# Fast Continuous and Integer L-shaped Heuristics Through Supervised Learning

arXiv: https://arxiv.org/abs/2205.00897 · HTML: https://mlsanity.com/paper/2205.00897/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 2 May 2022.

## Builds on (most cited first, 16 of 16)

- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [Reinforcement Learning for Combinatorial Optimization: A Survey](https://mlsanity.com/paper/2003.03600/) (2020)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Combinatorial Optimization with Physics-Inspired Graph Neural Networks](https://mlsanity.com/paper/2107.01188/) (2021)
- [Learning Combinatorial Optimization on Graphs: A Survey with Applications to Networking](https://mlsanity.com/paper/2005.11081/) (2020)
- [Combining Reinforcement Learning and Constraint Programming for Combinatorial Optimization](https://mlsanity.com/paper/2006.01610/) (2020)
- [Simulation optimization: A review of algorithms and applications](https://mlsanity.com/paper/1706.08591/) (2017)
- [Learning Hard Optimization Problems: A Data Generation Perspective](https://mlsanity.com/paper/2106.02601/) (2021)
- [A learning-based algorithm to quickly compute good primal solutions for Stochastic Integer Programs](https://mlsanity.com/paper/1912.08112/) (2019)
- [Predicting Tactical Solutions to Operational Planning Problems under Imperfect Information](https://mlsanity.com/paper/1807.11876/) (2018)
- [Neural Stochastic Dual Dynamic Programming](https://mlsanity.com/paper/2112.00874/) (2021)
- [Bilevel Optimization based on Iterative Approximation of Multiple Mappings](https://mlsanity.com/paper/1702.03394/) (2017)
- [A language processing algorithm for predicting tactical solutions to an operational planning problem under uncertainty](https://mlsanity.com/paper/1910.08216/) (2019)
- [SimPO: Simultaneous Prediction and Optimization](https://mlsanity.com/paper/2204.00062/) (2022)

## Built on by (most cited first, 6 of 6)

- [Neur2SP: Neural Two-Stage Stochastic Programming](https://mlsanity.com/paper/2205.12006/) (2022)
- [Taking the human out of decomposition-based optimization via artificial intelligence: Part II. Learning to initialize](https://mlsanity.com/paper/2310.07082/) (2023)
- [ICNN-enhanced 2SP: Leveraging input convex neural networks for solving two-stage stochastic programming](https://mlsanity.com/paper/2505.05261/) (2025)
- [Deep Learning for Two-Stage Robust Integer Optimization](https://mlsanity.com/paper/2310.04345/) (2023)
- [Graph-Based Imitation and Reinforcement Learning for Efficient Benders Decomposition](https://mlsanity.com/paper/2511.11870/) (2025)
- [HGCN2SP: Hierarchical Graph Convolutional Network for Two-Stage Stochastic Programming](https://mlsanity.com/paper/2511.16027/) (2025)

## Abstract (arXiv)

We propose a methodology at the nexus of operations research and machine learning (ML) leveraging generic approximators available from ML to accelerate the solution of mixed-integer linear two-stage stochastic programs. We aim at solving problems where the second stage is highly demanding. Our core idea is to gain large reductions in online solution time while incurring small reductions in first-stage solution accuracy by substituting the exact second-stage solutions with fast, yet accurate supervised ML predictions. This upfront investment in ML would be justified when similar problems are solved repeatedly over time, for example, in transport planning related to fleet management, routing and container yard management. Our numerical results focus on the problem class seminally addressed with the integer and continuous L-shaped cuts. Our extensive empirical analysis is grounded in standardized families of problems derived from stochastic server location (SSLP) and stochastic multi knapsack (SMKP) problems available in the literature. The proposed method can solve the hardest instances of SSLP in less than 9% of the time it takes the state-of-the-art exact method, and in the case of SMKP the same figure is 20%. Average optimality gaps are in most cases less than 0.1%.