},
author = {Sch{\"a}permeier, Lennart and Kerschke, Pascal and Grimme, Christian and Trautmann, Heike},
biburl = {https://puma.scadsai.uni-leipzig.de/bibtex/240940185b15225a6193be2cf112c01a1/scadsfct},
booktitle = {Evolutionary Multi-Criterion Optimization},
doi = {10.1007/978-3-031-27250-9_21},
editor = {Emmerich, Michael and Deutz, Andr{\'e} and Wang, Hao and Kononova, {Anna V.} and Naujoks, Boris and Li, Ke and Miettinen, Kaisa and Yevseyeva, Iryna},
interhash = {890e15afa608158cbc84643e67c1446a},
intrahash = {40940185b15225a6193be2cf112c01a1},
isbn = {978-3-031-27249-3},
keywords = {topic_engineering Benchmarking Multi-objective_optimization Multimodal_optimization Numeric_optimization Problem_generator n/a_OA_procedure},
language = {English},
note = {Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 12th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2023, EMO ; Conference date: 20-03-2023 Through 24-03-2023},
pages = {291--304},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
timestamp = {2024-11-28T17:41:02.000+0100},
title = {Peak-A-Boo! Generating Multi-objective Multiple Peaks Benchmark Problems with Precise Pareto Sets},
year = 2023
}
