[{"_id":"46384","publisher":"Springer","page":"141–150","volume":8672,"editor":[{"full_name":"Bartz-Beielstein, T","first_name":"T","last_name":"Bartz-Beielstein"},{"last_name":"Branke","first_name":"J","full_name":"Branke, J"},{"full_name":"Filipic, B","first_name":"B","last_name":"Filipic"},{"last_name":"Smith","first_name":"J","full_name":"Smith, J"}],"user_id":"15504","status":"public","place":"Ljubljana, Slovenia","citation":{"mla":"Wessing, S., et al. “Stopping Criteria for Multimodal Optimization.” <i>Proceedings of the Parallel Problem Solving from Nature — PPSN XIII</i>, edited by T Bartz-Beielstein et al., vol. 8672, Springer, 2014, pp. 141–150, doi:<a href=\"https://doi.org/10.1007/978-3-319-10762-2_14\">10.1007/978-3-319-10762-2_14</a>.","ama":"Wessing S, Preuss M, Trautmann H. Stopping Criteria for Multimodal Optimization. In: Bartz-Beielstein T, Branke J, Filipic B, Smith J, eds. <i>Proceedings of the Parallel Problem Solving from Nature — PPSN XIII</i>. Vol 8672. Lecture Notes in Computer Science. Springer; 2014:141–150. doi:<a href=\"https://doi.org/10.1007/978-3-319-10762-2_14\">10.1007/978-3-319-10762-2_14</a>","bibtex":"@inproceedings{Wessing_Preuss_Trautmann_2014, place={Ljubljana, Slovenia}, series={Lecture Notes in Computer Science}, title={Stopping Criteria for Multimodal Optimization}, volume={8672}, DOI={<a href=\"https://doi.org/10.1007/978-3-319-10762-2_14\">10.1007/978-3-319-10762-2_14</a>}, booktitle={Proceedings of the Parallel Problem Solving from Nature — PPSN XIII}, publisher={Springer}, author={Wessing, S and Preuss, M and Trautmann, Heike}, editor={Bartz-Beielstein, T and Branke, J and Filipic, B and Smith, J}, year={2014}, pages={141–150}, collection={Lecture Notes in Computer Science} }","apa":"Wessing, S., Preuss, M., &#38; Trautmann, H. (2014). Stopping Criteria for Multimodal Optimization. In T. Bartz-Beielstein, J. Branke, B. Filipic, &#38; J. Smith (Eds.), <i>Proceedings of the Parallel Problem Solving from Nature — PPSN XIII</i> (Vol. 8672, pp. 141–150). Springer. <a href=\"https://doi.org/10.1007/978-3-319-10762-2_14\">https://doi.org/10.1007/978-3-319-10762-2_14</a>","ieee":"S. Wessing, M. Preuss, and H. Trautmann, “Stopping Criteria for Multimodal Optimization,” in <i>Proceedings of the Parallel Problem Solving from Nature — PPSN XIII</i>, 2014, vol. 8672, pp. 141–150, doi: <a href=\"https://doi.org/10.1007/978-3-319-10762-2_14\">10.1007/978-3-319-10762-2_14</a>.","short":"S. Wessing, M. Preuss, H. Trautmann, in: T. Bartz-Beielstein, J. Branke, B. Filipic, J. Smith (Eds.), Proceedings of the Parallel Problem Solving from Nature — PPSN XIII, Springer, Ljubljana, Slovenia, 2014, pp. 141–150.","chicago":"Wessing, S, M Preuss, and Heike Trautmann. “Stopping Criteria for Multimodal Optimization.” In <i>Proceedings of the Parallel Problem Solving from Nature — PPSN XIII</i>, edited by T Bartz-Beielstein, J Branke, B Filipic, and J Smith, 8672:141–150. Lecture Notes in Computer Science. Ljubljana, Slovenia: Springer, 2014. <a href=\"https://doi.org/10.1007/978-3-319-10762-2_14\">https://doi.org/10.1007/978-3-319-10762-2_14</a>."},"series_title":"Lecture Notes in Computer Science","language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-10762-2_14","author":[{"first_name":"S","last_name":"Wessing","full_name":"Wessing, S"},{"first_name":"M","last_name":"Preuss","full_name":"Preuss, M"},{"last_name":"Trautmann","orcid":"0000-0002-9788-8282","first_name":"Heike","full_name":"Trautmann, Heike","id":"100740"}],"year":"2014","title":"Stopping Criteria for Multimodal Optimization","intvolume":"      8672","date_updated":"2023-10-16T13:44:15Z","date_created":"2023-08-04T15:36:01Z","department":[{"_id":"34"},{"_id":"819"}],"type":"conference","publication":"Proceedings of the Parallel Problem Solving from Nature — PPSN XIII","abstract":[{"text":"Multimodal optimization requires maintenance of a good search space coverage and approximation of several optima at the same time. We analyze two constitutive optimization algorithms and show that in many cases, a phase transition occurs at some point, so that either diversity collapses or optimization stagnates. But how to derive suitable stopping criteria for multimodal optimization? Experimental results indicate that an algorithm’s population contains sufficient information to estimate the point in time when several performance indicators reach their optimum. Thus, stopping criteria are formulated based on summary characteristics employing objective values and mutation strength.","lang":"eng"}]},{"status":"public","page":"189–205","_id":"46385","publisher":"Springer International Publishing","user_id":"15504","editor":[{"first_name":"M","last_name":"Emmerich","full_name":"Emmerich, M"},{"full_name":"Deutz, A","first_name":"A","last_name":"Deutz"},{"last_name":"Schuetze","first_name":"O","full_name":"Schuetze, O"},{"last_name":"Bäck","first_name":"T","full_name":"Bäck, T"},{"last_name":"Tantar","first_name":"A","full_name":"Tantar, A"},{"first_name":"PD","last_name":"Moral","full_name":"Moral, PD"},{"full_name":"Legrand, P","first_name":"P","last_name":"Legrand"},{"full_name":"Bouvry, P","first_name":"P","last_name":"Bouvry"},{"full_name":"Coello, CA","first_name":"CA","last_name":"Coello"}],"volume":227,"citation":{"ama":"Sosa HV, Schütze O, Rudolph G, Trautmann H. The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume. In: Emmerich M, Deutz A, Schuetze O, et al., eds. <i>EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV</i>. Vol 227. Advances in Intelligent Systems and Computing. Springer International Publishing; 2013:189–205. doi:<a href=\"https://doi.org/10.1007/978-3-319-01128-8_13\">10.1007/978-3-319-01128-8_13</a>","bibtex":"@inbook{Sosa_Schütze_Rudolph_Trautmann_2013, series={Advances in Intelligent Systems and Computing}, title={The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume}, volume={227}, DOI={<a href=\"https://doi.org/10.1007/978-3-319-01128-8_13\">10.1007/978-3-319-01128-8_13</a>}, booktitle={EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV}, publisher={Springer International Publishing}, author={Sosa, Hernández V and Schütze, O and Rudolph, G and Trautmann, Heike}, editor={Emmerich, M and Deutz, A and Schuetze, O and Bäck, T and Tantar, A and Moral, PD and Legrand, P and Bouvry, P and Coello, CA}, year={2013}, pages={189–205}, collection={Advances in Intelligent Systems and Computing} }","mla":"Sosa, Hernández V., et al. “The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume.” <i>EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV</i>, edited by M Emmerich et al., vol. 227, Springer International Publishing, 2013, pp. 189–205, doi:<a href=\"https://doi.org/10.1007/978-3-319-01128-8_13\">10.1007/978-3-319-01128-8_13</a>.","short":"H.V. Sosa, O. Schütze, G. Rudolph, H. Trautmann, in: M. Emmerich, A. Deutz, O. Schuetze, T. Bäck, A. Tantar, P. Moral, P. Legrand, P. Bouvry, C. Coello (Eds.), EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV, Springer International Publishing, 2013, pp. 189–205.","chicago":"Sosa, Hernández V, O Schütze, G Rudolph, and Heike Trautmann. “The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume.” In <i>EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV</i>, edited by M Emmerich, A Deutz, O Schuetze, T Bäck, A Tantar, PD Moral, P Legrand, P Bouvry, and CA Coello, 227:189–205. Advances in Intelligent Systems and Computing. Springer International Publishing, 2013. <a href=\"https://doi.org/10.1007/978-3-319-01128-8_13\">https://doi.org/10.1007/978-3-319-01128-8_13</a>.","apa":"Sosa, H. V., Schütze, O., Rudolph, G., &#38; Trautmann, H. (2013). The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume. In M. Emmerich, A. Deutz, O. Schuetze, T. Bäck, A. Tantar, P. Moral, P. Legrand, P. Bouvry, &#38; C. Coello (Eds.), <i>EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV</i> (Vol. 227, pp. 189–205). Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-319-01128-8_13\">https://doi.org/10.1007/978-3-319-01128-8_13</a>","ieee":"H. V. Sosa, O. Schütze, G. Rudolph, and H. Trautmann, “The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume,” in <i>EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV</i>, vol. 227, M. Emmerich, A. Deutz, O. Schuetze, T. Bäck, A. Tantar, P. Moral, P. Legrand, P. Bouvry, and C. Coello, Eds. Springer International Publishing, 2013, pp. 189–205."},"title":"The Directed Search Method for Pareto Front Approximations with Maximum Dominated Hypervolume","year":"2013","publication_identifier":{"isbn":["978-3-319-01127-1"]},"author":[{"full_name":"Sosa, Hernández V","first_name":"Hernández V","last_name":"Sosa"},{"full_name":"Schütze, O","last_name":"Schütze","first_name":"O"},{"full_name":"Rudolph, G","first_name":"G","last_name":"Rudolph"},{"full_name":"Trautmann, Heike","last_name":"Trautmann","first_name":"Heike","orcid":"0000-0002-9788-8282","id":"100740"}],"date_updated":"2023-10-16T13:44:50Z","intvolume":"       227","language":[{"iso":"eng"}],"series_title":"Advances in Intelligent Systems and Computing","doi":"10.1007/978-3-319-01128-8_13","publication":"EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV","abstract":[{"lang":"eng","text":"In many applications one is faced with the problem that multiple objectives have to be optimized at the same time. Since typically the solution set of such multi-objective optimization problems forms a manifold which cannot be computed analytically, one is in many cases interested in a suitable finite size approximation of this set. One widely used approach is to find a representative set that maximizes the dominated hypervolume that is defined by the images in objective space of these solutions and a given reference point.\r\n\r\nIn this paper, we propose a new point-wise iterative search procedure, Hypervolume Directed Search (HVDS), that aims to increase the hypervolume of a given point in an archive for bi-objective unconstrained optimization problems. We present the HVDS both as a standalone algorithm and as a local searcher within a specialized evolutionary algorithm. Numerical results confirm the strength of the novel approach."