Approximating multiobjective combinatorial optimization problems with the OWA criterion
Abstract
The paper deals with a multiobjective combinatorial optimization problem with linear cost functions. The popular Ordered Weighted Averaging (OWA) criterion is used to aggregate the cost functions and compute a solution. It is well known that minimizing OWA for most basic combinatorial problems is weakly NP-hard even if the number of objectives equals two, and strongly NP-hard when is a part of the input. In this paper, the problem with nonincreasing weights in the OWA criterion and a large is considered. A method of reducing the number of objectives by appropriately aggregating the objective costs before solving the problem is proposed. It is shown that an optimal solution to the reduced problem has a guaranteed worst-case approximation ratio. Some new approximation results for the Hurwicz criterion, which is a special case of OWA, are also presented.
Cite
@article{arxiv.1804.03594,
title = {Approximating multiobjective combinatorial optimization problems with the OWA criterion},
author = {André Chassein and Marc Goerigk and Adam Kasperski and Paweł Zieliński},
journal= {arXiv preprint arXiv:1804.03594},
year = {2018}
}