preprint
Inverse multiobjective optimization: Inferring decision criteria from data
Bennet
Gebken
author 32643
Sebastian
Peitz
author 47427https://orcid.org/0000-0002-3389-793X
101
department
It is a very challenging task to identify the objectives on which a certain
decision was based, in particular if several, potentially conflicting criteria
are equally important and a continuous set of optimal compromise decisions
exists. This task can be understood as the inverse problem of multiobjective
optimization, where the goal is to find the objective vector of a given Pareto
set. To this end, we present a method to construct the objective vector of a
multiobjective optimization problem (MOP) such that the Pareto critical set
contains a given set of data points or decision vectors. The key idea is to
consider the objective vector in the multiobjective KKT conditions as variable
and then search for the objectives that minimize the Euclidean norm of the
resulting system of equations. By expressing the objectives in a
finite-dimensional basis, we transform this problem into a homogeneous, linear
system of equations that can be solved efficiently. There are many important
potential applications of this approach. Besides the identification of
objectives (both from clean and noisy data), the method can be used for the
construction of surrogate models for expensive MOPs, which yields significant
speed-ups. Both applications are illustrated using several examples.
2019
eng
arXiv:1901.06141
Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization: Inferring Decision Criteria from Data.” <i>ArXiv:1901.06141</i>, 2019.
Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization: Inferring Decision Criteria from Data.” <i>ArXiv:1901.06141</i>, 2019.
B. Gebken and S. Peitz, “Inverse multiobjective optimization: Inferring decision criteria from data,” <i>arXiv:1901.06141</i>. 2019.
@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} }
Gebken B, Peitz S. Inverse multiobjective optimization: Inferring decision criteria from data. <i>arXiv:190106141</i>. 2019.
B. Gebken, S. Peitz, ArXiv:1901.06141 (2019).
Gebken, B., & Peitz, S. (2019). Inverse multiobjective optimization: Inferring decision criteria from data. <i>ArXiv:1901.06141</i>.
162952020-03-13T12:45:05Z2020-05-07T05:20:51Z