---
_id: '46407'
abstract:
- lang: eng
  text: Choosing and tuning an optimization procedure for a given class of nonlinear
    optimization problems is not an easy task. One way to proceed is to consider this
    as a tournament, where each procedure will compete in different ‘disciplines’.
    Here, disciplines could either be different functions, which we want to optimize,
    or specific performance measures of the optimization procedure. We would then
    be interested in the algorithm that performs best in a majority of cases or whose
    average performance is maximal. We will focus on evolutionary multiobjective optimization
    algorithms (EMOA), and will present a novel approach to the design and analysis
    of evolutionary multiobjective benchmark experiments based on similar work from
    the context of machine learning. We focus on deriving a consensus among several
    benchmarks over different test problems and illustrate the methodology by reanalyzing
    the results of the CEC 2007 EMOA competition.
author:
- first_name: Olaf
  full_name: Mersmann, Olaf
  last_name: Mersmann
- first_name: Heike
  full_name: Trautmann, Heike
  id: '100740'
  last_name: Trautmann
  orcid: 0000-0002-9788-8282
- first_name: Boris
  full_name: Naujoks, Boris
  last_name: Naujoks
- first_name: Claus
  full_name: Weihs, Claus
  last_name: Weihs
citation:
  ama: 'Mersmann O, Trautmann H, Naujoks B, Weihs C. Benchmarking evolutionary multiobjective
    optimization algorithms. In: <i>IEEE Congress on Evolutionary Computation</i>.
    ; 2010:1-8. doi:<a href="https://doi.org/10.1109/CEC.2010.5586241">10.1109/CEC.2010.5586241</a>'
  apa: Mersmann, O., Trautmann, H., Naujoks, B., &#38; Weihs, C. (2010). Benchmarking
    evolutionary multiobjective optimization algorithms. <i>IEEE Congress on Evolutionary
    Computation</i>, 1–8. <a href="https://doi.org/10.1109/CEC.2010.5586241">https://doi.org/10.1109/CEC.2010.5586241</a>
  bibtex: '@inproceedings{Mersmann_Trautmann_Naujoks_Weihs_2010, title={Benchmarking
    evolutionary multiobjective optimization algorithms}, DOI={<a href="https://doi.org/10.1109/CEC.2010.5586241">10.1109/CEC.2010.5586241</a>},
    booktitle={IEEE Congress on Evolutionary Computation}, author={Mersmann, Olaf
    and Trautmann, Heike and Naujoks, Boris and Weihs, Claus}, year={2010}, pages={1–8}
    }'
  chicago: Mersmann, Olaf, Heike Trautmann, Boris Naujoks, and Claus Weihs. “Benchmarking
    Evolutionary Multiobjective Optimization Algorithms.” In <i>IEEE Congress on Evolutionary
    Computation</i>, 1–8, 2010. <a href="https://doi.org/10.1109/CEC.2010.5586241">https://doi.org/10.1109/CEC.2010.5586241</a>.
  ieee: 'O. Mersmann, H. Trautmann, B. Naujoks, and C. Weihs, “Benchmarking evolutionary
    multiobjective optimization algorithms,” in <i>IEEE Congress on Evolutionary Computation</i>,
    2010, pp. 1–8, doi: <a href="https://doi.org/10.1109/CEC.2010.5586241">10.1109/CEC.2010.5586241</a>.'
  mla: Mersmann, Olaf, et al. “Benchmarking Evolutionary Multiobjective Optimization
    Algorithms.” <i>IEEE Congress on Evolutionary Computation</i>, 2010, pp. 1–8,
    doi:<a href="https://doi.org/10.1109/CEC.2010.5586241">10.1109/CEC.2010.5586241</a>.
  short: 'O. Mersmann, H. Trautmann, B. Naujoks, C. Weihs, in: IEEE Congress on Evolutionary
    Computation, 2010, pp. 1–8.'
date_created: 2023-08-04T16:05:53Z
date_updated: 2023-10-16T13:56:15Z
department:
- _id: '34'
- _id: '819'
doi: 10.1109/CEC.2010.5586241
language:
- iso: eng
page: 1-8
publication: IEEE Congress on Evolutionary Computation
publication_identifier:
  issn:
  - 1941-0026
status: public
title: Benchmarking evolutionary multiobjective optimization algorithms
type: conference
user_id: '15504'
year: '2010'
...
