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Analytics-Based Decomposition of a Class of Bilevel Problems

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Optimization of Complex Systems: Theory, Models, Algorithms and Applications (WCGO 2019)

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

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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.

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Notes

  1. 1.

    These are a way of expressing if-else relationships among variables [8].

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Acknowledgement

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

Author information

Authors and Affiliations

  1. School of Computing, National College of Ireland, Dublin, Ireland

    Adejuyigbe Fajemisin

  2. Computer Science Department, Cork Institute of Technology, Cork, Ireland

    Laura Climent

  3. Insight Centre for Data Analytics, University College Cork, Cork, Ireland

    Steven D. Prestwich

Authors
  1. Adejuyigbe Fajemisin
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  2. Laura Climent
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  3. Steven D. Prestwich
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Corresponding author

Correspondence to Steven D. Prestwich .

Editor information

Editors and Affiliations

  1. Computer science and Applications Department, LGIPM, University of Lorraine, Metz Cedex 03, France

    Hoai An Le Thi

  2. Computer Science and Applications Department, LGIPM, University of Lorraine, Metz Cedex 03, France

    Hoai Minh Le

  3. Laboratory of Mathematics, National Institute for Applied Sciences (INSA)-Rouen Normadie, Saint-Étienne-du-Rouvray Cedex, France

    Tao Pham Dinh

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Fajemisin, A., Climent, L., Prestwich, S.D. (2020). Analytics-Based Decomposition of a Class of Bilevel Problems. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_62

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