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

El-Ghazali Talbi 1 Ekaterina Alekseeva 2 Yuri Kochetov 3
1 DOLPHIN - Parallel Cooperative Multi-criteria Optimization
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
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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https://hal.inria.fr/hal-01654723
Contributor : Talbi El-Ghazali <>
Submitted on : Monday, December 4, 2017 - 12:30:51 PM
Last modification on : Thursday, May 28, 2020 - 9:22:09 AM

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El-Ghazali Talbi, Ekaterina Alekseeva, Yuri Kochetov. A matheuristic for the discrete bi-level problem with multiple objectives at the lower level. International Transactions in Operational Research, Wiley, 2017, 24 (5), pp.959-981. ⟨10.1111/itor.12268⟩. ⟨hal-01654723⟩

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