---
_id: '46412'
abstract:
- lang: eng
  text: In this paper, a concept for efficiently approximating the practically relevant
    regions of the Pareto front (PF) is introduced. Instead of the original objectives,
    desirability functions (DFs) of the objectives are optimized, which express the
    preferences of the decision maker. The original problem formulation and the optimization
    algorithm do not have to be modified. DFs map an objective to the domain [0, 1]
    and nonlinearly increase with better objective quality. By means of this mapping,
    values of different objectives and units become comparable. A biased distribution
    of the solutions in the PF approximation based on different scalings of the objectives
    is prevented. Thus, we propose the integration of DFs into the S-metric selection
    evolutionary multiobjective algorithm. The transformation ensures the meaning
    of the hypervolumes internally computed. Furthermore, it is shown that the reference
    point for the hypervolume calculation can be set intuitively. The approach is
    analyzed using standard test problems. Moreover, a practical validation by means
    of the optimization of a turning process is performed.
author:
- first_name: Tobias
  full_name: Wagner, Tobias
  last_name: Wagner
- first_name: Heike
  full_name: Trautmann, Heike
  id: '100740'
  last_name: Trautmann
  orcid: 0000-0002-9788-8282
citation:
  ama: Wagner T, Trautmann H. Integration of Preferences in Hypervolume-Based Multiobjective
    Evolutionary Algorithms by Means of Desirability Functions. <i>IEEE Transactions
    on Evolutionary Computation</i>. 2010;14(5):688-701. doi:<a href="https://doi.org/10.1109/TEVC.2010.2058119">10.1109/TEVC.2010.2058119</a>
  apa: Wagner, T., &#38; Trautmann, H. (2010). Integration of Preferences in Hypervolume-Based
    Multiobjective Evolutionary Algorithms by Means of Desirability Functions. <i>IEEE
    Transactions on Evolutionary Computation</i>, <i>14</i>(5), 688–701. <a href="https://doi.org/10.1109/TEVC.2010.2058119">https://doi.org/10.1109/TEVC.2010.2058119</a>
  bibtex: '@article{Wagner_Trautmann_2010, title={Integration of Preferences in Hypervolume-Based
    Multiobjective Evolutionary Algorithms by Means of Desirability Functions}, volume={14},
    DOI={<a href="https://doi.org/10.1109/TEVC.2010.2058119">10.1109/TEVC.2010.2058119</a>},
    number={5}, journal={IEEE Transactions on Evolutionary Computation}, author={Wagner,
    Tobias and Trautmann, Heike}, year={2010}, pages={688–701} }'
  chicago: 'Wagner, Tobias, and Heike Trautmann. “Integration of Preferences in Hypervolume-Based
    Multiobjective Evolutionary Algorithms by Means of Desirability Functions.” <i>IEEE
    Transactions on Evolutionary Computation</i> 14, no. 5 (2010): 688–701. <a href="https://doi.org/10.1109/TEVC.2010.2058119">https://doi.org/10.1109/TEVC.2010.2058119</a>.'
  ieee: 'T. Wagner and H. Trautmann, “Integration of Preferences in Hypervolume-Based
    Multiobjective Evolutionary Algorithms by Means of Desirability Functions,” <i>IEEE
    Transactions on Evolutionary Computation</i>, vol. 14, no. 5, pp. 688–701, 2010,
    doi: <a href="https://doi.org/10.1109/TEVC.2010.2058119">10.1109/TEVC.2010.2058119</a>.'
  mla: Wagner, Tobias, and Heike Trautmann. “Integration of Preferences in Hypervolume-Based
    Multiobjective Evolutionary Algorithms by Means of Desirability Functions.” <i>IEEE
    Transactions on Evolutionary Computation</i>, vol. 14, no. 5, 2010, pp. 688–701,
    doi:<a href="https://doi.org/10.1109/TEVC.2010.2058119">10.1109/TEVC.2010.2058119</a>.
  short: T. Wagner, H. Trautmann, IEEE Transactions on Evolutionary Computation 14
    (2010) 688–701.
date_created: 2023-08-04T16:10:02Z
date_updated: 2023-10-16T13:57:41Z
department:
- _id: '34'
- _id: '819'
doi: 10.1109/TEVC.2010.2058119
intvolume: '        14'
issue: '5'
language:
- iso: eng
page: 688-701
publication: IEEE Transactions on Evolutionary Computation
publication_identifier:
  issn:
  - 1941-0026
status: public
title: Integration of Preferences in Hypervolume-Based Multiobjective Evolutionary
  Algorithms by Means of Desirability Functions
type: journal_article
user_id: '15504'
volume: 14
year: '2010'
...
