Kronqvist J, Li B, Rolfes J, Zhao S (2024)
Publication Language: English
Publication Status: Accepted
Publication Type: Book chapter / Article in edited volumes
Future Publication Type: Conference contribution
Publication year: 2024
Publisher: Springer
Edited Volumes: Machine Learning, Optimization, and Data Science
Series: Lecture Notes in Computer Science
Book Volume: 14506
Event location: Grasmere, Lake District, England - UK
URI: https://arxiv.org/pdf/2305.06785.pdf
DOI: 10.1007/978-3-031-53966-4_10
The presented work addresses two-stage stochastic programs
(2SPs), a broadly applicable model to capture optimization problems
subject to uncertain parameters with adjustable decision variables. In
case the adjustable or second-stage variables contain discrete decisions,
the corresponding 2SPs are known to be NP-complete. The standard
approach of forming a single-stage deterministic equivalent problem can
be computationally challenging even for small instances, as the number
of variables and constraints scales with the number of scenarios. To avoid
forming a potentially huge MILP problem, we build upon an approach
of approximating the expected value of the second-stage problem by a
neural network (NN) and encoding the resulting NN into the first-stage
problem. The proposed algorithm alternates between optimizing the
first-stage variables and retraining the NN. We demonstrate the value of
our approach with the example of computing operating points in power
systems by showing that the alternating approach provides improved
first-stage decisions and a tighter approximation between the expected
objective and its neural network approximation.
APA:
Kronqvist, J., Li, B., Rolfes, J., & Zhao, S. (2024). Alternating mixed-integer programming and neural network training for approximating stochastic two-stage problems. In Machine Learning, Optimization, and Data Science. Springer.
MLA:
Kronqvist, Jan, et al. "Alternating mixed-integer programming and neural network training for approximating stochastic two-stage problems." Machine Learning, Optimization, and Data Science. Springer, 2024.
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