A matheuristic for the discrete bilevel problem with multiple objectives at the lower level

A matheuristic for the discrete bilevel problem with multiple objectives at the lower level

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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: , ,
Keywords: heuristics, programming: multiple criteria
Abstract:

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.

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