---
_id: '10596'
abstract:
- lang: eng
text: Multi-objective optimization is an active field of research that has many
applications. Owing to its success and because decision-making processes are becoming
more and more complex, there is a recent trend for incorporating many objectives
into such problems. The challenge with such problems, however, is that the dimensions
of the solution sets—the so-called Pareto sets and fronts—grow with the number
of objectives. It is thus no longer possible to compute or to approximate the
entire solution set of a given problem that contains many (e.g. more than three)
objectives. On the other hand, the computation of single solutions (e.g. via scalarization
methods) leads to unsatisfying results in many cases, even if user preferences
are incorporated. In this article, the Pareto Explorer tool is presented—a global/local
exploration tool for the treatment of many-objective optimization problems (MaOPs).
In the first step, a solution of the problem is computed via a global search algorithm
that ideally already includes user preferences. In the second step, a local search
along the Pareto set/front of the given MaOP is performed in user specified directions.
For this, several continuation-like procedures are proposed that can incorporate
preferences defined in decision, objective, or in weight space. The applicability
and usefulness of Pareto Explorer is demonstrated on benchmark problems as well
as on an application from industrial laundry design.
article_type: original
author:
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Oliver
full_name: Cuate, Oliver
last_name: Cuate
- first_name: Adanay
full_name: Martín, Adanay
last_name: Martín
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Schütze O, Cuate O, Martín A, Peitz S, Dellnitz M. Pareto Explorer: a global/local
exploration tool for many-objective optimization problems. Engineering Optimization.
2020;52(5):832-855. doi:10.1080/0305215x.2019.1617286'
apa: 'Schütze, O., Cuate, O., Martín, A., Peitz, S., & Dellnitz, M. (2020).
Pareto Explorer: a global/local exploration tool for many-objective optimization
problems. Engineering Optimization, 52(5), 832–855. https://doi.org/10.1080/0305215x.2019.1617286'
bibtex: '@article{Schütze_Cuate_Martín_Peitz_Dellnitz_2020, title={Pareto Explorer:
a global/local exploration tool for many-objective optimization problems}, volume={52},
DOI={10.1080/0305215x.2019.1617286},
number={5}, journal={Engineering Optimization}, author={Schütze, Oliver and Cuate,
Oliver and Martín, Adanay and Peitz, Sebastian and Dellnitz, Michael}, year={2020},
pages={832–855} }'
chicago: 'Schütze, Oliver, Oliver Cuate, Adanay Martín, Sebastian Peitz, and Michael
Dellnitz. “Pareto Explorer: A Global/Local Exploration Tool for Many-Objective
Optimization Problems.” Engineering Optimization 52, no. 5 (2020): 832–55.
https://doi.org/10.1080/0305215x.2019.1617286.'
ieee: 'O. Schütze, O. Cuate, A. Martín, S. Peitz, and M. Dellnitz, “Pareto Explorer:
a global/local exploration tool for many-objective optimization problems,” Engineering
Optimization, vol. 52, no. 5, pp. 832–855, 2020.'
mla: 'Schütze, Oliver, et al. “Pareto Explorer: A Global/Local Exploration Tool
for Many-Objective Optimization Problems.” Engineering Optimization, vol.
52, no. 5, 2020, pp. 832–55, doi:10.1080/0305215x.2019.1617286.'
short: O. Schütze, O. Cuate, A. Martín, S. Peitz, M. Dellnitz, Engineering Optimization
52 (2020) 832–855.
date_created: 2019-07-10T08:14:39Z
date_updated: 2022-01-06T06:50:46Z
department:
- _id: '101'
doi: 10.1080/0305215x.2019.1617286
intvolume: ' 52'
issue: '5'
language:
- iso: eng
page: 832-855
publication: Engineering Optimization
publication_identifier:
issn:
- 0305-215X
- 1029-0273
publication_status: published
status: public
title: 'Pareto Explorer: a global/local exploration tool for many-objective optimization
problems'
type: journal_article
user_id: '47427'
volume: 52
year: '2020'
...
