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Analytics-Based Decomposition of a Class of Bilevel Problems

Conference paper
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Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)

Abstract

This paper proposes a new class of multi-follower bilevel problems. In this class the followers may be nonlinear, do not share constraints or variables, and are at most weakly constrained. This allows the leader variables to be partitioned among the followers. The new class is formalised and compared with existing problems in the literature. We show that approaches currently in use for solving multi-follower problems are unsuitable for this class. Evolutionary algorithms can be used, but these are computationally intensive and do not scale up well. Instead we propose an analytics-based decomposition approach. Two example problems are solved using our approach and two evolutionary algorithms, and the decomposition approach produces much better and faster results as the problem size increases.

Keywords

Bilevel Analytics Clustering Decomposition 

Notes

Acknowledgement

This publication has emanated from research conducted with the financial support of Science Foundation Ireland (SFI) under Grant Number SFI/12/RC/2289.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of ComputingNational College of IrelandDublinIreland
  2. 2.Computer Science DepartmentCork Institute of TechnologyCorkIreland
  3. 3.Insight Centre for Data AnalyticsUniversity College CorkCorkIreland

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