A comparative study of linearization methods for Ordered Weighted Average

We consider a fair version of combinatorial optimization, which aims for both Pareto-efficiency and fairness of a solution. A possible approach to achieve the objectives simultaneously is to use the Ordered Weighted Average (OWA) aggregating function, which can be formulated into mix-integer programming (MIP) formulations. In this paper, we study two MIP formulations proposed in the literature for the OWA in the context of fair combinatorial optimization. On the one hand, we prove that both MIP formulations are equivalent in terms of linear relaxations. On the other hand, we estimate the quality with regard to the OWA value of an optimal solution of original combinatorial optimization. An experimental evaluation of the MIP formulations in tackling OWA Traveling Salesman Problem is also presented.