[{"abstract":[{"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.","lang":"eng"}],"status":"public","publication":"Engineering Optimization","type":"journal_article","article_type":"original","language":[{"iso":"eng"}],"_id":"10596","department":[{"_id":"101"}],"user_id":"47427","year":"2020","page":"832-855","intvolume":"        52","citation":{"apa":"Schütze, O., Cuate, O., Martín, A., Peitz, S., &#38; Dellnitz, M. (2020). Pareto Explorer: a global/local exploration tool for many-objective optimization problems. <i>Engineering Optimization</i>, <i>52</i>(5), 832–855. <a href=\"https://doi.org/10.1080/0305215x.2019.1617286\">https://doi.org/10.1080/0305215x.2019.1617286</a>","mla":"Schütze, Oliver, et al. “Pareto Explorer: A Global/Local Exploration Tool for Many-Objective Optimization Problems.” <i>Engineering Optimization</i>, vol. 52, no. 5, 2020, pp. 832–55, doi:<a href=\"https://doi.org/10.1080/0305215x.2019.1617286\">10.1080/0305215x.2019.1617286</a>.","short":"O. Schütze, O. Cuate, A. Martín, S. Peitz, M. Dellnitz, Engineering Optimization 52 (2020) 832–855.","bibtex":"@article{Schütze_Cuate_Martín_Peitz_Dellnitz_2020, title={Pareto Explorer: a global/local exploration tool for many-objective optimization problems}, volume={52}, DOI={<a href=\"https://doi.org/10.1080/0305215x.2019.1617286\">10.1080/0305215x.2019.1617286</a>}, 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.” <i>Engineering Optimization</i> 52, no. 5 (2020): 832–55. <a href=\"https://doi.org/10.1080/0305215x.2019.1617286\">https://doi.org/10.1080/0305215x.2019.1617286</a>.","ieee":"O. Schütze, O. Cuate, A. Martín, S. Peitz, and M. Dellnitz, “Pareto Explorer: a global/local exploration tool for many-objective optimization problems,” <i>Engineering Optimization</i>, vol. 52, no. 5, pp. 832–855, 2020.","ama":"Schütze O, Cuate O, Martín A, Peitz S, Dellnitz M. Pareto Explorer: a global/local exploration tool for many-objective optimization problems. <i>Engineering Optimization</i>. 2020;52(5):832-855. doi:<a href=\"https://doi.org/10.1080/0305215x.2019.1617286\">10.1080/0305215x.2019.1617286</a>"},"publication_identifier":{"issn":["0305-215X","1029-0273"]},"publication_status":"published","issue":"5","title":"Pareto Explorer: a global/local exploration tool for many-objective optimization problems","doi":"10.1080/0305215x.2019.1617286","date_updated":"2022-01-06T06:50:46Z","volume":52,"author":[{"first_name":"Oliver","full_name":"Schütze, Oliver","last_name":"Schütze"},{"first_name":"Oliver","full_name":"Cuate, Oliver","last_name":"Cuate"},{"first_name":"Adanay","last_name":"Martín","full_name":"Martín, Adanay"},{"last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427","first_name":"Sebastian"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"date_created":"2019-07-10T08:14:39Z"},{"doi":"10.1080/0305215x.2011.634407","title":"Handling high-dimensional problems with multi-objective continuation methods via successive approximation of the tangent space","author":[{"first_name":"Maik","last_name":"Ringkamp","full_name":"Ringkamp, Maik"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"first_name":"Oliver","last_name":"Schütze","full_name":"Schütze, Oliver"}],"date_created":"2020-04-16T09:34:05Z","date_updated":"2022-01-06T06:52:54Z","page":"1117-1146","citation":{"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,” <i>Engineering Optimization</i>, pp. 1117–1146, 2012.","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.” <i>Engineering Optimization</i>, 2012, 1117–46. <a href=\"https://doi.org/10.1080/0305215x.2011.634407\">https://doi.org/10.1080/0305215x.2011.634407</a>.","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. <i>Engineering Optimization</i>. 2012:1117-1146. doi:<a href=\"https://doi.org/10.1080/0305215x.2011.634407\">10.1080/0305215x.2011.634407</a>","mla":"Ringkamp, Maik, et al. “Handling High-Dimensional Problems with Multi-Objective Continuation Methods via Successive Approximation of the Tangent Space.” <i>Engineering Optimization</i>, 2012, pp. 1117–46, doi:<a href=\"https://doi.org/10.1080/0305215x.2011.634407\">10.1080/0305215x.2011.634407</a>.","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={<a href=\"https://doi.org/10.1080/0305215x.2011.634407\">10.1080/0305215x.2011.634407</a>}, journal={Engineering Optimization}, author={Ringkamp, Maik and Ober-Blöbaum, Sina and Dellnitz, Michael and Schütze, Oliver}, year={2012}, pages={1117–1146} }","short":"M. Ringkamp, S. Ober-Blöbaum, M. Dellnitz, O. Schütze, Engineering Optimization (2012) 1117–1146.","apa":"Ringkamp, M., Ober-Blöbaum, S., Dellnitz, M., &#38; Schütze, O. (2012). Handling high-dimensional problems with multi-objective continuation methods via successive approximation of the tangent space. <i>Engineering Optimization</i>, 1117–1146. <a href=\"https://doi.org/10.1080/0305215x.2011.634407\">https://doi.org/10.1080/0305215x.2011.634407</a>"},"year":"2012","publication_identifier":{"issn":["0305-215X","1029-0273"]},"publication_status":"published","language":[{"iso":"eng"}],"department":[{"_id":"101"}],"user_id":"15701","_id":"16659","status":"public","publication":"Engineering