Article ID: | iaor20171567 |
Volume: | 24 |
Issue: | 5 |
Start Page Number: | 959 |
End Page Number: | 981 |
Publication Date: | Sep 2017 |
Journal: | International Transactions in Operational Research |
Authors: | Alekseeva Ekaterina, Talbi El-Ghazali, Kochetov Yury |
Keywords: | heuristics, programming: multiple criteria |
In this paper, we solve a discrete bilevel problem with multiple objectives at the lower level and constraints at the upper level coupling variables of both levels. In the case of a multiobjective lower level, we deal with a set of Pareto‐efficient solutions rather than a single optimal lower level solution. To calculate the upper level objective function value, we need to select one solution out of a potentially large set of efficient lower level solutions. To avoid the enumeration of the whole set of Pareto solutions, we formulate an auxiliary mixed integer linear programming problem with a large number of constraints. We propose an iterative exact method to solve it. To find a near‐optimal upper level solution, we apply a metaheuristic. The method is tested on the discrete (r|p)‐centroid problem with multiple objectives at the lower level.