}],"date_created":"2023-08-04T15:37:00Z","type":"book_chapter","department":[{"_id":"34"},{"_id":"819"}]},{"_id":"46386","publisher":"Springer Berlin Heidelberg","page":"89–105","editor":[{"full_name":"Schütze, O","first_name":"O","last_name":"Schütze"},{"full_name":"Coello, Coello CA","last_name":"Coello","first_name":"Coello CA"},{"full_name":"Tantar, A","last_name":"Tantar","first_name":"A"},{"first_name":"E","last_name":"Tantar","full_name":"Tantar, E"},{"last_name":"Bouvry","first_name":"P","full_name":"Bouvry, P"},{"full_name":"Del, Moral P","first_name":"Moral P","last_name":"Del"},{"first_name":"P","last_name":"Legrand","full_name":"Legrand, P"}],"volume":175,"user_id":"15504","status":"public","citation":{"chicago":"Trautmann, Heike, G Rudolph, C Dominguez-Medina, and O Schütze. “Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems.” In <i>EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II</i>, edited by O Schütze, Coello CA Coello, A Tantar, E Tantar, P Bouvry, Moral P Del, and P Legrand, 175:89–105. Advances in Intelligent Systems and Computing. Springer Berlin Heidelberg, 2013. <a href=\"https://doi.org/10.1007/978-3-642-31519-0_6\">https://doi.org/10.1007/978-3-642-31519-0_6</a>.","short":"H. Trautmann, G. Rudolph, C. Dominguez-Medina, O. Schütze, in: O. Schütze, C.C. Coello, A. Tantar, E. Tantar, P. Bouvry, M.P. Del, P. Legrand (Eds.), EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II, Springer Berlin Heidelberg, 2013, pp. 89–105.","apa":"Trautmann, H., Rudolph, G., Dominguez-Medina, C., &#38; Schütze, O. (2013). Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems. In O. Schütze, C. C. Coello, A. Tantar, E. Tantar, P. Bouvry, M. P. Del, &#38; P. Legrand (Eds.), <i>EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II</i> (Vol. 175, pp. 89–105). Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/978-3-642-31519-0_6\">https://doi.org/10.1007/978-3-642-31519-0_6</a>","ieee":"H. Trautmann, G. Rudolph, C. Dominguez-Medina, and O. Schütze, “Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems,” in <i>EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II</i>, vol. 175, O. Schütze, C. C. Coello, A. Tantar, E. Tantar, P. Bouvry, M. P. Del, and P. Legrand, Eds. Springer Berlin Heidelberg, 2013, pp. 89–105.","ama":"Trautmann H, Rudolph G, Dominguez-Medina C, Schütze O. Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems. In: Schütze O, Coello CC, Tantar A, et al., eds. <i>EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II</i>. Vol 175. Advances in Intelligent Systems and Computing. Springer Berlin Heidelberg; 2013:89–105. doi:<a href=\"https://doi.org/10.1007/978-3-642-31519-0_6\">10.1007/978-3-642-31519-0_6</a>","bibtex":"@inbook{Trautmann_Rudolph_Dominguez-Medina_Schütze_2013, series={Advances in Intelligent Systems and Computing}, title={Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems}, volume={175}, DOI={<a href=\"https://doi.org/10.1007/978-3-642-31519-0_6\">10.1007/978-3-642-31519-0_6</a>}, booktitle={EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II}, publisher={Springer Berlin Heidelberg}, author={Trautmann, Heike and Rudolph, G and Dominguez-Medina, C and Schütze, O}, editor={Schütze, O and Coello, Coello CA and Tantar, A and Tantar, E and Bouvry, P and Del, Moral P and Legrand, P}, year={2013}, pages={89–105}, collection={Advances in Intelligent Systems and Computing} }","mla":"Trautmann, Heike, et al. “Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems.” <i>EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II</i>, edited by O Schütze et al., vol. 175, Springer Berlin Heidelberg, 2013, pp. 89–105, doi:<a href=\"https://doi.org/10.1007/978-3-642-31519-0_6\">10.1007/978-3-642-31519-0_6</a>."},"language":[{"iso":"eng"}],"series_title":"Advances in Intelligent Systems and Computing","doi":"10.1007/978-3-642-31519-0_6","publication_identifier":{"isbn":["978-3-642-31518-3"]},"author":[{"first_name":"Heike","orcid":"0000-0002-9788-8282","last_name":"Trautmann","full_name":"Trautmann, Heike","id":"100740"},{"first_name":"G","last_name":"Rudolph","full_name":"Rudolph, G"},{"full_name":"Dominguez-Medina, C","first_name":"C","last_name":"Dominguez-Medina"},{"full_name":"Schütze, O","first_name":"O","last_name":"Schütze"}],"year":"2013","title":"Finding Evenly Spaced Pareto Fronts for Three-Objective Optimization Problems","intvolume":"       175","date_updated":"2023-10-16T13:45:12Z","date_created":"2023-08-04T15:38:25Z","department":[{"_id":"34"},{"_id":"819"}],"type":"book_chapter","publication":"EVOLVE — A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation II","abstract":[{"text":"The averaged Hausdorff distance Δ p is a performance indicator in multi-objective evolutionary optimization which simultaneously takes into account proximity to the true Pareto front and uniform spread of solutions. Recently, the multi-objective evolutionary algorithm Δ p -EMOA was introduced which successfully generates evenly spaced Pareto front approximations for bi-objective problems by integrating an external archiving strategy into the SMS-EMOA based on Δ p . In this work a conceptual generalization of the Δ p -EMOA for higher objective space dimensions is presented and experimentally compared to state-of-the art EMOA as well as specialized EMOA variants on three-dimensional optimization problems.","lang":"eng"}]},{"year":"2013","title":"A Feature-Based Comparison of Local Search and the Christofides Algorithm for the Travelling Salesperson Problem","publication_identifier":{"isbn":["9781450319904"]},"author":[{"full_name":"Nallaperuma, Samadhi","last_name":"Nallaperuma","first_name":"Samadhi"},{"full_name":"Wagner, Markus","last_name":"Wagner","first_name":"Markus"},{"full_name":"Neumann, Frank","last_name":"Neumann","first_name":"Frank"},{"full_name":"Bischl, Bernd","last_name":"Bischl","first_name":"Bernd"},{"last_name":"Mersmann","first_name":"Olaf","full_name":"Mersmann, Olaf"},{"full_name":"Trautmann, Heike","last_name":"Trautmann","orcid":"0000-0002-9788-8282","first_name":"Heike","id":"100740"}],"date_updated":"2023-10-16T13:45:53Z","series_title":"FOGA XII ’13","language":[{"iso":"eng"}],"doi":"10.1145/2460239.2460253","publication":"Proceedings of the Twelfth Workshop on Foundations of Genetic Algorithms XII","abstract":[{"text":"Understanding the behaviour of well-known algorithms for classical NP-hard optimisation problems is still a difficult task. With this paper, we contribute to this research direction and carry out a feature based comparison of local search and the well-known Christofides approximation algorithm for the Traveling Salesperson Problem. We use an evolutionary algorithm approach to construct easy and hard instances for the Christofides algorithm, where we measure hardness in terms of approximation ratio. Our results point out important features and lead to hard and easy instances for this famous algorithm. Furthermore, our cross-comparison gives new insights on the complementary benefits of the different approaches.","lang":"eng"}],"date_created":"2023-08-04T15:42:03Z","keyword":["approximation algorithms","local search","traveling salesperson problem","feature selection","prediction","classification"],"type":"conference","department":[{"_id":"34"},{"_id":"819"}],"status":"public","page":"147–160","_id":"46388","publisher":"Association for Computing Machinery","user_id":"15504","citation":{"apa":"Nallaperuma, S., Wagner, M., Neumann, F., Bischl, B., Mersmann, O., &#38; Trautmann, H. (2013). A Feature-Based Comparison of Local Search and the Christofides Algorithm for the Travelling Salesperson Problem. <i>Proceedings of the Twelfth Workshop on Foundations of Genetic Algorithms XII</i>, 147–160. <a href=\"https://doi.org/10.1145/2460239.2460253\">https://doi.org/10.1145/2460239.2460253</a>","ieee":"S. Nallaperuma, M. Wagner, F. Neumann, B. Bischl, O. Mersmann, and H. Trautmann, “A Feature-Based Comparison of Local Search and the Christofides Algorithm for the Travelling Salesperson Problem,” in <i>Proceedings of the Twelfth Workshop on Foundations of Genetic Algorithms XII</i>, 2013, pp. 147–160, doi: <a href=\"https://doi.org/10.1145/2460239.2460253\">10.1145/2460239.2460253</a>.","short":"S. Nallaperuma, M. Wagner, F. Neumann, B. Bischl, O. Mersmann, H. Trautmann, in: Proceedings of the Twelfth Workshop on Foundations of Genetic Algorithms XII, Association for Computing Machinery, New York, NY, USA, 2013, pp. 147–160.","chicago":"Nallaperuma, Samadhi, Markus Wagner, Frank Neumann, Bernd Bischl, Olaf Mersmann, and Heike Trautmann. “A Feature-Based Comparison of Local Search and the Christofides Algorithm for the Travelling Salesperson Problem.” In <i>Proceedings of the Twelfth Workshop on Foundations of Genetic Algorithms XII</i>, 147–160. FOGA XII ’13. New York, NY, USA: Association for Computing Machinery, 2013. <a href=\"https://doi.org/10.1145/2460239.2460253\">https://doi.org/10.1145/2460239.2460253</a>.","mla":"Nallaperuma, Samadhi, et al. “A Feature-Based Comparison of Local Search and the Christofides Algorithm for the Travelling Salesperson Problem.” <i>Proceedings of the Twelfth Workshop on Foundations of Genetic Algorithms XII</i>, Association for Computing Machinery, 2013, pp. 147–160, doi:<a href=\"https://doi.org/10.1145/2460239.2460253\">10.1145/2460239.2460253</a>.","ama":"Nallaperuma S, Wagner M, Neumann F, Bischl B, Mersmann O, Trautmann H. A Feature-Based Comparison of Local Search and the Christofides Algorithm for the Travelling Salesperson Problem. In: <i>Proceedings of the Twelfth Workshop on Foundations of Genetic Algorithms XII</i>. FOGA XII ’13. Association for Computing Machinery; 2013:147–160. doi:<a href=\"https://doi.org/10.1145/2460239.2460253\">10.1145/2460239.2460253</a>","bibtex":"@inproceedings{Nallaperuma_Wagner_Neumann_Bischl_Mersmann_Trautmann_2013, place={New York, NY, USA}, series={FOGA XII ’13}, title={A Feature-Based Comparison of Local Search and the Christofides Algorithm for the Travelling Salesperson Problem}, DOI={<a href=\"https://doi.org/10.1145/2460239.2460253\">10.1145/2460239.2460253</a>}, booktitle={Proceedings of the Twelfth Workshop on Foundations of Genetic Algorithms XII}, publisher={Association for Computing Machinery}, author={Nallaperuma, Samadhi and Wagner, Markus and Neumann, Frank and Bischl, Bernd and Mersmann, Olaf and Trautmann, Heike}, year={2013}, pages={147–160}, collection={FOGA XII ’13} }"},"place":"New York, NY, USA"},{"department":[{"_id":"34"},{"_id":"819"}],"type":"conference","date_created":"2023-08-04T15:43:38Z","abstract":[{"text":"In some technical applications like multiobjective online control an evenly spaced approximation of the Pareto front is desired. Since standard evolutionary multiobjective optimization (EMO) algorithms have not been designed for that kind of approximation we propose an archive-based plug-in method that builds an evenly spaced approximation using averaged Hausdorff measure between archive and reference front. In case of three objectives this reference font is constructed from a triangulated approximation of the Pareto front from a previous experiment. The plug-in can be deployed in online or offline mode for any kind of EMO algorithm.","lang":"eng"}],"publication":"Evolutionary Multi-Criterion Optimization — 7$^th$ International Conference, EMO 2013, Sheffield, UK, Proceedings","doi":"https://doi.org/10.1007/978-3-642-37140-0_34","language":[{"iso":"eng"}],"series_title":"Lecture Notes in Computer Science","intvolume":"      