Obtaining Smoothly Navigable Approximation Sets in Bi-objective Multi-modal Optimization

Renzo J. Scholman; Anton Bouter; Leah R.M. Dickhoff; Tanja Alderliesten; Peter A.N. Bosman

doi:10.1007/978-3-031-14721-0_18

Obtaining Smoothly Navigable Approximation Sets in Bi-objective Multi-modal Optimization

Renzo J. Scholman^*, Anton Bouter, Leah R.M. Dickhoff, Tanja Alderliesten, Peter A.N. Bosman

^*Corresponding author for this work

Algorithmics

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

Even if a Multi-modal Multi-Objective Evolutionary Algorithm (MMOEA) is designed to find solutions well spread over all locally optimal approximation sets of a Multi-modal Multi-objective Optimization Problem (MMOP), there is a risk that the found set of solutions is not smoothly navigable because the solutions belong to various niches, reducing the insight for decision makers. To tackle this issue, a new MMOEAs is proposed: the Multi-Modal Bézier Evolutionary Algorithm (MM-BezEA), which produces approximation sets that cover individual niches and exhibit inherent decision-space smoothness as they are parameterized by Bézier curves. MM-BezEA combines the concepts behind the recently introduced BezEA and MO-HillVallEA to find all locally optimal approximation sets. When benchmarked against the MMOEAs MO_Ring_PSO_SCD and MO-HillVallEA on MMOPs with linear Pareto sets, MM-BezEA was found to perform best in terms of best hypervolume.

Original language	English
Title of host publication	Parallel Problem Solving from Nature – PPSN XVII - 17th International Conference, PPSN 2022, Proceedings
Editors	Günter Rudolph, Anna V. Kononova, Hernán Aguirre, Pascal Kerschke, Gabriela Ochoa, Tea Tušar
Publisher	Springer
Pages	247-262
Number of pages	16
ISBN (Print)	9783031147203
DOIs	https://doi.org/10.1007/978-3-031-14721-0_18
Publication status	Published - 2022
Event	17th International Conference on Parallel Problem Solving from Nature, PPSN 2022 - Dortmund, Germany Duration: 10 Sept 2022 → 14 Sept 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13399 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	17th International Conference on Parallel Problem Solving from Nature, PPSN 2022
Country/Territory	Germany
City	Dortmund
Period	10/09/22 → 14/09/22

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Bézier curve estimation
Evolutionary algorithms
Multi-modal multi-objective optimization
Niching

Access to Document

10.1007/978-3-031-14721-0_18

978-3-031-14721-0_18Final published version, 0.99 MB

Cite this

Scholman, R. J., Bouter, A., Dickhoff, L. R. M., Alderliesten, T., & Bosman, P. A. N. (2022). Obtaining Smoothly Navigable Approximation Sets in Bi-objective Multi-modal Optimization. In G. Rudolph, A. V. Kononova, H. Aguirre, P. Kerschke, G. Ochoa, & T. Tušar (Eds.), Parallel Problem Solving from Nature – PPSN XVII - 17th International Conference, PPSN 2022, Proceedings (pp. 247-262). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13399 LNCS). Springer. https://doi.org/10.1007/978-3-031-14721-0_18

Scholman, Renzo J. ; Bouter, Anton ; Dickhoff, Leah R.M. et al. / Obtaining Smoothly Navigable Approximation Sets in Bi-objective Multi-modal Optimization. Parallel Problem Solving from Nature – PPSN XVII - 17th International Conference, PPSN 2022, Proceedings. editor / Günter Rudolph ; Anna V. Kononova ; Hernán Aguirre ; Pascal Kerschke ; Gabriela Ochoa ; Tea Tušar. Springer, 2022. pp. 247-262 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Even if a Multi-modal Multi-Objective Evolutionary Algorithm (MMOEA) is designed to find solutions well spread over all locally optimal approximation sets of a Multi-modal Multi-objective Optimization Problem (MMOP), there is a risk that the found set of solutions is not smoothly navigable because the solutions belong to various niches, reducing the insight for decision makers. To tackle this issue, a new MMOEAs is proposed: the Multi-Modal B{\'e}zier Evolutionary Algorithm (MM-BezEA), which produces approximation sets that cover individual niches and exhibit inherent decision-space smoothness as they are parameterized by B{\'e}zier curves. MM-BezEA combines the concepts behind the recently introduced BezEA and MO-HillVallEA to find all locally optimal approximation sets. When benchmarked against the MMOEAs MO_Ring_PSO_SCD and MO-HillVallEA on MMOPs with linear Pareto sets, MM-BezEA was found to perform best in terms of best hypervolume.",

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Scholman, RJ, Bouter, A, Dickhoff, LRM, Alderliesten, T & Bosman, PAN 2022, Obtaining Smoothly Navigable Approximation Sets in Bi-objective Multi-modal Optimization. in G Rudolph, AV Kononova, H Aguirre, P Kerschke, G Ochoa & T Tušar (eds), Parallel Problem Solving from Nature – PPSN XVII - 17th International Conference, PPSN 2022, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13399 LNCS, Springer, pp. 247-262, 17th International Conference on Parallel Problem Solving from Nature, PPSN 2022, Dortmund, Germany, 10/09/22. https://doi.org/10.1007/978-3-031-14721-0_18

Obtaining Smoothly Navigable Approximation Sets in Bi-objective Multi-modal Optimization. / Scholman, Renzo J.; Bouter, Anton; Dickhoff, Leah R.M. et al.
Parallel Problem Solving from Nature – PPSN XVII - 17th International Conference, PPSN 2022, Proceedings. ed. / Günter Rudolph; Anna V. Kononova; Hernán Aguirre; Pascal Kerschke; Gabriela Ochoa; Tea Tušar. Springer, 2022. p. 247-262 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13399 LNCS).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Scholman RJ, Bouter A, Dickhoff LRM, Alderliesten T , Bosman PAN. Obtaining Smoothly Navigable Approximation Sets in Bi-objective Multi-modal Optimization. In Rudolph G, Kononova AV, Aguirre H, Kerschke P, Ochoa G, Tušar T, editors, Parallel Problem Solving from Nature – PPSN XVII - 17th International Conference, PPSN 2022, Proceedings. Springer. 2022. p. 247-262. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-14721-0_18