Approximating multiobjective combinatorial optimization problems with the OWA criterion

TL;DR

This paper proposes a method to approximate multiobjective combinatorial optimization problems using the OWA criterion by aggregating objectives, providing approximation guarantees and new results for the Hurwicz criterion.

Contribution

It introduces a novel objective aggregation technique for large K in OWA problems with approximation guarantees and extends results to the Hurwicz criterion.

Findings

Aggregation reduces problem complexity

Guaranteed worst-case approximation ratio

New approximation results for Hurwicz criterion

Abstract

The paper deals with a multiobjective combinatorial optimization problem with $K$ 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 $K$ equals two, and strongly NP-hard when $K$ is a part of the input. In this paper, the problem with nonincreasing weights in the OWA criterion and a large $K$ 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.