Bilevel optimization is a sub-field of optimization widely valued both in academia and business due to its suitability to identify the best solutions for hierarchical decision-making processes. The predominant approach to solving bilevel problems involves reformulating them as single-level equivalents that can be solved with commercial solvers. However, traditional reformulation techniques are often constrained by the complexity of the lower-level problem, particularly when the number of variables or constraints is large, or uncertain parameters are present.
Given the intrinsic presence of uncertainty in most real-world applications of bilevel optimization, this work proposes a metamodeling approach that approximates the lower level using a neural network. Although this strategy has been satisfactorily applied to deterministic bilevel models, we extend its use to stochastic bilevel problems by training a neural network that learns over a set of realizations of the uncertain parameters. Our methodology is tested on the short-term scheduling of a batch chemical process, a context where classical reformulation approaches become unmanageable due to the presence of differential equations. The results indicate that our approach successfully achieves a single-level reformulation that is computationally tractable and can be solved efficiently even in complex bilevel settings, provided that the lower-level remains manageable and the main complexity arises from its integration into the upper level.
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