Robust optimization with belief functions

In this paper, an optimization problem with uncertain objective function coefficients is considered. The uncertainty is specified by providing a discrete scenario set containing possible realizations of the objective function coefficients. The concept of belief function in the traditional and possibilistic setting is applied to define a set of admissible probability distributions over the scenario set. The generalized Hurwicz criterion is then used to compute a solution. In this paper, the complexity of the resulting problem is explored. Some exact and approximation methods of solving it are proposed. & COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

Automated summary

This paper investigates an optimization problem with uncertain objective function coefficients. The uncertainty is described by a discrete scenario set. The concept of belief function is used to define admissible probability distributions over the scenario set. The generalized Hurwicz criterion is applied to compute a solution. The complexity of the problem is explored and exact and approximation methods are proposed.