7811","date_updated":"2023-10-16T13:46:35Z","author":[{"full_name":"Rudolph, G","first_name":"G","last_name":"Rudolph"},{"orcid":"0000-0002-9788-8282","first_name":"Heike","last_name":"Trautmann","full_name":"Trautmann, Heike","id":"100740"},{"full_name":"Sengupta, S","first_name":"S","last_name":"Sengupta"},{"last_name":"Schütze","first_name":"O","full_name":"Schütze, O"}],"year":"2013","title":"Evenly Spaced Pareto Front Approximations for Tricriteria Problems Based on Triangulation","citation":{"short":"G. Rudolph, H. Trautmann, S. Sengupta, O. Schütze, in: R. Purshouse, P. Fleming, C. Fonseca, S. Greco, J. Shaw (Eds.), Evolutionary Multi-Criterion Optimization — 7$^th$ International Conference, EMO 2013, Sheffield, UK, Proceedings, Springer, 2013, pp. 443–458.","chicago":"Rudolph, G, Heike Trautmann, S Sengupta, and O Schütze. “Evenly Spaced Pareto Front Approximations for Tricriteria Problems Based on Triangulation.” In <i>Evolutionary Multi-Criterion Optimization — 7$^th$ International Conference, EMO 2013, Sheffield, UK, Proceedings</i>, edited by RC Purshouse, PJ Fleming, CM Fonseca, S Greco, and J Shaw, 7811:443–458. Lecture Notes in Computer Science. Springer, 2013. <a href=\"https://doi.org/10.1007/978-3-642-37140-0_34\">https://doi.org/10.1007/978-3-642-37140-0_34</a>.","ieee":"G. Rudolph, H. Trautmann, S. Sengupta, and O. Schütze, “Evenly Spaced Pareto Front Approximations for Tricriteria Problems Based on Triangulation,” in <i>Evolutionary Multi-Criterion Optimization — 7$^th$ International Conference, EMO 2013, Sheffield, UK, Proceedings</i>, 2013, vol. 7811, pp. 443–458, doi: <a href=\"https://doi.org/10.1007/978-3-642-37140-0_34\">https://doi.org/10.1007/978-3-642-37140-0_34</a>.","apa":"Rudolph, G., Trautmann, H., Sengupta, S., &#38; Schütze, O. (2013). Evenly Spaced Pareto Front Approximations for Tricriteria Problems Based on Triangulation. In R. Purshouse, P. Fleming, C. Fonseca, S. Greco, &#38; J. Shaw (Eds.), <i>Evolutionary Multi-Criterion Optimization — 7$^th$ International Conference, EMO 2013, Sheffield, UK, Proceedings</i> (Vol. 7811, pp. 443–458). Springer. <a href=\"https://doi.org/10.1007/978-3-642-37140-0_34\">https://doi.org/10.1007/978-3-642-37140-0_34</a>","bibtex":"@inproceedings{Rudolph_Trautmann_Sengupta_Schütze_2013, series={Lecture Notes in Computer Science}, title={Evenly Spaced Pareto Front Approximations for Tricriteria Problems Based on Triangulation}, volume={7811}, DOI={<a href=\"https://doi.org/10.1007/978-3-642-37140-0_34\">https://doi.org/10.1007/978-3-642-37140-0_34</a>}, booktitle={Evolutionary Multi-Criterion Optimization — 7$^th$ International Conference, EMO 2013, Sheffield, UK, Proceedings}, publisher={Springer}, author={Rudolph, G and Trautmann, Heike and Sengupta, S and Schütze, O}, editor={Purshouse, RC and Fleming, PJ and Fonseca, CM and Greco, S and Shaw, J}, year={2013}, pages={443–458}, collection={Lecture Notes in Computer Science} }","ama":"Rudolph G, Trautmann H, Sengupta S, Schütze O. Evenly Spaced Pareto Front Approximations for Tricriteria Problems Based on Triangulation. In: Purshouse R, Fleming P, Fonseca C, Greco S, Shaw J, eds. <i>Evolutionary Multi-Criterion Optimization — 7$^th$ International Conference, EMO 2013, Sheffield, UK, Proceedings</i>. Vol 7811. Lecture Notes in Computer Science. Springer; 2013:443–458. doi:<a href=\"https://doi.org/10.1007/978-3-642-37140-0_34\">https://doi.org/10.1007/978-3-642-37140-0_34</a>","mla":"Rudolph, G., et al. “Evenly Spaced Pareto Front Approximations for Tricriteria Problems Based on Triangulation.” <i>Evolutionary Multi-Criterion Optimization — 7$^th$ International Conference, EMO 2013, Sheffield, UK, Proceedings</i>, edited by RC Purshouse et al., vol. 7811, Springer, 2013, pp. 443–458, doi:<a href=\"https://doi.org/10.1007/978-3-642-37140-0_34\">https://doi.org/10.1007/978-3-642-37140-0_34</a>."},"volume":7811,"editor":[{"full_name":"Purshouse, RC","first_name":"RC","last_name":"Purshouse"},{"full_name":"Fleming, PJ","last_name":"Fleming","first_name":"PJ"},{"last_name":"Fonseca","first_name":"CM","full_name":"Fonseca, CM"},{"first_name":"S","last_name":"Greco","full_name":"Greco, S"},{"last_name":"Shaw","first_name":"J","full_name":"Shaw, J"}],"user_id":"15504","_id":"46390","publisher":"Springer","page":"443–458","status":"public"},{"author":[{"full_name":"Sosa-Hernandez, VA","last_name":"Sosa-Hernandez","first_name":"VA"},{"last_name":"Schütze","first_name":"O","full_name":"Schütze, O"},{"last_name":"Rudoph","first_name":"G","full_name":"Rudoph, G"},{"full_name":"Trautmann, Heike","first_name":"Heike","orcid":"0000-0002-9788-8282","last_name":"Trautmann","id":"100740"}],"title":"Directed Search Method for Indicator-based Multi-objective Evolutionary Algorithms","status":"public","year":"2013","date_updated":"2023-10-16T13:46:54Z","_id":"46391","series_title":"GECCO ’13 Companion","language":[{"iso":"eng"}],"publisher":"ACM","page":"1699–1702","user_id":"15504","doi":"10.1145/2464576.2482756","citation":{"short":"V. Sosa-Hernandez, O. Schütze, G. Rudoph, H. Trautmann, in: Proceeding of the Fifteenth Annual Conference Companion on Genetic and Evolutionary Computation Conference Companion, ACM, New York, NY, USA, 2013, pp. 1699–1702.","chicago":"Sosa-Hernandez, VA, O Schütze, G Rudoph, and Heike Trautmann. “Directed Search Method for Indicator-Based Multi-Objective Evolutionary Algorithms.” In <i>Proceeding of the Fifteenth Annual Conference Companion on Genetic and Evolutionary Computation Conference Companion</i>, 1699–1702. GECCO ’13 Companion. New York, NY, USA: ACM, 2013. <a href=\"https://doi.org/10.1145/2464576.2482756\">https://doi.org/10.1145/2464576.2482756</a>.","apa":"Sosa-Hernandez, V., Schütze, O., Rudoph, G., &#38; Trautmann, H. (2013). Directed Search Method for Indicator-based Multi-objective Evolutionary Algorithms. <i>Proceeding of the Fifteenth Annual Conference Companion on Genetic and Evolutionary Computation Conference Companion</i>, 1699–1702. <a href=\"https://doi.org/10.1145/2464576.2482756\">https://doi.org/10.1145/2464576.2482756</a>","ieee":"V. Sosa-Hernandez, O. Schütze, G. Rudoph, and H. Trautmann, “Directed Search Method for Indicator-based Multi-objective Evolutionary Algorithms,” in <i>Proceeding of the Fifteenth Annual Conference Companion on Genetic and Evolutionary Computation Conference Companion</i>, 2013, pp. 1699–1702, doi: <a href=\"https://doi.org/10.1145/2464576.2482756\">10.1145/2464576.2482756</a>.","ama":"Sosa-Hernandez V, Schütze O, Rudoph G, Trautmann H. Directed Search Method for Indicator-based Multi-objective Evolutionary Algorithms. In: <i>Proceeding of the Fifteenth Annual Conference Companion on Genetic and Evolutionary Computation Conference Companion</i>. GECCO ’13 Companion. ACM; 2013:1699–1702. doi:<a href=\"https://doi.org/10.1145/2464576.2482756\">10.1145/2464576.2482756</a>","bibtex":"@inproceedings{Sosa-Hernandez_Schütze_Rudoph_Trautmann_2013, place={New York, NY, USA}, series={GECCO ’13 Companion}, title={Directed Search Method for Indicator-based Multi-objective Evolutionary Algorithms}, DOI={<a href=\"https://doi.org/10.1145/2464576.2482756\">10.1145/2464576.2482756</a>}, booktitle={Proceeding of the Fifteenth Annual Conference Companion on Genetic and Evolutionary Computation Conference Companion}, publisher={ACM}, author={Sosa-Hernandez, VA and Schütze, O and Rudoph, G and Trautmann, Heike}, year={2013}, pages={1699–1702}, collection={GECCO ’13 Companion} }","mla":"Sosa-Hernandez, VA, et al. “Directed Search Method for Indicator-Based Multi-Objective Evolutionary Algorithms.” <i>Proceeding of the Fifteenth Annual Conference Companion on Genetic and Evolutionary Computation Conference Companion</i>, ACM, 2013, pp. 1699–1702, doi:<a href=\"https://doi.org/10.1145/2464576.2482756\">10.1145/2464576.2482756</a>."},"publication":"Proceeding of the Fifteenth Annual Conference Companion on Genetic and Evolutionary Computation Conference Companion","abstract":[{"lang":"eng","text":"Indicator based evolutionary algorithms have caught the interest of many researchers for the treatment of multi-objective optimization problems in the recent past since they deliver the desired approximation of the solution set and due to a usually better performance compared to dominance based algorithms. Nevertheless, these methods still suffer the drawback that many function evaluations are required to obtain a suitable representation of the solution set. The aim of this study is to present the Directed Search (DS) Method as local searcher within global indicator based optimization algorithms. For this, we will present the DS in the context of hypervolume maximization leading to both a new local search algorithm and a new memetic algorithm. Further, we will present first attempts to adapt the DS to a class of parameter dependent problems."}],"date_created":"2023-08-04T15:45:26Z","place":"New York, NY, USA","department":[{"_id":"34"},{"_id":"819"}],"type":"conference"},{"place":"Cancun, Mexico","date_created":"2023-08-04T15:40:15Z","department":[{"_id":"34"},{"_id":"819"}],"type":"conference","citation":{"mla":"Dominguez-Medina, C., et al. “Evenly Spaced Pareto Fronts of Quad-Objective Problems Using PSA Partitioning Technique.” <i>Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC)</i>, 2013, pp. 3190–3197, doi:<a href=\"https://doi.org/10.1109/CEC.2013.6557960\">https://doi.org/10.1109/CEC.2013.6557960</a>.","ama":"Dominguez-Medina C, Rudolph G, Schütze O, Trautmann H. Evenly spaced Pareto fronts of quad-objective problems using PSA partitioning technique. In: <i>Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC)</i>. ; 2013:3190–3197. doi:<a href=\"https://doi.org/10.1109/CEC.2013.6557960\">https://doi.org/10.1109/CEC.2013.6557960</a>","bibtex":"@inproceedings{Dominguez-Medina_Rudolph_Schütze_Trautmann_2013, place={Cancun, Mexico}, title={Evenly spaced Pareto fronts of quad-objective problems using PSA partitioning technique}, DOI={<a href=\"https://doi.org/10.1109/CEC.2013.6557960\">https://doi.org/10.1109/CEC.2013.6557960</a>}, booktitle={Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC)}, author={Dominguez-Medina, C and Rudolph, G and Schütze, O and Trautmann, Heike}, year={2013}, pages={3190–3197} }","apa":"Dominguez-Medina, C., Rudolph, G., Schütze, O., &#38; Trautmann, H. (2013). Evenly spaced Pareto fronts of quad-objective problems using PSA partitioning technique. <i>Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC)</i>, 3190–3197. <a href=\"https://doi.org/10.1109/CEC.2013.6557960\">https://doi.org/10.1109/CEC.2013.6557960</a>","ieee":"C. Dominguez-Medina, G. Rudolph, O. Schütze, and H. Trautmann, “Evenly spaced Pareto fronts of quad-objective problems using PSA partitioning technique,” in <i>Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC)</i>, 2013, pp. 3190–3197, doi: <a href=\"https://doi.org/10.1109/CEC.2013.6557960\">https://doi.org/10.1109/CEC.2013.6557960</a>.","chicago":"Dominguez-Medina, C, G Rudolph, O Schütze, and Heike Trautmann. “Evenly Spaced Pareto Fronts of Quad-Objective Problems Using PSA Partitioning Technique.” In <i>Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC)</i>, 3190–3197. Cancun, Mexico, 2013. <a href=\"https://doi.org/10.1109/CEC.2013.6557960\">https://doi.org/10.1109/CEC.2013.6557960</a>.","short":"C. Dominguez-Medina, G. Rudolph, O. Schütze, H. Trautmann, in: Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC), Cancun, Mexico, 2013, pp. 3190–3197."