---
_id: '46410'
abstract:
- lang: eng
  text: The design and application of termination criteria has become an important
    aspect in evolutionary multi-objective optimization. Online convergence detection
    (OCD) determines when further generations are no longer promising based on statistical
    tests on a set of performance indicators. The behavior of OCD mainly depends on
    two parameters, the number of preceding generations considered in the statistical
    tests and the desired variance limit. In this paper, guidelines for selecting
    appropriate combinations of these parameters are empirically derived based on
    design-of-experiment methods. Furthermore, a variant of OCD is introduced which
    directly operates on the hypervolume indicator - the internal measure of the SMS-EMOA.
    This allows a separated analysis of the variance criterion and reduces the complexity
    of OCD. Based on the experimental design, a systematic comparison with the classical
    OCD approach is performed and differences between the appropriate parameterizations
    of both variants are highlighted.
author:
- first_name: Tobias
  full_name: Wagner, Tobias
  last_name: Wagner
- first_name: Heike
  full_name: Trautmann, Heike
  id: '100740'
  last_name: Trautmann
  orcid: 0000-0002-9788-8282
citation:
  ama: 'Wagner T, Trautmann H. Online convergence detection for evolutionary multi-objective
    algorithms revisited. In: <i>IEEE Congress on Evolutionary Computation</i>. ;
    2010:1-8. doi:<a href="https://doi.org/10.1109/CEC.2010.5586474">10.1109/CEC.2010.5586474</a>'
  apa: Wagner, T., &#38; Trautmann, H. (2010). Online convergence detection for evolutionary
    multi-objective algorithms revisited. <i>IEEE Congress on Evolutionary Computation</i>,
    1–8. <a href="https://doi.org/10.1109/CEC.2010.5586474">https://doi.org/10.1109/CEC.2010.5586474</a>
  bibtex: '@inproceedings{Wagner_Trautmann_2010, title={Online convergence detection
    for evolutionary multi-objective algorithms revisited}, DOI={<a href="https://doi.org/10.1109/CEC.2010.5586474">10.1109/CEC.2010.5586474</a>},
    booktitle={IEEE Congress on Evolutionary Computation}, author={Wagner, Tobias
    and Trautmann, Heike}, year={2010}, pages={1–8} }'
  chicago: Wagner, Tobias, and Heike Trautmann. “Online Convergence Detection for
    Evolutionary Multi-Objective Algorithms Revisited.” In <i>IEEE Congress on Evolutionary
    Computation</i>, 1–8, 2010. <a href="https://doi.org/10.1109/CEC.2010.5586474">https://doi.org/10.1109/CEC.2010.5586474</a>.
  ieee: 'T. Wagner and H. Trautmann, “Online convergence detection for evolutionary
    multi-objective algorithms revisited,” in <i>IEEE Congress on Evolutionary Computation</i>,
    2010, pp. 1–8, doi: <a href="https://doi.org/10.1109/CEC.2010.5586474">10.1109/CEC.2010.5586474</a>.'
  mla: Wagner, Tobias, and Heike Trautmann. “Online Convergence Detection for Evolutionary
    Multi-Objective Algorithms Revisited.” <i>IEEE Congress on Evolutionary Computation</i>,
    2010, pp. 1–8, doi:<a href="https://doi.org/10.1109/CEC.2010.5586474">10.1109/CEC.2010.5586474</a>.
  short: 'T. Wagner, H. Trautmann, in: IEEE Congress on Evolutionary Computation,
    2010, pp. 1–8.'
date_created: 2023-08-04T16:08:41Z
date_updated: 2023-10-16T13:57:05Z
department:
- _id: '34'
- _id: '819'
doi: 10.1109/CEC.2010.5586474
language:
- iso: eng
page: 1-8
publication: IEEE Congress on Evolutionary Computation
publication_identifier:
  issn:
  - 1941-0026
status: public
title: Online convergence detection for evolutionary multi-objective algorithms revisited
type: conference
user_id: '15504'
year: '2010'
...
