Hybrid Models for the OWA Optimization

Abstract

When dealing with multicriteria problems, the aggregation of multiple outcomes plays an essential role in finding a solution, as it reflects the decision-maker's preference relation. The Ordered Weighted Averaging (OWA) operator provides a exible preference model that generalizes many objective functions. It also ensures the impartiality and allow to obtain equitable solutions, which is vital when the criteria represent evaluations of independent individuals. These features make the OWA operator very useful in many fields, one of which is location analysis. However, in general the OWA aggregation makes the problem nonlinear and hinder its computational complexity. Therefore, problems with the OWA operator need to be devised in an efficient way. The paper introduces new general formulations for OWA optimization and proposes for them some simple valid inequalities to improve efficiency. A hybrid structure of proposed models makes the number of binary variables problem type dependent and may reduce it signicantly. Computational results show that for certain problem types, some of which are very useful in practical applications, the hybrid models perform much better than previous general models from literature.