Predicting Tactical Solutions to Operational Planning Problems Under Imperfect Information

Eric Larsen (), Sébastien Lachapelle (), Yoshua Bengio (), Emma Frejinger (), Simon Lacoste-Julien () and Andrea Lodi ()
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Eric Larsen: Department of Computer Science and Operations Research, Université de Montréal, Montréal, Québec H3T 1J4, Canada; CIRRELT, Université de Montréal, Montréal, Québec H3C 3J7, Canada
Sébastien Lachapelle: Department of Computer Science and Operations Research, Université de Montréal, Montréal, Québec H3T 1J4, Canada; Mila, Université de Montréal, Montréal, Québec H2S 3H1, Canada
Yoshua Bengio: Department of Computer Science and Operations Research, Université de Montréal, Montréal, Québec H3T 1J4, Canada; Mila, Université de Montréal, Montréal, Québec H2S 3H1, Canada
Emma Frejinger: Department of Computer Science and Operations Research, Université de Montréal, Montréal, Québec H3T 1J4, Canada; CIRRELT, Université de Montréal, Montréal, Québec H3C 3J7, Canada
Simon Lacoste-Julien: Department of Computer Science and Operations Research, Université de Montréal, Montréal, Québec H3T 1J4, Canada; Mila, Université de Montréal, Montréal, Québec H2S 3H1, Canada
Andrea Lodi: CERC, Polytechnique Montréal, Montréal, Québec H3T 1J4, Canada

INFORMS Journal on Computing, 2022, vol. 34, issue 1, 227-242

Abstract: This paper offers a methodological contribution at the intersection of machine learning and operations research. Namely, we propose a methodology to quickly predict expected tactical descriptions of operational solutions (TDOSs). The problem we address occurs in the context of two-stage stochastic programming, where the second stage is demanding computationally. We aim to predict at a high speed the expected TDOS associated with the second-stage problem, conditionally on the first-stage variables. This may be used in support of the solution to the overall two-stage problem by avoiding the online generation of multiple second-stage scenarios and solutions. We formulate the tactical prediction problem as a stochastic optimal prediction program, whose solution we approximate with supervised machine learning. The training data set consists of a large number of deterministic operational problems generated by controlled probabilistic sampling. The labels are computed based on solutions to these problems (solved independently and offline), employing appropriate aggregation and subselection methods to address uncertainty. Results on our motivating application on load planning for rail transportation show that deep learning models produce accurate predictions in very short computing time (milliseconds or less). The predictive accuracy is close to the lower bounds calculated based on sample average approximation of the stochastic prediction programs.

Keywords: supervised learning; deep learning; integer linear programming; stochastic programming (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:34:y:2022:i:1:p:227-242

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