Learning to Optimize at Scale: A Benders Decomposition-TransfORmers Framework for Stochastic Combinatorial Optimization

Abstract:We propose a learning-augmented Benders decomposition framework to solve large-scale two-stage stochastic mixed-integer programs. We focus on the two-stage stochastic capacitated lot-sizing problem (TSSCLSP) under demand uncertainty. Our method accelerates the convergence of the decomposition by using a pre-trained TransfORmer model to rapidly generate high-quality approximate solutions for the scenario subproblems. This hybrid strategy uses the TransfORmer predictions to generate strong optimality and feasibility cuts, effectively guiding the Benders master problem. Our framework includes a novel expandable generation mechanism, allowing a model trained on a fixed horizon to solve instances of arbitrary length. For the test set considered, our method solves instances up to T = 270, a scale previously intractable for this approach, while maintaining zero infeasibility in the generated subproblem solutions. This demonstrates the potential of TransfORmers as powerful surrogate solvers embedded within classical decomposition algorithms.

Optimization and Control (math.OC); Machine Learning (cs.LG)

arXiv:2607.22550 [math.OC]

(or arXiv:2607.22550v1 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2607.22550 Focus to learn more arXiv-issued DOI via DataCite

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