---
_id: '46415'
abstract:
- lang: eng
  text: Noisy environments are a challenging task for multiobjective evolutionary
    algorithms. The algorithms may be trapped in local optima or even become a random
    search in the decision and objective space. In the course of the paper the classical
    definition of Pareto-dominance is enhanced subject to noisy objective functions
    in order to make the evolutionary search process more robust and to generate a
    reliable Pareto front. At each point in the decision space the objective functions
    are evaluated a fixed number of times and the convex hull of the objective function
    vectors is computed. Expectation is associated with the median of the objective
    function values while uncertainty is reflected by the average distance of the
    median in each dimension to the points defining the convex hull. By combining
    these two indicators a new concept of Pareto-dominance is set up. An implementation
    in NSGA-II and application to test problems show a gain in robustness and search
    quality.
author:
- first_name: Heike
  full_name: Trautmann, Heike
  id: '100740'
  last_name: Trautmann
  orcid: 0000-0002-9788-8282
- first_name: Jorn
  full_name: Mehnen, Jorn
  last_name: Mehnen
- first_name: Boris
  full_name: Naujoks, Boris
  last_name: Naujoks
citation:
  ama: 'Trautmann H, Mehnen J, Naujoks B. Pareto-dominance in noisy environments.
    In: <i>2009 IEEE Congress on Evolutionary Computation</i>. ; 2009:3119-3126. doi:<a
    href="https://doi.org/10.1109/CEC.2009.4983338">10.1109/CEC.2009.4983338</a>'
  apa: Trautmann, H., Mehnen, J., &#38; Naujoks, B. (2009). Pareto-dominance in noisy
    environments. <i>2009 IEEE Congress on Evolutionary Computation</i>, 3119–3126.
    <a href="https://doi.org/10.1109/CEC.2009.4983338">https://doi.org/10.1109/CEC.2009.4983338</a>
  bibtex: '@inproceedings{Trautmann_Mehnen_Naujoks_2009, title={Pareto-dominance in
    noisy environments}, DOI={<a href="https://doi.org/10.1109/CEC.2009.4983338">10.1109/CEC.2009.4983338</a>},
    booktitle={2009 IEEE Congress on Evolutionary Computation}, author={Trautmann,
    Heike and Mehnen, Jorn and Naujoks, Boris}, year={2009}, pages={3119–3126} }'
  chicago: Trautmann, Heike, Jorn Mehnen, and Boris Naujoks. “Pareto-Dominance in
    Noisy Environments.” In <i>2009 IEEE Congress on Evolutionary Computation</i>,
    3119–26, 2009. <a href="https://doi.org/10.1109/CEC.2009.4983338">https://doi.org/10.1109/CEC.2009.4983338</a>.
  ieee: 'H. Trautmann, J. Mehnen, and B. Naujoks, “Pareto-dominance in noisy environments,”
    in <i>2009 IEEE Congress on Evolutionary Computation</i>, 2009, pp. 3119–3126,
    doi: <a href="https://doi.org/10.1109/CEC.2009.4983338">10.1109/CEC.2009.4983338</a>.'
  mla: Trautmann, Heike, et al. “Pareto-Dominance in Noisy Environments.” <i>2009
    IEEE Congress on Evolutionary Computation</i>, 2009, pp. 3119–26, doi:<a href="https://doi.org/10.1109/CEC.2009.4983338">10.1109/CEC.2009.4983338</a>.
  short: 'H. Trautmann, J. Mehnen, B. Naujoks, in: 2009 IEEE Congress on Evolutionary
    Computation, 2009, pp. 3119–3126.'
date_created: 2023-08-04T16:16:32Z
date_updated: 2023-10-16T13:58:36Z
department:
- _id: '34'
- _id: '819'
doi: 10.1109/CEC.2009.4983338
language:
- iso: eng
page: 3119-3126
publication: 2009 IEEE Congress on Evolutionary Computation
publication_identifier:
  issn:
  - 1941-0026
status: public
title: Pareto-dominance in noisy environments
type: conference
user_id: '15504'
year: '2009'
...
