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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 iswell known that minimizing OWA for most basic combinatorial problems is weaklyNP-hard even if the number of objectives $K$ equals two, and strongly NP-hardwhen $K$ is a part of the input. In this paper, the problem with nonincreasingweights in the OWA criterion and a large $K$ is considered. A method ofreducing the number of objectives by appropriately aggregating the objectivecosts before solving the problem is proposed. It is shown that an optimalsolution to the reduced problem has a guaranteed worst-case approximationratio. Some new approximation results for the Hurwicz criterion, which is aspecial case of OWA, are also presented.

Approximating multiobjective combinatorial optimization problems with the OWA criterion