},"publication":"Proceedings of the 2013 IEEE Congress on Evolutionary Computation (CEC)","abstract":[{"text":"Here we address the problem of computing finite size Hausdorff approximations of the Pareto front of four-objective optimization problems by means of evolutionary computing. Since many applications desire an approximation evenly spread along the Pareto front and approximations that are good in the Hausdorff sense are typically evenly spread along the Pareto front we consider three different evolutionary multi-objective algorithms tailored to that purpose, where two of them are based on the Part and Selection Algorithm (PSA). Finally, we present some numerical results indicating the strength of the novel methods.","lang":"eng"}],"_id":"46387","language":[{"iso":"eng"}],"page":"3190–3197","doi":"https://doi.org/10.1109/CEC.2013.6557960","user_id":"15504","author":[{"first_name":"C","last_name":"Dominguez-Medina","full_name":"Dominguez-Medina, C"},{"full_name":"Rudolph, G","last_name":"Rudolph","first_name":"G"},{"full_name":"Schütze, O","last_name":"Schütze","first_name":"O"},{"id":"100740","full_name":"Trautmann, Heike","last_name":"Trautmann","orcid":"0000-0002-9788-8282","first_name":"Heike"}],"year":"2013","title":"Evenly spaced Pareto fronts of quad-objective problems using PSA partitioning technique","status":"public","date_updated":"2023-10-16T13:45:34Z"},{"citation":{"ama":"Preuss M, Kozakowski D, Hagelbäck J, Trautmann H. Reactive strategy choice in StarCraft by means of Fuzzy Control. In: <i>2013 IEEE Conference on Computational Inteligence in Games (CIG)</i>. ; 2013:1-8. doi:<a href=\"https://doi.org/10.1109/CIG.2013.6633627\">10.1109/CIG.2013.6633627</a>","bibtex":"@inproceedings{Preuss_Kozakowski_Hagelbäck_Trautmann_2013, title={Reactive strategy choice in StarCraft by means of Fuzzy Control}, DOI={<a href=\"https://doi.org/10.1109/CIG.2013.6633627\">10.1109/CIG.2013.6633627</a>}, booktitle={2013 IEEE Conference on Computational Inteligence in Games (CIG)}, author={Preuss, Mike and Kozakowski, Daniel and Hagelbäck, Johan and Trautmann, Heike}, year={2013}, pages={1–8} }","mla":"Preuss, Mike, et al. “Reactive Strategy Choice in StarCraft by Means of Fuzzy Control.” <i>2013 IEEE Conference on Computational Inteligence in Games (CIG)</i>, 2013, pp. 1–8, doi:<a href=\"https://doi.org/10.1109/CIG.2013.6633627\">10.1109/CIG.2013.6633627</a>.","chicago":"Preuss, Mike, Daniel Kozakowski, Johan Hagelbäck, and Heike Trautmann. “Reactive Strategy Choice in StarCraft by Means of Fuzzy Control.” In <i>2013 IEEE Conference on Computational Inteligence in Games (CIG)</i>, 1–8, 2013. <a href=\"https://doi.org/10.1109/CIG.2013.6633627\">https://doi.org/10.1109/CIG.2013.6633627</a>.","short":"M. Preuss, D. Kozakowski, J. Hagelbäck, H. Trautmann, in: 2013 IEEE Conference on Computational Inteligence in Games (CIG), 2013, pp. 1–8.","apa":"Preuss, M., Kozakowski, D., Hagelbäck, J., &#38; Trautmann, H. (2013). Reactive strategy choice in StarCraft by means of Fuzzy Control. <i>2013 IEEE Conference on Computational Inteligence in Games (CIG)</i>, 1–8. <a href=\"https://doi.org/10.1109/CIG.2013.6633627\">https://doi.org/10.1109/CIG.2013.6633627</a>","ieee":"M. Preuss, D. Kozakowski, J. Hagelbäck, and H. Trautmann, “Reactive strategy choice in StarCraft by means of Fuzzy Control,” in <i>2013 IEEE Conference on Computational Inteligence in Games (CIG)</i>, 2013, pp. 1–8, doi: <a href=\"https://doi.org/10.1109/CIG.2013.6633627\">10.1109/CIG.2013.6633627</a>."},"publication":"2013 IEEE Conference on Computational Inteligence in Games (CIG)","abstract":[{"text":"Current StarCraft bots are not very flexible in their strategy choice, most of them just follow a manually optimized one, usually a rush. We suggest a method of augmenting existing bots via Fuzzy Control in order to make them react on the current game situation. According to the available information, the best matching of a pool of strategies is chosen. While the method is very general and can be applied easily to many bots, we implement it for the existing BTHAI bot and show experimentally how the modifications affects its gameplay, and how it is improved compared to the original version.","lang":"eng"}],"date_created":"2023-08-04T15:42:58Z","department":[{"_id":"34"},{"_id":"819"}],"type":"conference","author":[{"last_name":"Preuss","first_name":"Mike","full_name":"Preuss, Mike"},{"last_name":"Kozakowski","first_name":"Daniel","full_name":"Kozakowski, Daniel"},{"full_name":"Hagelbäck, Johan","last_name":"Hagelbäck","first_name":"Johan"},{"id":"100740","first_name":"Heike","last_name":"Trautmann","orcid":"0000-0002-9788-8282","full_name":"Trautmann, Heike"}],"title":"Reactive strategy choice in StarCraft by means of Fuzzy Control","status":"public","year":"2013","date_updated":"2023-10-16T13:46:13Z","language":[{"iso":"eng"}],"_id":"46389","page":"1-8","user_id":"15504","doi":"10.1109/CIG.2013.6633627"},{"date_updated":"2023-10-16T13:48:31Z","intvolume":"        20","title":"Indicator-based Selection in Evolutionary Multiobjective Optimization Algorithms Based On the Desirability Index","year":"2013","status":"public","author":[{"full_name":"Trautmann, Heike","orcid":"0000-0002-9788-8282","first_name":"Heike","last_name":"Trautmann","id":"100740"},{"full_name":"Wagner, T","first_name":"T","last_name":"Wagner"},{"first_name":"D","last_name":"Biermann","full_name":"Biermann, D"},{"first_name":"C","last_name":"Weihs","full_name":"Weihs, C"}],"user_id":"15504","doi":"https://doi.org/10.1002/mcda.1503","volume":20,"page":"319–337","_id":"46395","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"In multiobjective optimization, the identification of practically relevant solutions on the Pareto-optimal front is an important research topic. Desirability functions (DFs) allow the preferences of the decision maker to be specified in an intuitive way. Recently, it has been shown for continuous optimization problems that an a priori transformation of the objectives by means of DFs can be used to focus the search of a hypervolume-based evolutionary algorithm on the desired part of the front. In many-objective optimization, however, the computational complexity of the hypervolume can become a crucial part. Thus, an alternative to this approach will be presented in this paper. The new algorithm operates in the untransformed objective space, but the desirability index (DI), that is, a DF-based scalarization, will be used as the second-level selection criterion in the non-dominated sorting. The diversity and uniform distribution of the resulting approximation are ensured by the use of an external archive. In the experiments, different preferences are specified as DFs, and their effects are investigated. It is shown that trade-off solutions are generated in the desired regions of the Pareto-optimal front and with a density adaptive to the DI. The efficiency of the approach with respect to increasing objective space dimension is also analysed using scalable test functions. The convergence speed is superior to other set-based and preference-based evolutionary multiobjective algorithms while the approach is of low computational complexity due to cheap DI evaluations. Copyright © 2013 John Wiley & Sons, Ltd."}],"publication":"Journal of Multi-Criteria Decision Analysis","issue":"5-6","citation":{"apa":"Trautmann, H., Wagner, T., Biermann, D., &#38; Weihs, C. (2013). Indicator-based Selection in Evolutionary Multiobjective Optimization Algorithms Based On the Desirability Index. <i>Journal of Multi-Criteria Decision Analysis</i>, <i>20</i>(5–6), 319–337. <a href=\"https://doi.org/10.1002/mcda.1503\">https://doi.org/10.1002/mcda.1503</a>","ieee":"H. Trautmann, T. Wagner, D. Biermann, and C. Weihs, “Indicator-based Selection in Evolutionary Multiobjective Optimization Algorithms Based On the Desirability Index,” <i>Journal of Multi-Criteria Decision Analysis</i>, vol. 20, no. 5–6, pp. 319–337, 2013, doi: <a href=\"https://doi.org/10.1002/mcda.1503\">https://doi.org/10.1002/mcda.1503</a>.","short":"H. Trautmann, T. Wagner, D. Biermann, C. Weihs, Journal of Multi-Criteria Decision Analysis 20 (2013) 319–337.","chicago":"Trautmann, Heike, T Wagner, D Biermann, and C Weihs. “Indicator-Based Selection in Evolutionary Multiobjective Optimization Algorithms Based On the Desirability Index.” <i>Journal of Multi-Criteria Decision Analysis</i> 20, no. 5–6 (2013): 319–337. <a href=\"https://doi.org/10.1002/mcda.1503\">https://doi.org/10.1002/mcda.1503</a>.","mla":"Trautmann, Heike, et al. “Indicator-Based Selection in Evolutionary Multiobjective Optimization Algorithms Based On the Desirability Index.” <i>Journal of Multi-Criteria Decision Analysis</i>, vol. 20, no. 5–6, 2013, pp. 319–337, doi:<a href=\"https://doi.org/10.1002/mcda.1503\">https://doi.org/10.1002/mcda.1503</a>.","ama":"Trautmann H, Wagner T, Biermann D, Weihs C. Indicator-based Selection in Evolutionary Multiobjective Optimization Algorithms Based On the Desirability Index. <i>Journal of Multi-Criteria Decision Analysis</i>. 