---
_id: '16659'
author:
- first_name: Maik
full_name: Ringkamp, Maik
last_name: Ringkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
citation:
ama: Ringkamp M, Ober-Blöbaum S, Dellnitz M, Schütze O. Handling high-dimensional
problems with multi-objective continuation methods via successive approximation
of the tangent space. Engineering Optimization. 2012:1117-1146. doi:10.1080/0305215x.2011.634407
apa: Ringkamp, M., Ober-Blöbaum, S., Dellnitz, M., & Schütze, O. (2012). Handling
high-dimensional problems with multi-objective continuation methods via successive
approximation of the tangent space. Engineering Optimization, 1117–1146.
https://doi.org/10.1080/0305215x.2011.634407
bibtex: '@article{Ringkamp_Ober-Blöbaum_Dellnitz_Schütze_2012, title={Handling high-dimensional
problems with multi-objective continuation methods via successive approximation
of the tangent space}, DOI={10.1080/0305215x.2011.634407},
journal={Engineering Optimization}, author={Ringkamp, Maik and Ober-Blöbaum, Sina
and Dellnitz, Michael and Schütze, Oliver}, year={2012}, pages={1117–1146} }'
chicago: Ringkamp, Maik, Sina Ober-Blöbaum, Michael Dellnitz, and Oliver Schütze.
“Handling High-Dimensional Problems with Multi-Objective Continuation Methods
via Successive Approximation of the Tangent Space.” Engineering Optimization,
2012, 1117–46. https://doi.org/10.1080/0305215x.2011.634407.
ieee: M. Ringkamp, S. Ober-Blöbaum, M. Dellnitz, and O. Schütze, “Handling high-dimensional
problems with multi-objective continuation methods via successive approximation
of the tangent space,” Engineering Optimization, pp. 1117–1146, 2012.
mla: Ringkamp, Maik, et al. “Handling High-Dimensional Problems with Multi-Objective
Continuation Methods via Successive Approximation of the Tangent Space.” Engineering
Optimization, 2012, pp. 1117–46, doi:10.1080/0305215x.2011.634407.
short: M. Ringkamp, S. Ober-Blöbaum, M. Dellnitz, O. Schütze, Engineering Optimization
(2012) 1117–1146.
date_created: 2020-04-16T09:34:05Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1080/0305215x.2011.634407
language:
- iso: eng
page: 1117-1146
publication: Engineering Optimization
publication_identifier:
issn:
- 0305-215X
- 1029-0273
publication_status: published
status: public
title: Handling high-dimensional problems with multi-objective continuation methods
via successive approximation of the tangent space
type: journal_article
user_id: '15701'
year: '2012'
...
---
_id: '16669'
author:
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Massimiliano
full_name: Vasile, Massimiliano
last_name: Vasile
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Dario
full_name: Izzo, Dario
last_name: Izzo
citation:
ama: Schütze O, Vasile M, Junge O, Dellnitz M, Izzo D. Designing optimal low-thrust
gravity-assist trajectories using space pruning and a multi-objective approach.
Engineering Optimization. 2009:155-181. doi:10.1080/03052150802391734
apa: Schütze, O., Vasile, M., Junge, O., Dellnitz, M., & Izzo, D. (2009). Designing
optimal low-thrust gravity-assist trajectories using space pruning and a multi-objective
approach. Engineering Optimization, 155–181. https://doi.org/10.1080/03052150802391734
bibtex: '@article{Schütze_Vasile_Junge_Dellnitz_Izzo_2009, title={Designing optimal
low-thrust gravity-assist trajectories using space pruning and a multi-objective
approach}, DOI={10.1080/03052150802391734},
journal={Engineering Optimization}, author={Schütze, Oliver and Vasile, Massimiliano
and Junge, Oliver and Dellnitz, Michael and Izzo, Dario}, year={2009}, pages={155–181}
}'
chicago: Schütze, Oliver, Massimiliano Vasile, Oliver Junge, Michael Dellnitz, and
Dario Izzo. “Designing Optimal Low-Thrust Gravity-Assist Trajectories Using Space
Pruning and a Multi-Objective Approach.” Engineering Optimization, 2009,
155–81. https://doi.org/10.1080/03052150802391734.
