Ordered weighted enhancement of preference modeling in the reference point method for multiple criteria optimization

The Reference Point Method (RPM) is an interactive technique for multiple criteria optimization problems. It is based on optimization of the scalarizing achievement function built as the augmented maxmin aggregation of individual outcomes with respect to the given reference levels. Actually, the worst individual achievement is optimized, but regularized with the term representing the average achievement. In order to avoid inconsistencies caused by the regularization, we apply the Ordered Weighted Averages (OWA) with monotonic weights to combine all the individual achievements. Further, following the concept of the Weighted OWA (WOWA), we incorporate the importance weighting of several achievements into the RPM. We show that the resulting WOWA RPM can be quite effectively implemented as an extension of the original constraints and criteria with simple linear inequalities.