  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.
