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Bilevel Discrete Optimisation: Computational Complexity and Applications

In: The Palgrave Handbook of Operations Research

Author

Listed:
  • Yury Kochetov

    (Sobolev Institute of Mathematics)

  • Alexander Plyasunov

    (Sobolev Institute of Mathematics)

  • Arteam Panin

    (Sobolev Institute of Mathematics)

Abstract

Bilevel optimisation is an important class of hierarchical optimisation problems with two decision-makers: the leader and the follower. The leader cannot control the follower’s decisions but can change his constraints and the objective function. The goal or profit of the leader depends on the optimal decision of the follower. Over the last 30 years, the bilevel problems have received significant attention from the mathematical programming and operational research communities. This chapter provides an overview of bilevel discrete optimisation including basic definitions, properties, relationships to other classes of optimisation problems and applications, computational and approximation complexity. We aim to encourage researchers to pay more attention to this interesting area both from the theoretical point of view and applications.

Suggested Citation

  • Yury Kochetov & Alexander Plyasunov & Arteam Panin, 2022. "Bilevel Discrete Optimisation: Computational Complexity and Applications," Springer Books, in: Saïd Salhi & John Boylan (ed.), The Palgrave Handbook of Operations Research, chapter 0, pages 3-42, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-96935-6_1
    DOI: 10.1007/978-3-030-96935-6_1
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