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.