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Analytics-based decomposition of a class of bilevel problems
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Prestwich, Steven D.
Springer Nature Switzerland AG
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.
Bilevel , Analytics , Clustering , Decomposition
Fajemisin A., Climent L. and Prestwich S. D. (2019) ) ‘Analytics-based decomposition of a class of bilevel problems’, in Le Thi, H., Le, H. and Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. World Congress on Global Optimization 2019. Advances in Intelligent Systems and Computing, 991, pp. 617-626. doi: 10.1007/978-3-030-21803-4_62
© 2019, Springer Nature Switzerland AG. This is a post-peer-review, pre-copyedit version of a paper published 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, 991. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-21803-4_62