2013;20(5-6):319–337. doi:<a href=\"https://doi.org/10.1002/mcda.1503\">https://doi.org/10.1002/mcda.1503</a>","bibtex":"@article{Trautmann_Wagner_Biermann_Weihs_2013, title={Indicator-based Selection in Evolutionary Multiobjective Optimization Algorithms Based On the Desirability Index}, volume={20}, DOI={<a href=\"https://doi.org/10.1002/mcda.1503\">https://doi.org/10.1002/mcda.1503</a>}, number={5–6}, journal={Journal of Multi-Criteria Decision Analysis}, author={Trautmann, Heike and Wagner, T and Biermann, D and Weihs, C}, year={2013}, pages={319–337} }"},"type":"journal_article","department":[{"_id":"34"},{"_id":"819"}],"date_created":"2023-08-04T15:50:03Z"},{"date_created":"2023-08-04T15:47:49Z","place":"Berlin, Heidelberg","type":"conference","department":[{"_id":"34"},{"_id":"819"}],"publication":"Evolutionary Multi-Criterion Optimization","citation":{"ama":"Wagner T, Trautmann H, Brockhoff D. Preference Articulation by Means of the R2 Indicator. In: Purshouse RC, Fleming PJ, Fonseca CM, Greco S, Shaw J, eds. <i>Evolutionary Multi-Criterion Optimization</i>. Springer Berlin Heidelberg; 2013:81–95.","bibtex":"@inproceedings{Wagner_Trautmann_Brockhoff_2013, place={Berlin, Heidelberg}, title={Preference Articulation by Means of the R2 Indicator}, booktitle={Evolutionary Multi-Criterion Optimization}, publisher={Springer Berlin Heidelberg}, author={Wagner, Tobias and Trautmann, Heike and Brockhoff, Dimo}, editor={Purshouse, Robin C. and Fleming, Peter J. and Fonseca, Carlos M. and Greco, Salvatore and Shaw, Jane}, year={2013}, pages={81–95} }","mla":"Wagner, Tobias, et al. “Preference Articulation by Means of the R2 Indicator.” <i>Evolutionary Multi-Criterion Optimization</i>, edited by Robin C. Purshouse et al., Springer Berlin Heidelberg, 2013, pp. 81–95.","chicago":"Wagner, Tobias, Heike Trautmann, and Dimo Brockhoff. “Preference Articulation by Means of the R2 Indicator.” In <i>Evolutionary Multi-Criterion Optimization</i>, edited by Robin C. Purshouse, Peter J. Fleming, Carlos M. Fonseca, Salvatore Greco, and Jane Shaw, 81–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.","short":"T. Wagner, H. Trautmann, D. Brockhoff, in: R.C. Purshouse, P.J. Fleming, C.M. Fonseca, S. Greco, J. Shaw (Eds.), Evolutionary Multi-Criterion Optimization, Springer Berlin Heidelberg, Berlin, Heidelberg, 2013, pp. 81–95.","apa":"Wagner, T., Trautmann, H., &#38; Brockhoff, D. (2013). Preference Articulation by Means of the R2 Indicator. In R. C. Purshouse, P. J. Fleming, C. M. Fonseca, S. Greco, &#38; J. Shaw (Eds.), <i>Evolutionary Multi-Criterion Optimization</i> (pp. 81–95). Springer Berlin Heidelberg.","ieee":"T. Wagner, H. Trautmann, and D. Brockhoff, “Preference Articulation by Means of the R2 Indicator,” in <i>Evolutionary Multi-Criterion Optimization</i>, 2013, pp. 81–95."},"abstract":[{"text":"In multi-objective optimization, set-based performance indicators have become the state of the art for assessing the quality of Pareto front approximations. As a consequence, they are also more and more used within the design of multi-objective optimization algorithms. The R2 and the Hypervolume (HV) indicator represent two popular examples. In order to understand the behavior and the approximations preferred by these indicators and algorithms, a comprehensive knowledge of the indicator’s properties is required. Whereas this knowledge is available for the HV, we presented a first approach in this direction for the R2 indicator just recently. In this paper, we build upon this knowledge and enhance the considerations with respect to the integration of preferences into the R2 indicator. More specifically, we analyze the effect of the reference point, the domain of the weights, and the distribution of weight vectors on the optimization of $\\mu$ solutions with respect to the R2 indicator. By means of theoretical findings and empirical evidence, we show the potentials of these three possibilities using the optimal distribution of $\\mu$ solutions for exemplary setups.","lang":"eng"}],"page":"81–95","_id":"46393","language":[{"iso":"eng"}],"publisher":"Springer Berlin Heidelberg","user_id":"15504","editor":[{"last_name":"Purshouse","first_name":"Robin C.","full_name":"Purshouse, Robin C."},{"last_name":"Fleming","first_name":"Peter J.","full_name":"Fleming, Peter J."},{"last_name":"Fonseca","first_name":"Carlos M.","full_name":"Fonseca, Carlos M."},{"full_name":"Greco, Salvatore","first_name":"Salvatore","last_name":"Greco"},{"full_name":"Shaw, Jane","first_name":"Jane","last_name":"Shaw"}],"title":"Preference Articulation by Means of the R2 Indicator","year":"2013","status":"public","author":[{"last_name":"Wagner","first_name":"Tobias","full_name":"Wagner, Tobias"},{"id":"100740","orcid":"0000-0002-9788-8282","first_name":"Heike","last_name":"Trautmann","full_name":"Trautmann, Heike"},{"full_name":"Brockhoff, Dimo","first_name":"Dimo","last_name":"Brockhoff"}],"publication_identifier":{"isbn":["978-3-642-37140-0"]},"date_updated":"2023-10-16T13:47:58Z"},{"year":"2013","title":"R2-EMOA: Focused Multiobjective Search Using R2-Indicator-Based Selection","status":"public","author":[{"id":"100740","full_name":"Trautmann, Heike","first_name":"Heike","orcid":"0000-0002-9788-8282","last_name":"Trautmann"},{"full_name":"Wagner, Tobias","first_name":"Tobias","last_name":"Wagner"},{"last_name":"Brockhoff","first_name":"Dimo","full_name":"Brockhoff, Dimo"}],"publication_identifier":{"isbn":["978-3-642-44973-4"]},"date_updated":"2023-10-16T13:47:41Z","page":"70–74","_id":"46392","publisher":"Springer Berlin Heidelberg","language":[{"iso":"eng"}],"user_id":"15504","editor":[{"full_name":"Nicosia, Giuseppe","last_name":"Nicosia","first_name":"Giuseppe"},{"full_name":"Pardalos, Panos","first_name":"Panos","last_name":"Pardalos"}],"publication":"Learning and Intelligent Optimization","citation":{"apa":"Trautmann, H., Wagner, T., &#38; Brockhoff, D. (2013). R2-EMOA: Focused Multiobjective Search Using R2-Indicator-Based Selection. In G. Nicosia &#38; P. Pardalos (Eds.), <i>Learning and Intelligent Optimization</i> (pp. 70–74). Springer Berlin Heidelberg.","ieee":"H. Trautmann, T. Wagner, and D. Brockhoff, “R2-EMOA: Focused Multiobjective Search Using R2-Indicator-Based Selection,” in <i>Learning and Intelligent Optimization</i>, 2013, pp. 70–74.","short":"H. Trautmann, T. Wagner, D. Brockhoff, in: G. Nicosia, P. Pardalos (Eds.), Learning and Intelligent Optimization, Springer Berlin Heidelberg, Berlin, Heidelberg, 2013, pp. 70–74.","chicago":"Trautmann, Heike, Tobias Wagner, and Dimo Brockhoff. “R2-EMOA: Focused Multiobjective Search Using R2-Indicator-Based Selection.” In <i>Learning and Intelligent Optimization</i>, edited by Giuseppe Nicosia and Panos Pardalos, 70–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.","mla":"Trautmann, Heike, et al. “R2-EMOA: Focused Multiobjective Search Using R2-Indicator-Based Selection.” <i>Learning and Intelligent Optimization</i>, edited by Giuseppe Nicosia and Panos Pardalos, Springer Berlin Heidelberg, 2013, pp. 70–74.","ama":"Trautmann H, Wagner T, Brockhoff D. R2-EMOA: Focused Multiobjective Search Using R2-Indicator-Based Selection. In: Nicosia G, Pardalos P, eds. <i>Learning and Intelligent Optimization</i>. Springer Berlin Heidelberg; 2013:70–74.","bibtex":"@inproceedings{Trautmann_Wagner_Brockhoff_2013, place={Berlin, Heidelberg}, title={R2-EMOA: Focused Multiobjective Search Using R2-Indicator-Based Selection}, booktitle={Learning and Intelligent Optimization}, publisher={Springer Berlin Heidelberg}, author={Trautmann, Heike and Wagner, Tobias and Brockhoff, Dimo}, editor={Nicosia, Giuseppe and Pardalos, Panos}, year={2013}, pages={70–74} }"},"abstract":[{"lang":"eng","text":"An indicator-based evolutionary multiobjective optimization algorithm (EMOA) is introduced which incorporates the contribution to the unary R2-indicator as the secondary selection criterion. First experiments indicate that the R2-EMOA accurately approximates the Pareto front of the considered continuous multiobjective optimization problems. Furthermore, decision makers’ preferences can be included by adjusting the weight vector distributions of the indicator which results in a focused search behavior."}],"date_created":"2023-08-04T15:47:00Z","place":"Berlin, Heidelberg","type":"conference","department":[{"_id":"34"},{"_id":"819"}]},{"date_created":"2023-08-04T15:48:57Z","department":[{"_id":"34"},{"_id":"819"}],"type":"journal_article","citation":{"bibtex":"@article{Mersmann_Bischl_Trautmann_Wagner_Bossek_Neumann_2013, title={A Novel Feature-Based Approach to Characterize Algorithm Performance for the Traveling Salesman Problem}, volume={69}, journal={Annals of Mathematics and Artificial Intelligence}, author={Mersmann, O and Bischl, B and Trautmann, Heike and Wagner, M and Bossek, Jakob and Neumann, F}, year={2013}, pages={151–182} }","chicago":"Mersmann, O, B Bischl, Heike Trautmann, M Wagner, Jakob Bossek, and F Neumann. “A Novel Feature-Based Approach to Characterize Algorithm Performance for the Traveling Salesman Problem.” <i>Annals of Mathematics and Artificial Intelligence</i> 69 (2013): 151–182.","ama":"Mersmann O, Bischl B, Trautmann H, Wagner M, Bossek J, Neumann F. A Novel Feature-Based Approach to Characterize Algorithm Performance for the Traveling Salesman Problem. <i>Annals of Mathematics and Artificial Intelligence</i>. 2013;69:151–182.","short":"O. Mersmann, B. Bischl, H. Trautmann, M. Wagner, J. Bossek, F. Neumann, Annals of Mathematics and Artificial Intelligence 69 (2013) 151–182.","ieee":"O. Mersmann, B. Bischl, H. Trautmann, M. Wagner, J. Bossek, and F. Neumann, “A Novel Feature-Based Approach to Characterize Algorithm Performance for the Traveling Salesman Problem,” <i>Annals of Mathematics and Artificial Intelligence</i>, vol. 69, pp. 151–182, 2013.","apa":"Mersmann, O., Bischl, B., Trautmann, H., Wagner, M., Bossek, J., &#38; Neumann, F. (2013). A Novel Feature-Based Approach to Characterize Algorithm Performance for the Traveling Salesman Problem. <i>Annals of Mathematics and Artificial Intelligence</i>, <i>69</i>, 151–182.","mla":"Mersmann, O., et al. “A Novel Feature-Based Approach to Characterize Algorithm Performance for the Traveling Salesman Problem.” <i>Annals of Mathematics and Artificial Intelligence</i>, vol. 69, 2013, pp. 151–182."},"publication":"Annals of Mathematics and Artificial Intelligence","abstract":[{"text":"Meta-heuristics are frequently used to tackle NP-hard combinatorial optimization problems. With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesperson problem (TSP). Although 2-opt is widely used in practice, it is hard to understand its success from a theoretical perspective. We take a statistical approach and examine the features of TSP instances that make the problem either hard or easy to solve. As a measure of problem difficulty for 2-opt we use the approximation ratio that it achieves on a given instance. Our investigations point out important features that make TSP instances hard or easy to be approximated by 2-opt.","lang":"eng"}],"language":[{"iso":"eng"}],"_id":"46394","page":"151–182","volume":69,"user_id":"15504","author":[{"full_name":"Mersmann, O","last_name":"Mersmann","first_name":"O"},{"full_name":"Bischl, B","last_name":"Bischl","first_name":"B"},{"id":"100740","first_name":"Heike","last_name":"Trautmann","orcid":"0000-0002-9788-8282","full_name":"Trautmann, Heike"},{"full_name":"Wagner, M","first_name":"M","last_name":"Wagner"},{"id":"102979","orcid":"0000-0002-4121-4668","last_name":"Bossek","first_name":"Jakob","full_name":"Bossek, Jakob"},{"full_name":"Neumann, F","last_name":"Neumann","first_name":"F"}],"status":"public","title":"A Novel Feature-Based Approach to Characterize Algorithm Performance for the Traveling Salesman Problem","year":"2013","intvolume":"        69","date_updated":"2024-06-10T11:57:43Z"},{"publication_identifier":{"isbn":["9781450311779"]},"author":[{"full_name":"Brockhoff, Dimo","first_name":"Dimo","last_name":"Brockhoff"},{"full_name":"Wagner, Tobias","first_name":"Tobias","last_name":"Wagner"},{"full_name":"Trautmann, Heike","first_name":"Heike","orcid":"0000-0002-9788-8282","last_name":"Trautmann","id":"100740"}],"year":"2012","title":"On