---
_id: '46413'
abstract:
- lang: eng
  text: Industry applications of multiobjective optimization problems mostly are characterized
    by the demand for high quality solutions on the one hand. On the other hand an
    optimization result is desired which at any rate meets the time constraints for
    the evolutionary multiobjective algorithms (EMOA). The handling of this trade-off
    is a frequently discussed issue in multiobjective evolutionary optimization.
author:
- first_name: Boris
  full_name: Naujoks, Boris
  last_name: Naujoks
- first_name: Heike
  full_name: Trautmann, Heike
  id: '100740'
  last_name: Trautmann
  orcid: 0000-0002-9788-8282
citation:
  ama: 'Naujoks B, Trautmann H. Online convergence detection for multiobjective aerodynamic
    applications. In: <i>2009 IEEE Congress on Evolutionary Computation</i>. ; 2009:332-339.
    doi:<a href="https://doi.org/10.1109/CEC.2009.4982966">10.1109/CEC.2009.4982966</a>'
  apa: Naujoks, B., &#38; Trautmann, H. (2009). Online convergence detection for multiobjective
    aerodynamic applications. <i>2009 IEEE Congress on Evolutionary Computation</i>,
    332–339. <a href="https://doi.org/10.1109/CEC.2009.4982966">https://doi.org/10.1109/CEC.2009.4982966</a>
  bibtex: '@inproceedings{Naujoks_Trautmann_2009, title={Online convergence detection
    for multiobjective aerodynamic applications}, DOI={<a href="https://doi.org/10.1109/CEC.2009.4982966">10.1109/CEC.2009.4982966</a>},
    booktitle={2009 IEEE Congress on Evolutionary Computation}, author={Naujoks, Boris
    and Trautmann, Heike}, year={2009}, pages={332–339} }'
  chicago: Naujoks, Boris, and Heike Trautmann. “Online Convergence Detection for
    Multiobjective Aerodynamic Applications.” In <i>2009 IEEE Congress on Evolutionary
    Computation</i>, 332–39, 2009. <a href="https://doi.org/10.1109/CEC.2009.4982966">https://doi.org/10.1109/CEC.2009.4982966</a>.
  ieee: 'B. Naujoks and H. Trautmann, “Online convergence detection for multiobjective
    aerodynamic applications,” in <i>2009 IEEE Congress on Evolutionary Computation</i>,
    2009, pp. 332–339, doi: <a href="https://doi.org/10.1109/CEC.2009.4982966">10.1109/CEC.2009.4982966</a>.'
  mla: Naujoks, Boris, and Heike Trautmann. “Online Convergence Detection for Multiobjective
    Aerodynamic Applications.” <i>2009 IEEE Congress on Evolutionary Computation</i>,
    2009, pp. 332–39, doi:<a href="https://doi.org/10.1109/CEC.2009.4982966">10.1109/CEC.2009.4982966</a>.
  short: 'B. Naujoks, H. Trautmann, in: 2009 IEEE Congress on Evolutionary Computation,
    2009, pp. 332–339.'
date_created: 2023-08-04T16:14:08Z
date_updated: 2023-10-16T13:57:58Z
department:
- _id: '34'
- _id: '819'
doi: 10.1109/CEC.2009.4982966
language:
- iso: eng
page: 332-339
publication: 2009 IEEE Congress on Evolutionary Computation
publication_identifier:
  issn:
  - 1941-0026
status: public
title: Online convergence detection for multiobjective aerodynamic applications
type: conference
user_id: '15504'
year: '2009'
...
---
_id: '46421'
abstract:
- lang: eng
  text: Multi-objective evolutionary algorithms (MOEAs) are generally designed to
    find a well spread Pareto-front approximation. Often, only a small section of
    this front may be of practical interest. Desirability functions (DFs) are able
    to describe user preferences intuitively. Furthermore, DFs can be attached to
    any fitness function easily. This way, desirability functions can help in guiding
    MOEAs without introducing additional restrictions or changes to the algorithm.
