{"_id":"46371","title":"Optimal averaged Hausdorff archives for bi-objective problems: theoretical and numerical results","citation":{"bibtex":"@article{Rudolph_Schütze_Grimme_Domínguez-Medina_Trautmann_2016, title={Optimal averaged Hausdorff archives for bi-objective problems: theoretical and numerical results}, volume={64}, DOI={<a href=\"https://doi.org/10.1007/s10589-015-9815-8\">10.1007/s10589-015-9815-8</a>}, number={2}, journal={Computational Optimization and Applications (Comput. Optim. Appl.)}, author={Rudolph, G and Schütze, O and Grimme, C and Domínguez-Medina, C and Trautmann, Heike}, year={2016}, pages={589–618} }","mla":"Rudolph, G., et al. “Optimal Averaged Hausdorff Archives for Bi-Objective Problems: Theoretical and Numerical Results.” <i>Computational Optimization and Applications (Comput. Optim. Appl.)</i>, vol. 64, no. 2, 2016, pp. 589–618, doi:<a href=\"https://doi.org/10.1007/s10589-015-9815-8\">10.1007/s10589-015-9815-8</a>.","ieee":"G. Rudolph, O. Schütze, C. Grimme, C. Domínguez-Medina, and H. Trautmann, “Optimal averaged Hausdorff archives for bi-objective problems: theoretical and numerical results,” <i>Computational Optimization and Applications (Comput. Optim. Appl.)</i>, vol. 64, no. 2, pp. 589–618, 2016, doi: <a href=\"https://doi.org/10.1007/s10589-015-9815-8\">10.1007/s10589-015-9815-8</a>.","apa":"Rudolph, G., Schütze, O., Grimme, C., Domínguez-Medina, C., &#38; Trautmann, H. (2016). Optimal averaged Hausdorff archives for bi-objective problems: theoretical and numerical results. <i>Computational Optimization and Applications (Comput. Optim. Appl.)</i>, <i>64</i>(2), 589–618. <a href=\"https://doi.org/10.1007/s10589-015-9815-8\">https://doi.org/10.1007/s10589-015-9815-8</a>","chicago":"Rudolph, G, O Schütze, C Grimme, C Domínguez-Medina, and Heike Trautmann. “Optimal Averaged Hausdorff Archives for Bi-Objective Problems: Theoretical and Numerical Results.” <i>Computational Optimization and Applications (Comput. Optim. Appl.)</i> 64, no. 2 (2016): 589–618. <a href=\"https://doi.org/10.1007/s10589-015-9815-8\">https://doi.org/10.1007/s10589-015-9815-8</a>.","short":"G. Rudolph, O. Schütze, C. Grimme, C. Domínguez-Medina, H. Trautmann, Computational Optimization and Applications (Comput. Optim. Appl.) 64 (2016) 589–618.","ama":"Rudolph G, Schütze O, Grimme C, Domínguez-Medina C, Trautmann H. Optimal averaged Hausdorff archives for bi-objective problems: theoretical and numerical results. <i>Computational Optimization and Applications (Comput Optim Appl)</i>. 2016;64(2):589–618. doi:<a href=\"https://doi.org/10.1007/s10589-015-9815-8\">10.1007/s10589-015-9815-8</a>"},"page":"589–618","year":"2016","issue":"2","publication":"Computational Optimization and Applications (Comput. Optim. Appl.)","user_id":"15504","department":[{"_id":"34"},{"_id":"819"}],"author":[{"first_name":"G","full_name":"Rudolph, G","last_name":"Rudolph"},{"full_name":"Schütze, O","last_name":"Schütze","first_name":"O"},{"full_name":"Grimme, C","last_name":"Grimme","first_name":"C"},{"first_name":"C","last_name":"Domínguez-Medina","full_name":"Domínguez-Medina, C"},{"id":"100740","first_name":"Heike","last_name":"Trautmann","orcid":"0000-0002-9788-8282","full_name":"Trautmann, Heike"}],"status":"public","language":[{"iso":"eng"}],"abstract":[{"text":"One main task in evolutionary multiobjective optimization (EMO) is to obtain a suitable finite size approximation of the Pareto front which is the image of the solution set, termed the Pareto set, of a given multiobjective optimization problem. In the technical literature, the characteristic of the desired approximation is commonly expressed by closeness to the Pareto front and a sufficient spread of the solutions obtained. In this paper, we first make an effort to show by theoretical and empirical findings that the recently proposed Averaged Hausdorff (or Δ𝑝-) indicator indeed aims at fulfilling both performance criteria for bi-objective optimization problems. In the second part of this paper, standard EMO algorithms combined with a specialized archiver and a postprocessing step based on the Δ𝑝 indicator are introduced which sufficiently approximate the Δ𝑝-optimal archives and generate solutions evenly spread along the Pareto front.","lang":"eng"}],"doi":"10.1007/s10589-015-9815-8","intvolume":"        64","date_updated":"2023-10-16T13:40:21Z","date_created":"2023-08-04T15:17:48Z","volume":64,"type":"journal_article"}