the Properties of the R2 Indicator","date_updated":"2023-10-16T13:47:23Z","language":[{"iso":"eng"}],"series_title":"GECCO ’12","doi":"10.1145/2330163.2330230","publication":"Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation","abstract":[{"text":"In multiobjective optimization, set-based performance indicators are commonly used to assess the quality of a Pareto front approximation. Based on the scalarization obtained by these indicators, a performance comparison of multiobjective optimization algorithms becomes possible. The R2 and the Hypervolume (HV) indicator represent two recommended approaches which have shown a correlated behavior in recent empirical studies. Whereas the HV indicator has been comprehensively analyzed in the last years, almost no studies on the R2 indicator exist. In this paper, we thus perform a comprehensive investigation of the properties of the R2 indicator in a theoretical and empirical way. The influence of the number and distribution of the weight vectors on the optimal distribution of μ solutions is analyzed. Based on a comparative analysis, specific characteristics and differences of the R2 and HV indicator are presented.","lang":"eng"}],"date_created":"2023-08-04T15:52:42Z","department":[{"_id":"34"},{"_id":"819"}],"type":"conference","keyword":["hypervolume indicator","multiobjective optimization","performance assessment","r2 indicator"],"status":"public","_id":"46397","publisher":"Association for Computing Machinery","page":"465–472","user_id":"15504","citation":{"short":"D. Brockhoff, T. Wagner, H. Trautmann, in: Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation, Association for Computing Machinery, New York, NY, USA, 2012, pp. 465–472.","chicago":"Brockhoff, Dimo, Tobias Wagner, and Heike Trautmann. “On the Properties of the R2 Indicator.” In <i>Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation</i>, 465–472. GECCO ’12. New York, NY, USA: Association for Computing Machinery, 2012. <a href=\"https://doi.org/10.1145/2330163.2330230\">https://doi.org/10.1145/2330163.2330230</a>.","apa":"Brockhoff, D., Wagner, T., &#38; Trautmann, H. (2012). On the Properties of the R2 Indicator. <i>Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation</i>, 465–472. <a href=\"https://doi.org/10.1145/2330163.2330230\">https://doi.org/10.1145/2330163.2330230</a>","ieee":"D. Brockhoff, T. Wagner, and H. Trautmann, “On the Properties of the R2 Indicator,” in <i>Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation</i>, 2012, pp. 465–472, doi: <a href=\"https://doi.org/10.1145/2330163.2330230\">10.1145/2330163.2330230</a>.","ama":"Brockhoff D, Wagner T, Trautmann H. On the Properties of the R2 Indicator. In: <i>Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation</i>. GECCO ’12. Association for Computing Machinery; 2012:465–472. doi:<a href=\"https://doi.org/10.1145/2330163.2330230\">10.1145/2330163.2330230</a>","bibtex":"@inproceedings{Brockhoff_Wagner_Trautmann_2012, place={New York, NY, USA}, series={GECCO ’12}, title={On the Properties of the R2 Indicator}, DOI={<a href=\"https://doi.org/10.1145/2330163.2330230\">10.1145/2330163.2330230</a>}, booktitle={Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation}, publisher={Association for Computing Machinery}, author={Brockhoff, Dimo and Wagner, Tobias and Trautmann, Heike}, year={2012}, pages={465–472}, collection={GECCO ’12} }","mla":"Brockhoff, Dimo, et al. “On the Properties of the R2 Indicator.” <i>Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation</i>, Association for Computing Machinery, 2012, pp. 465–472, doi:<a href=\"https://doi.org/10.1145/2330163.2330230\">10.1145/2330163.2330230</a>."},"place":"New York, NY, USA"},{"series_title":"GECCO ’12","language":[{"iso":"eng"}],"doi":"10.1145/2330163.2330209","author":[{"last_name":"Bischl","first_name":"Bernd","full_name":"Bischl, Bernd"},{"first_name":"Olaf","last_name":"Mersmann","full_name":"Mersmann, Olaf"},{"last_name":"Trautmann","first_name":"Heike","orcid":"0000-0002-9788-8282","full_name":"Trautmann, Heike","id":"100740"},{"full_name":"Preuß, Mike","first_name":"Mike","last_name":"Preuß"}],"publication_identifier":{"isbn":["9781450311779"]},"title":"Algorithm Selection Based on Exploratory Landscape Analysis and Cost-Sensitive Learning","year":"2012","date_updated":"2023-10-16T13:48:48Z","date_created":"2023-08-04T15:51:56Z","department":[{"_id":"34"},{"_id":"819"}],"keyword":["machine learning","exploratory landscape analysis","fitness landscape","benchmarking","evolutionary optimization","bbob test set","algorithm selection"],"type":"conference","publication":"Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation","abstract":[{"text":"The steady supply of new optimization methods makes the algorithm selection problem (ASP) an increasingly pressing and challenging task, specially for real-world black-box optimization problems. The introduced approach considers the ASP as a cost-sensitive classification task which is based on Exploratory Landscape Analysis. Low-level features gathered by systematic sampling of the function on the feasible set are used to predict a well-performing algorithm out of a given portfolio. Example-specific label costs are defined by the expected runtime of each candidate algorithm. We use one-sided support vector regression to solve this learning problem. The approach is illustrated by means of the optimization problems and algorithms of the BBOB’09/10 workshop.","lang":"eng"}],"_id":"46396","publisher":"Association for Computing Machinery","page":"313–320","user_id":"15504","status":"public","place":"New York, NY, USA","citation":{"ama":"Bischl B, Mersmann O, Trautmann H, Preuß M. Algorithm Selection Based on Exploratory Landscape Analysis and Cost-Sensitive Learning. In: <i>Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation</i>. GECCO ’12. Association for Computing Machinery; 2012:313–320. doi:<a href=\"https://doi.org/10.1145/2330163.2330209\">10.1145/2330163.2330209</a>","bibtex":"@inproceedings{Bischl_Mersmann_Trautmann_Preuß_2012, place={New York, NY, USA}, series={GECCO ’12}, title={Algorithm Selection Based on Exploratory Landscape Analysis and Cost-Sensitive Learning}, DOI={<a href=\"https://doi.org/10.1145/2330163.2330209\">10.1145/2330163.2330209</a>}, booktitle={Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation}, publisher={Association for Computing Machinery}, author={Bischl, Bernd and Mersmann, Olaf and Trautmann, Heike and Preuß, Mike}, year={2012}, pages={313–320}, collection={GECCO ’12} }","mla":"Bischl, Bernd, et al. “Algorithm Selection Based on Exploratory Landscape Analysis and Cost-Sensitive Learning.” <i>Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation</i>, Association for Computing Machinery, 2012, pp. 313–320, doi:<a href=\"https://doi.org/10.1145/2330163.2330209\">10.1145/2330163.2330209</a>.","chicago":"Bischl, Bernd, Olaf Mersmann, Heike Trautmann, and Mike Preuß. “Algorithm Selection Based on Exploratory Landscape Analysis and Cost-Sensitive Learning.” In <i>Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation</i>, 313–320. GECCO ’12. New York, NY, USA: Association for Computing Machinery, 2012. <a href=\"https://doi.org/10.1145/2330163.2330209\">https://doi.org/10.1145/2330163.2330209</a>.","short":"B. Bischl, O. Mersmann, H. Trautmann, M. Preuß, in: Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation, Association for Computing Machinery, New York, NY, USA, 2012, pp. 313–320.","apa":"Bischl, B., Mersmann, O., Trautmann, H., &#38; Preuß, M. (2012). Algorithm Selection Based on Exploratory Landscape Analysis and Cost-Sensitive Learning. <i>Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation</i>, 313–320. <a href=\"https://doi.org/10.1145/2330163.2330209\">https://doi.org/10.1145/2330163.2330209</a>","ieee":"B. Bischl, O. Mersmann, H. Trautmann, and M. Preuß, “Algorithm Selection Based on Exploratory Landscape Analysis and Cost-Sensitive Learning,” in <i>Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation</i>, 2012, pp. 313–320, doi: <a href=\"https://doi.org/10.1145/2330163.2330209\">10.1145/2330163.2330209</a>."}},{"page":"249–275","language":[{"iso":"eng"}],"_id":"46399","user_id":"15504","doi":"10.1162/EVCO_a_00069","volume":20,"title":"Resampling Methods in Model Validation","status":"public","year":"2012","author":[{"first_name":"B","last_name":"Bischl","full_name":"Bischl, B"},{"last_name":"Mersmann","first_name":"O","full_name":"Mersmann, O"},{"id":"100740","last_name":"Trautmann","first_name":"Heike","orcid":"0000-0002-9788-8282","full_name":"Trautmann, Heike"},{"full_name":"Weihs, C","last_name":"Weihs","first_name":"C"}],"date_updated":"2023-10-16T13:53:58Z","intvolume":"        20","date_created":"2023-08-04T15:54:41Z","type":"journal_article","department":[{"_id":"34"},{"_id":"819"}],"issue":"2","publication":"Evolutionary Computation Journal","citation":{"ieee":"B. Bischl, O. Mersmann, H. Trautmann, and C. Weihs, “Resampling Methods in Model Validation,” <i>Evolutionary Computation Journal</i>, vol. 20, no. 2, pp. 249–275, 2012, doi: <a href=\"https://doi.org/10.1162/EVCO_a_00069\">10.1162/EVCO_a_00069</a>.","apa":"Bischl, B., Mersmann, O., Trautmann, H., &#38; Weihs, C. (2012). Resampling Methods in Model Validation. <i>Evolutionary Computation Journal</i>, <i>20</i>(2), 249–275. <a href=\"https://doi.org/10.1162/EVCO_a_00069\">https://doi.org/10.1162/EVCO_a_00069</a>","short":"B. Bischl, O. Mersmann, H. Trautmann, C. Weihs, Evolutionary Computation Journal 20 (2012) 249–275.","chicago":"Bischl, B, O Mersmann, Heike Trautmann, and C Weihs. “Resampling Methods in Model Validation.” <i>Evolutionary Computation Journal</i> 20, no. 2 (2012): 249–275. <a href=\"https://doi.org/10.1162/EVCO_a_00069\">https://doi.org/10.1162/EVCO_a_00069</a>.","mla":"Bischl, B., et al. “Resampling Methods in Model Validation.” <i>Evolutionary Computation Journal</i>, vol. 20, no. 2, 2012, pp. 249–275, doi:<a href=\"https://doi.org/10.1162/EVCO_a_00069\">10.1162/EVCO_a_00069</a>.","bibtex":"@article{Bischl_Mersmann_Trautmann_Weihs_2012, title={Resampling Methods in Model Validation}, volume={20}, DOI={<a href=\"https://doi.org/10.1162/EVCO_a_00069\">10.1162/EVCO_a_00069</a>}, number={2}, journal={Evolutionary Computation Journal}, author={Bischl, B and Mersmann, O and Trautmann, Heike and Weihs, C}, year={2012}, pages={249–275} }","ama":"Bischl B, Mersmann O, Trautmann H, Weihs C. Resampling Methods in Model Validation. <i>Evolutionary Computation Journal</i>. 