Bottleneck combinatorial optimization problems with uncertain costs and the OWA criterion

TL;DR

This paper studies bottleneck combinatorial optimization problems under uncertain costs, using the OWA operator to aggregate scenarios, and provides new complexity and approximation results applicable to various network problems.

Contribution

It introduces new complexity and approximation results for bottleneck problems with uncertainty modeled by scenarios, generalizing traditional decision criteria.

Findings

New complexity results for uncertain bottleneck problems.

Approximation algorithms applicable to network problems.

General results valid for various decision criteria.

Abstract

In this paper a class of bottleneck combinatorial optimization problems with uncertain costs is discussed. The uncertainty is modeled by specifying a discrete scenario set containing a finite number of cost vectors, called scenarios. In order to choose a solution the Ordered Weighted Averaging aggregation operator (shortly OWA) is applied. The OWA operator generalizes traditional criteria in decision making under uncertainty such as the maximum, minimum, average, median, or Hurwicz criterion. New complexity and approximation results in this area are provided. These results are general and remain valid for many problems, in particular for a wide class of network problems.