---
_id: '16295'
abstract:
- lang: eng
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."
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
citation:
ama: 'Gebken B, Peitz S. Inverse multiobjective optimization: Inferring decision
criteria from data. *arXiv:190106141*. 2019.'
apa: 'Gebken, B., & Peitz, S. (2019). Inverse multiobjective optimization: Inferring
decision criteria from data. *ArXiv:1901.06141*.'
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} }'
chicago: '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.'
mla: '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).
date_created: 2020-03-13T12:45:05Z
date_updated: 2020-05-07T05:20:51Z
department:
- _id: '101'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/1901.06141.pdf
oa: 1
publication: arXiv:1901.06141
status: public
title: 'Inverse multiobjective optimization: Inferring decision criteria from data'
type: preprint
user_id: '47427'
year: '2019'
...