A memetic algorithm for solving bilevel optimization problems with multiple followers

Islam, Monjurul; Singh, Hemant Kumar; Ray, Tapabrata

doi:10.1109/cec.2016.7744020

Cited by 5 publications

(2 citation statements)

References 23 publications

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“…Liu (1998) presents a genetic algorithm for solving nonlinear multilevel problems with multiple followers. Also, (Islam et al 2016) extend their bilevel memetic algorithm to solve problems with multiple followers using a combination of global and local search. The authors in Ke et al (2016) combine fuzzy programming with an evolutionary algorithm, as well as neural networks to solve a multi-follower problem with non-cooperative followers.…”

Section: Decomposition Approaches In the Literaturementioning

confidence: 99%

“…Most classical methods for handling bilevel problems require assumptions of smoothness, linearity or convexity, while we make no such assumptions. Evolutionary and meta-heuristic techniques also do not make these assumptions (Angelo and Barbosa 2015;Islam et al 2016;Liu 1998) but most are computationally intensive nested strategies. They are efficient for smaller problems but do not scale up well to large-scale problems.…”

Section: Motivation For the Analytics-based Heuristic Decomposition Approachmentioning

confidence: 99%

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An analytics-based heuristic decomposition of a bilevel multiple-follower cutting stock problem

2021

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This paper presents a new class of multiple-follower bilevel problems and a heuristic approach to solving them. In this new class of problems, 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. We show that current approaches for solving multiple-follower problems are unsuitable for our new class of problems and instead we propose a novel analytics-based heuristic decomposition approach. This approach uses Monte Carlo simulation and k-medoids clustering to reduce the bilevel problem to a single level, which can then be solved using integer programming techniques. The examples presented show that our approach produces better solutions and scales up better than the other approaches in the literature. Furthermore, for large problems, we combine our approach with the use of self-organising maps in place of k-medoids clustering, which significantly reduces the clustering times. Finally, we apply our approach to a real-life cutting stock problem. Here a forest harvesting problem is reformulated as a multiple-follower bilevel problem and solved using our approach.

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Section: Decomposition Approaches In the Literaturementioning

confidence: 99%

Section: Motivation For the Analytics-based Heuristic Decomposition Approachmentioning

confidence: 99%