Optimization","type":"journal_article"},{"language":[{"iso":"eng"}],"user_id":"15701","department":[{"_id":"101"}],"_id":"16669","status":"public","type":"journal_article","publication":"Engineering Optimization","doi":"10.1080/03052150802391734","title":"Designing optimal low-thrust gravity-assist trajectories using space pruning and a multi-objective approach","date_created":"2020-04-16T10:04:50Z","author":[{"full_name":"Schütze, Oliver","last_name":"Schütze","first_name":"Oliver"},{"first_name":"Massimiliano","full_name":"Vasile, Massimiliano","last_name":"Vasile"},{"full_name":"Junge, Oliver","last_name":"Junge","first_name":"Oliver"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"full_name":"Izzo, Dario","last_name":"Izzo","first_name":"Dario"}],"date_updated":"2022-01-06T06:52:54Z","citation":{"apa":"Schütze, O., Vasile, M., Junge, O., Dellnitz, M., &#38; Izzo, D. (2009). Designing optimal low-thrust gravity-assist trajectories using space pruning and a multi-objective approach. <i>Engineering Optimization</i>, 155–181. <a href=\"https://doi.org/10.1080/03052150802391734\">https://doi.org/10.1080/03052150802391734</a>","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={<a href=\"https://doi.org/10.1080/03052150802391734\">10.1080/03052150802391734</a>}, journal={Engineering Optimization}, author={Schütze, Oliver and Vasile, Massimiliano and Junge, Oliver and Dellnitz, Michael and Izzo, Dario}, year={2009}, pages={155–181} }","short":"O. Schütze, M. Vasile, O. Junge, M. Dellnitz, D. Izzo, Engineering Optimization (2009) 155–181.","mla":"Schütze, Oliver, et al. “Designing Optimal Low-Thrust Gravity-Assist Trajectories Using Space Pruning and a Multi-Objective Approach.” <i>Engineering Optimization</i>, 2009, pp. 155–81, doi:<a href=\"https://doi.org/10.1080/03052150802391734\">10.1080/03052150802391734</a>.","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. <i>Engineering Optimization</i>. 2009:155-181. doi:<a href=\"https://doi.org/10.1080/03052150802391734\">10.1080/03052150802391734</a>","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,” <i>Engineering Optimization</i>, pp. 155–181, 2009.","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.” <i>Engineering Optimization</i>, 2009, 155–81. <a href=\"https://doi.org/10.1080/03052150802391734\">https://doi.org/10.1080/03052150802391734</a>."},"page":"155-181","year":"2009","publication_status":"published","publication_identifier":{"issn":["0305-215X","1029-0273"]}},{"publication_status":"published","publication_identifier":{"issn":["0305-215X","1029-0273"]},"year":"2008","citation":{"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,” <i>Engineering Optimization</i>, pp. 383–402, 2008.","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.” <i>Engineering Optimization</i>, 2008, 383–402. <a href=\"https://doi.org/10.1080/03052150701821328\">https://doi.org/10.1080/03052150701821328</a>.","ama":"Schütze O, Coello Coello CA, Mostaghim S, Talbi E-G, Dellnitz M. Hybridizing evolutionary strategies with continuation methods for solving multi-objective problems. <i>Engineering Optimization</i>. 2008:383-402. doi:<a href=\"https://doi.org/10.1080/03052150701821328\">10.1080/03052150701821328</a>","bibtex":"@article{Schütze_Coello Coello_Mostaghim_Talbi_Dellnitz_2008, title={Hybridizing evolutionary strategies with continuation methods for solving multi-objective problems}, DOI={<a href=\"https://doi.org/10.1080/03052150701821328\">10.1080/03052150701821328</a>}, 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} }","short":"O. Schütze, C.A. Coello Coello, S. Mostaghim, E.-G. Talbi, M. Dellnitz, Engineering Optimization (2008) 383–402.","mla":"Schütze, Oliver, et al. “Hybridizing Evolutionary Strategies with Continuation Methods for Solving Multi-Objective Problems.” <i>Engineering Optimization</i>, 2008, pp. 383–402, doi:<a href=\"https://doi.org/10.1080/03052150701821328\">10.1080/03052150701821328</a>.","apa":"Schütze, O., Coello Coello, C. A., Mostaghim, S., Talbi, E.-G., &#38; Dellnitz, M. (2008). Hybridizing evolutionary strategies with continuation methods for solving multi-objective problems. <i>Engineering Optimization</i>, 383–402. <a href=\"https://doi.org/10.1080/03052150701821328\">https://doi.org/10.1080/03052150701821328</a>"},"page":"383-402","date_updated":"2022-01-06T06:52:54Z","date_created":"2020-04-16T10:01:07Z","author":[{"full_name":"Schütze, Oliver","last_name":"Schütze","first_name":"Oliver"},{"first_name":"Carlos A.","full_name":"Coello Coello, Carlos A.","last_name":"Coello Coello"},{"full_name":"Mostaghim, Sanaz","last_name":"Mostaghim","first_name":"Sanaz"},{"full_name":"Talbi, El-Ghazali","last_name":"Talbi","first_name":"El-Ghazali"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"}],"title":"Hybridizing evolutionary strategies with continuation methods for solving multi-objective problems","doi":"10.1080/03052150701821328","type":"journal_article","publication":"Engineering Optimization","status":"public","_id":"16667","user_id":"15701","department":[{"_id":"101"}],"language":[{"iso":"eng"}]}]