Multi-objective Learning Using HV Maximization

Timo M. Deist*, Monika Grewal, Frank J.W.M. Dankers, Tanja Alderliesten, Peter A.N. Bosman

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

1 Citation (Scopus)
68 Downloads (Pure)


Real-world problems are often multi-objective, with decision-makers unable to specify a priori which trade-off between the conflicting objectives is preferable. Intuitively, building machine learning solutions in such cases would entail providing multiple predictions that span and uniformly cover the Pareto front of all optimal trade-off solutions. We propose a novel approach for multi-objective training of neural networks to approximate the Pareto front during inference. In our approach, we train the neural networks multi-objectively using a dynamic loss function, wherein each network’s losses (corresponding to multiple objectives) are weighted by their hypervolume maximizing gradients. Experiments on different multi-objective problems show that our approach returns well-spread outputs across different trade-offs on the approximated Pareto front without requiring the trade-off vectors to be specified a priori. Further, results of comparisons with the state-of-the-art approaches highlight the added value of our proposed approach, especially in cases where the Pareto front is asymmetric.

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
Place of PublicationCham
Number of pages15
ISBN (Electronic)978-3-031-27250-9
ISBN (Print)978-3-031-27249-3
Publication statusPublished - 2023
Event12th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2023 - Leiden, Netherlands
Duration: 20 Mar 202324 Mar 2023

Publication series

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


Conference12th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project 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.


  • Hypervolume
  • Multi-objective learning
  • Multi-objective optimization
  • Neural networks
  • Pareto front


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