[{"date_updated":"2023-10-16T13:56:15Z","status":"public","title":"Benchmarking evolutionary multiobjective optimization algorithms","year":"2010","author":[{"last_name":"Mersmann","first_name":"Olaf","full_name":"Mersmann, Olaf"},{"id":"100740","full_name":"Trautmann, Heike","first_name":"Heike","last_name":"Trautmann","orcid":"0000-0002-9788-8282"},{"full_name":"Naujoks, Boris","first_name":"Boris","last_name":"Naujoks"},{"last_name":"Weihs","first_name":"Claus","full_name":"Weihs, Claus"}],"publication_identifier":{"issn":["1941-0026"]},"user_id":"15504","doi":"10.1109/CEC.2010.5586241","page":"1-8","language":[{"iso":"eng"}],"_id":"46407","abstract":[{"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.","lang":"eng"}],"publication":"IEEE Congress on Evolutionary Computation","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>","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} }","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>.","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>.","short":"O. Mersmann, H. Trautmann, B. Naujoks, C. Weihs, in: IEEE Congress on Evolutionary Computation, 2010, pp. 1–8.","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>","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>."},"type":"conference","department":[{"_id":"34"},{"_id":"819"}],"date_created":"2023-08-04T16:05:53Z"},{"title":"Integration of Preferences in Hypervolume-Based Multiobjective Evolutionary Algorithms by Means of Desirability Functions","status":"public","year":"2010","author":[{"last_name":"Wagner","first_name":"Tobias","full_name":"Wagner, Tobias"},{"full_name":"Trautmann, Heike","first_name":"Heike","last_name":"Trautmann","orcid":"0000-0002-9788-8282","id":"100740"}],"publication_identifier":{"issn":["1941-0026"]},"date_updated":"2023-10-16T13:57:41Z","intvolume":"        14","page":"688-701","_id":"46412","language":[{"iso":"eng"}],"user_id":"15504","doi":"10.1109/TEVC.2010.2058119","volume":14,"publication":"IEEE Transactions on Evolutionary Computation","issue":"5","citation":{"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>.","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>","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} }","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>","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>.","short":"T. Wagner, H. Trautmann, IEEE Transactions on Evolutionary Computation 14 (2010) 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>."},"abstract":[{"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.","lang":"eng"}],"date_created":"2023-08-04T16:10:02Z","type":"journal_article","department":[{"_id":"34"},{"_id":"819"}]},{"user_id":"15504","doi":"10.1109/CEC.2010.5586474","language":[{"iso":"eng"}],"_id":"46410","page":"1-8","date_updated":"2023-10-16T13:57:05Z","author":[{"full_name":"Wagner, Tobias","first_name":"Tobias","last_name":"Wagner"},{"first_name":"Heike","orcid":"0000-0002-9788-8282","last_name":"Trautmann","full_name":"Trautmann, Heike","id":"100740"}],"publication_identifier":{"issn":["1941-0026"]},"status":"public","year":"2010","title":"Online convergence detection for evolutionary multi-objective algorithms revisited","department":[{"_id":"34"},{"_id":"819"}],"type":"conference","date_created":"2023-08-04T16:08:41Z","abstract":[{"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.","lang":"eng"}],"citation":{"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>","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>.","short":"T. Wagner, H. Trautmann, in: IEEE Congress on Evolutionary Computation, 2010, pp. 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>.","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>.","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>","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} }"},"publication":"IEEE Congress on Evolutionary Computation"},{"user_id":"15504","doi":"10.1109/CEC.2009.4983338","language":[{"iso":"eng"}],"_id":"46415","page":"3119-3126","date_updated":"2023-10-16T13:58:36Z","author":[{"id":"100740","first_name":"Heike","last_name":"Trautmann","orcid":"0000-0002-9788-8282","full_name":"Trautmann, Heike"},{"full_name":"Mehnen, Jorn","first_name":"Jorn","last_name":"Mehnen"},{"full_name":"Naujoks, Boris","first_name":"Boris","last_name":"Naujoks"}],"publication_identifier":{"issn":["1941-0026"]},"year":"2009","status":"public","title":"Pareto-dominance in noisy environments","department":[{"_id":"34"},{"_id":"819"}],"type":"conference","date_created":"2023-08-04T16:16:32Z","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."}],"citation":{"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} }","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>","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.","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>.","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>"},"publication":"2009 IEEE Congress on Evolutionary Computation"},{"doi":"10.1109/CEC.2009.4982966","user_id":"15504","page":"332-339","language":[{"iso":"eng"}],"_id":"46413","date_updated":"2023-10-16T13:57:58Z","year":"2009","status":"public","title":"Online convergence detection for multiobjective aerodynamic applications","author":[{"first_name":"Boris","last_name":"Naujoks","full_name":"Naujoks, Boris"},{"full_name":"Trautmann, Heike","orcid":"0000-0002-9788-8282","last_name":"Trautmann","first_name":"Heike","id":"100740"}],"publication_identifier":{"issn":["1941-0026"]},"type":"conference","department":[{"_id":"34"},{"_id":"819"}],"date_created":"2023-08-04T16:14:08Z","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."}],"publication":"2009 IEEE Congress on Evolutionary Computation","citation":{"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>.","short":"B. Naujoks, H. Trautmann, in: 2009 IEEE Congress on Evolutionary Computation, 2009, pp. 332–339.","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>.","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} }","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>","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>."}},{"_id":"46421","language":[{"iso":"eng"}],"page":"2687-2694","user_id":"15504","doi":"10.1109/CEC.2007.4424810","author":[{"first_name":"Jorn","last_name":"Mehnen","full_name":"Mehnen, Jorn"},{"id":"100740","orcid":"0000-0002-9788-8282","last_name":"Trautmann","first_name":"Heike","full_name":"Trautmann, Heike"},{"full_name":"Tiwari, Ashutosh","first_name":"Ashutosh","last_name":"Tiwari"}],"publication_identifier":{"issn":["1941-0026"]},"year":"2007","title":"Introducing user preference using Desirability Functions in Multi-Objective Evolutionary Optimisation of noisy processes","status":"public","date_updated":"2023-10-16T14:00:44Z","date_created":"2023-08-04T16:21:27Z","department":[{"_id":"34"},{"_id":"819"}],"type":"conference","citation":{"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>.","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>","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} }","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>","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>.","short":"J. Mehnen, H. Trautmann, A. Tiwari, in: 2007 IEEE Congress on Evolutionary Computation, 2007, pp. 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>."},"publication":"2007 IEEE Congress on Evolutionary Computation","abstract":[{"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.","lang":"eng"}]}]