[{"title":"Inverse multiobjective optimization: Inferring decision criteria from data","department":[{"_id":"101"}],"user_id":"47427","type":"preprint","date_created":"2020-03-13T12:45:05Z","_id":"16295","year":"2019","status":"public","abstract":[{"text":"It is a very challenging task to identify the objectives on which a certain\r\ndecision was based, in particular if several, potentially conflicting criteria\r\nare equally important and a continuous set of optimal compromise decisions\r\nexists. This task can be understood as the inverse problem of multiobjective\r\noptimization, where the goal is to find the objective vector of a given Pareto\r\nset. To this end, we present a method to construct the objective vector of a\r\nmultiobjective optimization problem (MOP) such that the Pareto critical set\r\ncontains a given set of data points or decision vectors. The key idea is to\r\nconsider the objective vector in the multiobjective KKT conditions as variable\r\nand then search for the objectives that minimize the Euclidean norm of the\r\nresulting system of equations. By expressing the objectives in a\r\nfinite-dimensional basis, we transform this problem into a homogeneous, linear\r\nsystem of equations that can be solved efficiently. There are many important\r\npotential applications of this approach. Besides the identification of\r\nobjectives (both from clean and noisy data), the method can be used for the\r\nconstruction of surrogate models for expensive MOPs, which yields significant\r\nspeed-ups. Both applications are illustrated using several examples.","lang":"eng"}],"main_file_link":[{"url":"https://arxiv.org/pdf/1901.06141.pdf","open_access":"1"}],"language":[{"iso":"eng"}],"citation":{"mla":"Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization: Inferring Decision Criteria from Data.” *ArXiv:1901.06141*, 2019.","ieee":"B. Gebken and S. Peitz, “Inverse multiobjective optimization: Inferring decision criteria from data,” *arXiv:1901.06141*. 2019.","chicago":"Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization: Inferring Decision Criteria from Data.” *ArXiv:1901.06141*, 2019.","short":"B. Gebken, S. Peitz, ArXiv:1901.06141 (2019).","ama":"Gebken B, Peitz S. Inverse multiobjective optimization: Inferring decision criteria from data. *arXiv:190106141*. 2019.","bibtex":"@article{Gebken_Peitz_2019, title={Inverse multiobjective optimization: Inferring decision criteria from data}, journal={arXiv:1901.06141}, author={Gebken, Bennet and Peitz, Sebastian}, year={2019} }","apa":"Gebken, B., & Peitz, S. (2019). Inverse multiobjective optimization: Inferring decision criteria from data. *ArXiv:1901.06141*."},"date_updated":"2020-05-07T05:20:51Z","author":[{"first_name":"Bennet","last_name":"Gebken","full_name":"Gebken, Bennet","id":"32643"},{"orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","first_name":"Sebastian"}],"publication":"arXiv:1901.06141","oa":1}]