    The application of noisy fitness functions is not straight forward but relevant
    to many real-world problems. Therefore, a variant of Harrington’s one-sided desirability
    function using expectations is introduced which takes noise into account. A deterministic
    strategy as well as the XSGA-II are used in combination with DF to solve a noisy
    Binh problem and a noisy cost estimation problem for turning processes.
author:
- first_name: Jorn
  full_name: Mehnen, Jorn
  last_name: Mehnen
- first_name: Heike
  full_name: Trautmann, Heike
  id: '100740'
  last_name: Trautmann
  orcid: 0000-0002-9788-8282
- first_name: Ashutosh
  full_name: Tiwari, Ashutosh
  last_name: Tiwari
citation:
  ama: 'Mehnen J, Trautmann H, Tiwari A. Introducing user preference using Desirability
    Functions in Multi-Objective Evolutionary Optimisation of noisy processes. In:
    <i>2007 IEEE Congress on Evolutionary Computation</i>. ; 2007:2687-2694. doi:<a
    href="https://doi.org/10.1109/CEC.2007.4424810">10.1109/CEC.2007.4424810</a>'
  apa: Mehnen, J., Trautmann, H., &#38; Tiwari, A. (2007). Introducing user preference
    using Desirability Functions in Multi-Objective Evolutionary Optimisation of noisy
    processes. <i>2007 IEEE Congress on Evolutionary Computation</i>, 2687–2694. <a
    href="https://doi.org/10.1109/CEC.2007.4424810">https://doi.org/10.1109/CEC.2007.4424810</a>
  bibtex: '@inproceedings{Mehnen_Trautmann_Tiwari_2007, title={Introducing user preference
    using Desirability Functions in Multi-Objective Evolutionary Optimisation of noisy
    processes}, DOI={<a href="https://doi.org/10.1109/CEC.2007.4424810">10.1109/CEC.2007.4424810</a>},
    booktitle={2007 IEEE Congress on Evolutionary Computation}, author={Mehnen, Jorn
    and Trautmann, Heike and Tiwari, Ashutosh}, year={2007}, pages={2687–2694} }'
  chicago: Mehnen, Jorn, Heike Trautmann, and Ashutosh Tiwari. “Introducing User Preference
    Using Desirability Functions in Multi-Objective Evolutionary Optimisation of Noisy
    Processes.” In <i>2007 IEEE Congress on Evolutionary Computation</i>, 2687–94,
    2007. <a href="https://doi.org/10.1109/CEC.2007.4424810">https://doi.org/10.1109/CEC.2007.4424810</a>.
  ieee: 'J. Mehnen, H. Trautmann, and A. Tiwari, “Introducing user preference using
    Desirability Functions in Multi-Objective Evolutionary Optimisation of noisy processes,”
    in <i>2007 IEEE Congress on Evolutionary Computation</i>, 2007, pp. 2687–2694,
    doi: <a href="https://doi.org/10.1109/CEC.2007.4424810">10.1109/CEC.2007.4424810</a>.'
  mla: Mehnen, Jorn, et al. “Introducing User Preference Using Desirability Functions
    in Multi-Objective Evolutionary Optimisation of Noisy Processes.” <i>2007 IEEE
    Congress on Evolutionary Computation</i>, 2007, pp. 2687–94, doi:<a href="https://doi.org/10.1109/CEC.2007.4424810">10.1109/CEC.2007.4424810</a>.
  short: 'J. Mehnen, H. Trautmann, A. Tiwari, in: 2007 IEEE Congress on Evolutionary
    Computation, 2007, pp. 2687–2694.'
date_created: 2023-08-04T16:21:27Z
date_updated: 2023-10-16T14:00:44Z
department:
- _id: '34'
- _id: '819'
doi: 10.1109/CEC.2007.4424810
language:
- iso: eng
page: 2687-2694
publication: 2007 IEEE Congress on Evolutionary Computation
publication_identifier:
  issn:
  - 1941-0026
status: public
title: Introducing user preference using Desirability Functions in Multi-Objective
  Evolutionary Optimisation of noisy processes
type: conference
user_id: '15504'
year: '2007'
...