Reference point method with importance weighted ordered partial achievements |
| |
Authors: | Włodzimierz Ogryczak Bartosz Kozłowski |
| |
Institution: | (1) Institute of Control and Computation Engineering, Warsaw University of Technology, 00-665 Warsaw, Poland |
| |
Abstract: | The Reference Point Method (RPM) is a very convenient technique for interactive analysis of the multiple criteria optimization
problems. The interactive analysis is navigated with the commonly accepted control parameters expressing reference levels
for the individual objective functions. The partial achievement functions quantify the DM satisfaction from the individual
outcomes with respect to the given reference levels, while the final scalarizing achievement function is built as the augmented
max–min aggregation of the partial achievements. In order to avoid inconsistencies caused by the regularization, the max–min
solution may be regularized by the Ordered Weighted Averages (OWA) with monotonic weights which combines all the partial achievements
allocating the largest weight to the worst achievement, the second largest weight to the second worst achievement, and so
on. Further, following the concept of the Weighted OWA (WOWA), the importance weighting of several achievements may be incorporated
into the RPM. Such a WOWA RPM approach uses importance weights to affect achievement importance by rescaling accordingly its
measure within the distribution of achievements rather than by straightforward rescaling of achievement values. The recent
progress in optimization methods for ordered averages allows one to implement the WOWA RPM quite effectively as extension
of the original constraints and criteria with simple linear inequalities. There is shown that the OWA and WOWA RPM models
meet the crucial requirements with respect to the efficiency of generated solutions as well as the controllability of interactive
analysis by the reference levels. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|