2012;20(2):249–275. doi:<a href=\"https://doi.org/10.1162/EVCO_a_00069\">10.1162/EVCO_a_00069</a>"},"abstract":[{"lang":"eng","text":"Meta-modeling has become a crucial tool in solving expensive optimization problems. Much of the work in the past has focused on finding a good regression method to model the fitness function. Examples include classical linear regression, splines, neural networks, Kriging and support vector regression. This paper specifically draws attention to the fact that assessing model accuracy is a crucial aspect in the meta-modeling framework. Resampling strategies such as cross-validation, subsampling, bootstrapping, and nested resampling are prominent methods for model validation and are systematically discussed with respect to possible pitfalls, shortcomings, and specific features. A survey of meta-modeling techniques within evolutionary optimization is provided. In addition, practical examples illustrating some of the pitfalls associated with model selection and performance assessment are presented. Finally, recommendations are given for choosing a model validation technique for a particular setting."}]},{"_id":"46400","language":[{"iso":"eng"}],"page":"610–621","volume":60,"user_id":"15504","doi":"10.1524/auto.2012.1033","author":[{"first_name":"G","last_name":"Rudolph","full_name":"Rudolph, G"},{"full_name":"Trautmann, Heike","first_name":"Heike","last_name":"Trautmann","orcid":"0000-0002-9788-8282","id":"100740"},{"first_name":"O","last_name":"Schütze","full_name":"Schütze, O"}],"status":"public","title":"Homogene Approximation der Paretofront bei mehrkriteriellen Kontrollproblemen","year":"2012","intvolume":"        60","date_updated":"2023-10-16T13:54:17Z","date_created":"2023-08-04T15:55:34Z","department":[{"_id":"34"},{"_id":"819"}],"type":"journal_article","citation":{"chicago":"Rudolph, G, Heike Trautmann, and O Schütze. “Homogene Approximation Der Paretofront Bei Mehrkriteriellen Kontrollproblemen.” <i>At-Automatisierungstechnik</i> 60 (2012): 610–621. <a href=\"https://doi.org/10.1524/auto.2012.1033\">https://doi.org/10.1524/auto.2012.1033</a>.","short":"G. Rudolph, H. Trautmann, O. Schütze, At-Automatisierungstechnik 60 (2012) 610–621.","apa":"Rudolph, G., Trautmann, H., &#38; Schütze, O. (2012). Homogene Approximation der Paretofront bei mehrkriteriellen Kontrollproblemen. <i>At-Automatisierungstechnik</i>, <i>60</i>, 610–621. <a href=\"https://doi.org/10.1524/auto.2012.1033\">https://doi.org/10.1524/auto.2012.1033</a>","ieee":"G. Rudolph, H. Trautmann, and O. Schütze, “Homogene Approximation der Paretofront bei mehrkriteriellen Kontrollproblemen,” <i>at-Automatisierungstechnik</i>, vol. 60, pp. 610–621, 2012, doi: <a href=\"https://doi.org/10.1524/auto.2012.1033\">10.1524/auto.2012.1033</a>.","ama":"Rudolph G, Trautmann H, Schütze O. Homogene Approximation der Paretofront bei mehrkriteriellen Kontrollproblemen. <i>at-Automatisierungstechnik</i>. 2012;60:610–621. doi:<a href=\"https://doi.org/10.1524/auto.2012.1033\">10.1524/auto.2012.1033</a>","bibtex":"@article{Rudolph_Trautmann_Schütze_2012, title={Homogene Approximation der Paretofront bei mehrkriteriellen Kontrollproblemen}, volume={60}, DOI={<a href=\"https://doi.org/10.1524/auto.2012.1033\">10.1524/auto.2012.1033</a>}, journal={at-Automatisierungstechnik}, author={Rudolph, G and Trautmann, Heike and Schütze, O}, year={2012}, pages={610–621} }","mla":"Rudolph, G., et al. “Homogene Approximation Der Paretofront Bei Mehrkriteriellen Kontrollproblemen.” <i>At-Automatisierungstechnik</i>, vol. 60, 2012, pp. 610–621, doi:<a href=\"https://doi.org/10.1524/auto.2012.1033\">10.1524/auto.2012.1033</a>."},"publication":"at-Automatisierungstechnik","abstract":[{"text":"Es   werden   mehrkriterielle   evolutio-näre   Algorithmen   (EMOA)   für   zwei-   und   höherdimensio-nale   Probleme   vorgestellt,   die   gleichmäßig   verteilte   Lö-sungen   entlang   der   wahren   Paretofront   generieren.   Diesist   insbesondere   wichtig   im   Kontext   mehrkriterieller   Kon-trollprobleme.   Die   Methodik   beruht   auf   der   Minimierungdes   gemittelten   Hausdorff-Abstandes in   Bezug   aufdie  Paretofront.  Die  EMOA-Varianten  werden  vergleichendzu  aktuellen   Verfahren  auf  Benchmarkproblemen   getestet.","lang":"ger"}]},{"date_updated":"2024-06-10T11:57:32Z","status":"public","title":"Local Search and the Traveling Salesman Problem: A Feature-Based Characterization of Problem Hardness","year":"2012","author":[{"first_name":"Olaf","last_name":"Mersmann","full_name":"Mersmann, Olaf"},{"first_name":"Bernd","last_name":"Bischl","full_name":"Bischl, Bernd"},{"full_name":"Bossek, Jakob","last_name":"Bossek","first_name":"Jakob","orcid":"0000-0002-4121-4668","id":"102979"},{"full_name":"Trautmann, Heike","first_name":"Heike","last_name":"Trautmann","orcid":"0000-0002-9788-8282","id":"100740"},{"last_name":"Wagner","first_name":"Markus","full_name":"Wagner, Markus"},{"full_name":"Neumann, Frank","last_name":"Neumann","first_name":"Frank"}],"publication_identifier":{"isbn":["978-3-642-34413-8"]},"doi":"https://doi.org/10.1007/978-3-642-34413-8_9","user_id":"15504","editor":[{"first_name":"Youssef","last_name":"Hamadi","full_name":"Hamadi, Youssef"},{"full_name":"Schoenauer, Marc","first_name":"Marc","last_name":"Schoenauer"}],"page":"115–129","_id":"46398","publisher":"Springer Berlin Heidelberg","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem (TSP). Although 2-opt is widely used in practice, it is hard to understand its success from a theoretical perspective. We take a statistical approach and examine the features of TSP instances that make the problem either hard or easy to solve. As a measure of problem difficulty for 2-opt we use the approximation ratio that it achieves on a given instance. Our investigations point out important features that make TSP instances hard or easy to be approximated by 2-opt."}],"publication":"Learning and Intelligent Optimization","citation":{"ama":"Mersmann O, Bischl B, Bossek J, Trautmann H, Wagner M, Neumann F. Local Search and the Traveling Salesman Problem: A Feature-Based Characterization of Problem Hardness. In: Hamadi Y, Schoenauer M, eds. <i>Learning and Intelligent Optimization</i>. Springer Berlin Heidelberg; 2012:115–129. doi:<a href=\"https://doi.org/10.1007/978-3-642-34413-8_9\">https://doi.org/10.1007/978-3-642-34413-8_9</a>","bibtex":"@inproceedings{Mersmann_Bischl_Bossek_Trautmann_Wagner_Neumann_2012, place={Berlin, Heidelberg}, title={Local Search and the Traveling Salesman Problem: A Feature-Based Characterization of Problem Hardness}, DOI={<a href=\"https://doi.org/10.1007/978-3-642-34413-8_9\">https://doi.org/10.1007/978-3-642-34413-8_9</a>}, booktitle={Learning and Intelligent Optimization}, publisher={Springer Berlin Heidelberg}, author={Mersmann, Olaf and Bischl, Bernd and Bossek, Jakob and Trautmann, Heike and Wagner, Markus and Neumann, Frank}, editor={Hamadi, Youssef and Schoenauer, Marc}, year={2012}, pages={115–129} }","mla":"Mersmann, Olaf, et al. “Local Search and the Traveling Salesman Problem: A Feature-Based Characterization of Problem Hardness.” <i>Learning and Intelligent Optimization</i>, edited by Youssef Hamadi and Marc Schoenauer, Springer Berlin Heidelberg, 2012, pp. 115–129, doi:<a href=\"https://doi.org/10.1007/978-3-642-34413-8_9\">https://doi.org/10.1007/978-3-642-34413-8_9</a>.","short":"O. Mersmann, B. Bischl, J. Bossek, H. Trautmann, M. Wagner, F. Neumann, in: Y. Hamadi, M. Schoenauer (Eds.), Learning and Intelligent Optimization, Springer Berlin Heidelberg, Berlin, Heidelberg, 2012, pp. 115–129.","chicago":"Mersmann, Olaf, Bernd Bischl, Jakob Bossek, Heike Trautmann, Markus Wagner, and Frank Neumann. “Local Search and the Traveling Salesman Problem: A Feature-Based Characterization of Problem Hardness.” In <i>Learning and Intelligent Optimization</i>, edited by Youssef Hamadi and Marc Schoenauer, 115–129. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. <a href=\"https://doi.org/10.1007/978-3-642-34413-8_9\">https://doi.org/10.1007/978-3-642-34413-8_9</a>.","apa":"Mersmann, O., Bischl, B., Bossek, J., Trautmann, H., Wagner, M., &#38; Neumann, F. (2012). Local Search and the Traveling Salesman Problem: A Feature-Based Characterization of Problem Hardness. In Y. Hamadi &#38; M. Schoenauer (Eds.), <i>Learning and Intelligent Optimization</i> (pp. 115–129). Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/978-3-642-34413-8_9\">https://doi.org/10.1007/978-3-642-34413-8_9</a>","ieee":"O. Mersmann, B. Bischl, J. Bossek, H. Trautmann, M. Wagner, and F. Neumann, “Local Search and the Traveling Salesman Problem: A Feature-Based Characterization of Problem Hardness,” in <i>Learning and Intelligent Optimization</i>, 2012, pp. 115–129, doi: <a href=\"https://doi.org/10.1007/978-3-642-34413-8_9\">https://doi.org/10.1007/978-3-642-34413-8_9</a>."},"type":"conference","department":[{"_id":"34"},{"_id":"819"}],"place":"Berlin, Heidelberg","date_created":"2023-08-04T15:53:33Z"},{"user_id":"15504","page":"829–836","_id":"46401","publisher":"Association for Computing Machinery","status":"public","place":"New York, NY, USA","citation":{"bibtex":"@inproceedings{Mersmann_Bischl_Trautmann_Preuss_Weihs_Rudolph_2011, place={New York, NY, USA}, series={GECCO ’11}, title={Exploratory Landscape Analysis}, DOI={<a href=\"https://doi.org/10.1145/2001576.2001690\">10.1145/2001576.2001690</a>}, booktitle={Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation}, publisher={Association for Computing Machinery}, author={Mersmann, Olaf and Bischl, Bernd and Trautmann, Heike and Preuss, Mike and Weihs, Claus and Rudolph, Günter}, year={2011}, pages={829–836}, collection={GECCO ’11} }","ama":"Mersmann O, Bischl B, Trautmann H, Preuss M, Weihs C, Rudolph G. Exploratory Landscape Analysis. In: <i>Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation</i>. GECCO ’11. Association for Computing Machinery; 2011:829–836. doi:<a href=\"https://doi.org/10.1145/2001576.2001690\">10.1145/2001576.2001690</a>","mla":"Mersmann, Olaf, et al. “Exploratory Landscape Analysis.” <i>Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation</i>, Association for Computing Machinery, 2011, pp. 829–836, doi:<a href=\"https://doi.org/10.1145/2001576.2001690\">10.1145/2001576.2001690</a>.","chicago":"Mersmann, Olaf, Bernd Bischl, Heike Trautmann, Mike Preuss, Claus Weihs, and Günter Rudolph. “Exploratory Landscape Analysis.” In <i>Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation</i>, 829–836. GECCO ’11. New York, NY, USA: Association for Computing Machinery, 2011. <a href=\"https://doi.org/10.1145/2001576.2001690\">https://doi.org/10.1145/2001576.2001690</a>.","short":"O. Mersmann, B. Bischl, H. Trautmann, M. Preuss, C. Weihs, G. Rudolph, in: Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, Association for Computing Machinery, New York, NY, USA, 2011, pp. 829–836.","ieee":"O. Mersmann, B. Bischl, H. Trautmann, M. Preuss, C. Weihs, and G. Rudolph, “Exploratory Landscape Analysis,” in <i>Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation</i>, 2011, pp. 829–836, doi: <a href=\"https://doi.org/10.1145/2001576.2001690\">10.1145/2001576.2001690</a>.","apa":"Mersmann, O., Bischl, B., Trautmann, H., Preuss, M., Weihs, C., &#38; Rudolph, G. (2011). Exploratory