ieee: O. Schütze, M. Vasile, O. Junge, M. Dellnitz, and D. Izzo, “Designing optimal
low-thrust gravity-assist trajectories using space pruning and a multi-objective
approach,” Engineering Optimization, pp. 155–181, 2009.
mla: Schütze, Oliver, et al. “Designing Optimal Low-Thrust Gravity-Assist Trajectories
Using Space Pruning and a Multi-Objective Approach.” Engineering Optimization,
2009, pp. 155–81, doi:10.1080/03052150802391734.
short: O. Schütze, M. Vasile, O. Junge, M. Dellnitz, D. Izzo, Engineering Optimization
(2009) 155–181.
date_created: 2020-04-16T10:04:50Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1080/03052150802391734
language:
- iso: eng
page: 155-181
publication: Engineering Optimization
publication_identifier:
issn:
- 0305-215X
- 1029-0273
publication_status: published
status: public
title: Designing optimal low-thrust gravity-assist trajectories using space pruning
and a multi-objective approach
type: journal_article
user_id: '15701'
year: '2009'
...
---
_id: '16667'
author:
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Carlos A.
full_name: Coello Coello, Carlos A.
last_name: Coello Coello
- first_name: Sanaz
full_name: Mostaghim, Sanaz
last_name: Mostaghim
- first_name: El-Ghazali
full_name: Talbi, El-Ghazali
last_name: Talbi
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Schütze O, Coello Coello CA, Mostaghim S, Talbi E-G, Dellnitz M. Hybridizing
evolutionary strategies with continuation methods for solving multi-objective
problems. Engineering Optimization. 2008:383-402. doi:10.1080/03052150701821328
apa: Schütze, O., Coello Coello, C. A., Mostaghim, S., Talbi, E.-G., & Dellnitz,
M. (2008). Hybridizing evolutionary strategies with continuation methods for solving
multi-objective problems. Engineering Optimization, 383–402. https://doi.org/10.1080/03052150701821328
bibtex: '@article{Schütze_Coello Coello_Mostaghim_Talbi_Dellnitz_2008, title={Hybridizing
evolutionary strategies with continuation methods for solving multi-objective
problems}, DOI={10.1080/03052150701821328},
journal={Engineering Optimization}, author={Schütze, Oliver and Coello Coello,
Carlos A. and Mostaghim, Sanaz and Talbi, El-Ghazali and Dellnitz, Michael}, year={2008},
pages={383–402} }'
chicago: Schütze, Oliver, Carlos A. Coello Coello, Sanaz Mostaghim, El-Ghazali Talbi,
and Michael Dellnitz. “Hybridizing Evolutionary Strategies with Continuation Methods
for Solving Multi-Objective Problems.” Engineering Optimization, 2008,
383–402. https://doi.org/10.1080/03052150701821328.
ieee: O. Schütze, C. A. Coello Coello, S. Mostaghim, E.-G. Talbi, and M. Dellnitz,
“Hybridizing evolutionary strategies with continuation methods for solving multi-objective
problems,” Engineering Optimization, pp. 383–402, 2008.
mla: Schütze, Oliver, et al. “Hybridizing Evolutionary Strategies with Continuation
Methods for Solving Multi-Objective Problems.” Engineering Optimization,
2008, pp. 383–402, doi:10.1080/03052150701821328.
short: O. Schütze, C.A. Coello Coello, S. Mostaghim, E.-G. Talbi, M. Dellnitz, Engineering
Optimization (2008) 383–402.
date_created: 2020-04-16T10:01:07Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1080/03052150701821328
language:
- iso: eng
page: 383-402
publication: Engineering Optimization
publication_identifier:
issn:
- 0305-215X
- 1029-0273
publication_status: published
status: public
title: Hybridizing evolutionary strategies with continuation methods for solving multi-objective
problems
type: journal_article
user_id: '15701'
year: '2008'
...