Combinatorial optimization problems with uncertain costs and the OWA criterion

TL;DR

This paper explores a class of combinatorial optimization problems with uncertain costs, utilizing the OWA criterion to generalize traditional approaches and analyze their computational complexity and approximability.

Contribution

It introduces the use of the OWA aggregation operator in combinatorial optimization with uncertain costs, extending traditional criteria and providing new complexity and approximation results.

Findings

OWA generalizes max, min, average, Hurwicz, median criteria

Complexity results for minimizing OWA are established

Applicable to network and resource allocation problems

Abstract

In this paper a class of combinatorial optimization problems with uncertain costs is discussed. The uncertainty is modeled by specifying a discrete scenario set containing $K$ distinct cost scenarios. The Ordered Weighted Averaging (OWA for short) aggregation operator is applied to choose a solution. The well-known criteria such as: the maximum, minimum, average, Hurwicz and median are special cases of OWA. By using OWA, the traditional min-max approach to combinatorial optimization problems with uncertain costs, often regarded as too conservative, can be generalized. The computational complexity and approximability of the problem of minimizing OWA for the considered class of problems are investigated and some new positive and negative results in this area are provided. These results remain valid for many important problems, such as network or resource allocation problems.