Landscape Analysis. <i>Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation</i>, 829–836. <a href=\"https://doi.org/10.1145/2001576.2001690\">https://doi.org/10.1145/2001576.2001690</a>"},"doi":"10.1145/2001576.2001690","series_title":"GECCO ’11","language":[{"iso":"eng"}],"date_updated":"2023-10-16T13:54:34Z","title":"Exploratory Landscape Analysis","year":"2011","publication_identifier":{"isbn":["9781450305570"]},"author":[{"last_name":"Mersmann","first_name":"Olaf","full_name":"Mersmann, Olaf"},{"full_name":"Bischl, Bernd","first_name":"Bernd","last_name":"Bischl"},{"full_name":"Trautmann, Heike","first_name":"Heike","orcid":"0000-0002-9788-8282","last_name":"Trautmann","id":"100740"},{"full_name":"Preuss, Mike","first_name":"Mike","last_name":"Preuss"},{"full_name":"Weihs, Claus","last_name":"Weihs","first_name":"Claus"},{"last_name":"Rudolph","first_name":"Günter","full_name":"Rudolph, Günter"}],"type":"conference","keyword":["exploratory landscape analysis","evolutionary optimization","fitness landscape","benchmarking","BBOB test set"],"department":[{"_id":"34"},{"_id":"819"}],"date_created":"2023-08-04T15:58:22Z","abstract":[{"lang":"eng","text":"Exploratory Landscape Analysis subsumes a number of techniques employed to obtain knowledge about the properties of an unknown optimization problem, especially insofar as these properties are important for the performance of optimization algorithms. Where in a first attempt, one could rely on high-level features designed by experts, we approach the problem from a different angle here, namely by using relatively cheap low-level computer generated features. Interestingly, very few features are needed to separate the BBOB problem groups and also for relating a problem to high-level, expert designed features, paving the way for automatic algorithm selection."}],"publication":"Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation"},{"page":"16–30","language":[{"iso":"eng"}],"_id":"46402","publisher":"Springer Berlin Heidelberg","user_id":"15504","doi":"https://doi.org/10.1007/978-3-642-19893-9_2","editor":[{"full_name":"Takahashi, Ricardo H. C.","last_name":"Takahashi","first_name":"Ricardo H. C."},{"full_name":"Deb, Kalyanmoy","first_name":"Kalyanmoy","last_name":"Deb"},{"first_name":"Elizabeth F.","last_name":"Wanner","full_name":"Wanner, Elizabeth F."},{"first_name":"Salvatore","last_name":"Greco","full_name":"Greco, Salvatore"}],"title":"A Taxonomy of Online Stopping Criteria for Multi-Objective Evolutionary Algorithms","year":"2011","status":"public","publication_identifier":{"isbn":["978-3-642-19893-9"]},"author":[{"last_name":"Wagner","first_name":"Tobias","full_name":"Wagner, Tobias"},{"id":"100740","full_name":"Trautmann, Heike","last_name":"Trautmann","first_name":"Heike","orcid":"0000-0002-9788-8282"},{"full_name":"Martí, Luis","first_name":"Luis","last_name":"Martí"}],"date_updated":"2023-10-16T13:54:50Z","date_created":"2023-08-04T15:59:18Z","place":"Berlin, Heidelberg","type":"conference","department":[{"_id":"34"},{"_id":"819"}],"publication":"Evolutionary Multi-Criterion Optimization","citation":{"apa":"Wagner, T., Trautmann, H., &#38; Martí, L. (2011). A Taxonomy of Online Stopping Criteria for Multi-Objective Evolutionary Algorithms. In R. H. C. Takahashi, K. Deb, E. F. Wanner, &#38; S. Greco (Eds.), <i>Evolutionary Multi-Criterion Optimization</i> (pp. 16–30). Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/978-3-642-19893-9_2\">https://doi.org/10.1007/978-3-642-19893-9_2</a>","ieee":"T. Wagner, H. Trautmann, and L. Martí, “A Taxonomy of Online Stopping Criteria for Multi-Objective Evolutionary Algorithms,” in <i>Evolutionary Multi-Criterion Optimization</i>, 2011, pp. 16–30, doi: <a href=\"https://doi.org/10.1007/978-3-642-19893-9_2\">https://doi.org/10.1007/978-3-642-19893-9_2</a>.","short":"T. Wagner, H. Trautmann, L. Martí, in: R.H.C. Takahashi, K. Deb, E.F. Wanner, S. Greco (Eds.), Evolutionary Multi-Criterion Optimization, Springer Berlin Heidelberg, Berlin, Heidelberg, 2011, pp. 16–30.","chicago":"Wagner, Tobias, Heike Trautmann, and Luis Martí. “A Taxonomy of Online Stopping Criteria for Multi-Objective Evolutionary Algorithms.” In <i>Evolutionary Multi-Criterion Optimization</i>, edited by Ricardo H. C. Takahashi, Kalyanmoy Deb, Elizabeth F. Wanner, and Salvatore Greco, 16–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. <a href=\"https://doi.org/10.1007/978-3-642-19893-9_2\">https://doi.org/10.1007/978-3-642-19893-9_2</a>.","mla":"Wagner, Tobias, et al. “A Taxonomy of Online Stopping Criteria for Multi-Objective Evolutionary Algorithms.” <i>Evolutionary Multi-Criterion Optimization</i>, edited by Ricardo H. C. Takahashi et al., Springer Berlin Heidelberg, 2011, pp. 16–30, doi:<a href=\"https://doi.org/10.1007/978-3-642-19893-9_2\">https://doi.org/10.1007/978-3-642-19893-9_2</a>.","ama":"Wagner T, Trautmann H, Martí L. A Taxonomy of Online Stopping Criteria for Multi-Objective Evolutionary Algorithms. In: Takahashi RHC, Deb K, Wanner EF, Greco S, eds. <i>Evolutionary Multi-Criterion Optimization</i>. Springer Berlin Heidelberg; 2011:16–30. doi:<a href=\"https://doi.org/10.1007/978-3-642-19893-9_2\">https://doi.org/10.1007/978-3-642-19893-9_2</a>","bibtex":"@inproceedings{Wagner_Trautmann_Martí_2011, place={Berlin, Heidelberg}, title={A Taxonomy of Online Stopping Criteria for Multi-Objective Evolutionary Algorithms}, DOI={<a href=\"https://doi.org/10.1007/978-3-642-19893-9_2\">https://doi.org/10.1007/978-3-642-19893-9_2</a>}, booktitle={Evolutionary Multi-Criterion Optimization}, publisher={Springer Berlin Heidelberg}, author={Wagner, Tobias and Trautmann, Heike and Martí, Luis}, editor={Takahashi, Ricardo H. C. and Deb, Kalyanmoy and Wanner, Elizabeth F. and Greco, Salvatore}, year={2011}, pages={16–30} }"},"abstract":[{"text":"The use of multi-objective evolutionary algorithms for solving black-box problems with multiple conflicting objectives has become an important research area. However, when no gradient information is available, the examination of formal convergence or optimality criteria is often impossible. Thus, sophisticated heuristic online stopping criteria (OSC) have recently become subject of intensive research. In order to establish formal guidelines for a systematic research, we present a taxonomy of OSC in this paper. We integrate the known approaches within the taxonomy and discuss them by extracting their building blocks. The formal structure of the taxonomy is used as a basis for the implementation of a comprehensive MATLAB toolbox. Both contributions, the formal taxonomy and the MATLAB implementation, provide a framework for the analysis and evaluation of existing and new OSC approaches.","lang":"eng"}]},{"status":"public","title":"Advanced concepts for multi-objective evolutionary optimization in aircraft industry","year":"2011","author":[{"first_name":"B","last_name":"Naujoks","full_name":"Naujoks, B"},{"full_name":"Trautmann, Heike","orcid":"0000-0002-9788-8282","first_name":"Heike","last_name":"Trautmann","id":"100740"},{"last_name":"Wessing","first_name":"S","full_name":"Wessing, S"},{"full_name":"Weihs, C","last_name":"Weihs","first_name":"C"}],"date_updated":"2023-10-16T13:55:07Z","intvolume":"       225","page":"1081-1096","_id":"46403","language":[{"iso":"eng"}],"user_id":"15504","doi":"10.1177/0954410011414120","volume":225,"publication":"Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering","issue":"10","citation":{"apa":"Naujoks, B., Trautmann, H., Wessing, S., &#38; Weihs, C. (2011). Advanced concepts for multi-objective evolutionary optimization in aircraft industry. <i>Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering</i>, <i>225</i>(10), 1081–1096. <a href=\"https://doi.org/10.1177/0954410011414120\">https://doi.org/10.1177/0954410011414120</a>","ieee":"B. Naujoks, H. Trautmann, S. Wessing, and C. Weihs, “Advanced concepts for multi-objective evolutionary optimization in aircraft industry,” <i>Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering</i>, vol. 225, no. 10, pp. 1081–1096, 2011, doi: <a href=\"https://doi.org/10.1177/0954410011414120\">10.1177/0954410011414120</a>.","short":"B. Naujoks, H. Trautmann, S. Wessing, C. Weihs, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 225 (2011) 1081–1096.","chicago":"Naujoks, B, Heike Trautmann, S Wessing, and C Weihs. “Advanced Concepts for Multi-Objective Evolutionary Optimization in Aircraft Industry.” <i>Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering</i> 225, no. 10 (2011): 1081–96. <a href=\"https://doi.org/10.1177/0954410011414120\">https://doi.org/10.1177/0954410011414120</a>.","mla":"Naujoks, B., et al. “Advanced Concepts for Multi-Objective Evolutionary Optimization in Aircraft Industry.” <i>Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering</i>, vol. 225, no. 10, 2011, pp. 1081–96, doi:<a href=\"https://doi.org/10.1177/0954410011414120\">10.1177/0954410011414120</a>.","ama":"Naujoks B, Trautmann H, Wessing S, Weihs C. Advanced concepts for multi-objective evolutionary optimization in aircraft industry. <i>Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering</i>. 2011;225(10):1081-1096. doi:<a href=\"https://doi.org/10.1177/0954410011414120\">10.1177/0954410011414120</a>","bibtex":"@article{Naujoks_Trautmann_Wessing_Weihs_2011, title={Advanced concepts for multi-objective evolutionary optimization in aircraft industry}, volume={225}, DOI={<a href=\"https://doi.org/10.1177/0954410011414120\">10.1177/0954410011414120</a>}, number={10}, journal={Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering}, author={Naujoks, B and Trautmann, Heike and Wessing, S and Weihs, C}, year={2011}, pages={1081–1096} }"},"abstract":[{"lang":"eng","text":" Evolutionary (multi-objective optimization) algorithms (EMOAs) are widely accepted to be competitive optimization methods in industry today. However, normally only standard techniques are employed by the engineering experts. Here, it is shown how these standard techniques can be completed and improved with respect to interactivity to other tools, runtime, and parameterization. The coupling with metamodels serves as an example for the interactivity to other tools, while the online convergence detection relates to runtime, i.e. stopping criteria. Finally, sequential parameter optimization improves results focussing on parameter tuning. We show that invoking all these methods on their own already enhances EMOAs for aerodynamic applications. It is concluded with an outlook on how these methods might come together to foster aerospace applications and, at a time, widen the application area to multi-disciplinary optimization tasks. "}],"date_created":"2023-08-04T16:00:28Z","type":"journal_article","department":[{"_id":"34"},{"_id":"819"}]}]