Alternating mixed-integer programming and neural network training for approximating stochastic two-stage problems

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 GB

URI: https://arxiv.org/pdf/2305.06785.pdf

DOI: 10.1007/978-3-031-53966-4_10

Abstract

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.

Authors with CRIS profile

Jan Rolfes Economics - Discrete Optimization - Mathematics (EDOM)

Involved external institutions

ABB Corporate Research Center in Germany - ABB Group DE Germany (DE) Royal Institute of Technology / Kungliga Tekniska Högskolan (KTH) SE Sweden (SE)

How to cite

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.

BibTeX: Download