# Neural Combinatorial Optimization for Stochastic Flexible Job Shop Scheduling Problems

arXiv: https://arxiv.org/abs/2412.14052 · HTML: https://mlsanity.com/paper/2412.14052/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 18 Dec 2024.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Learning to Dispatch for Job Shop Scheduling via Deep Reinforcement Learning](https://mlsanity.com/paper/2010.12367/) (2020)
- [Learning to schedule job-shop problems: Representation and policy learning using graph neural network and reinforcement learning](https://mlsanity.com/paper/2106.01086/) (2021)
- [Graph Neural Networks for Job Shop Scheduling Problems: A Survey](https://mlsanity.com/paper/2406.14096/) (2024)
- [Job Shop Scheduling Benchmark: Environments and Instances for Learning and Non-learning Methods](https://mlsanity.com/paper/2308.12794/) (2023)

## Built on by (most cited first, 1 of 1)

- [N(CO)2: Neural Combinatorial Optimization with Chance Constraints to Solve Stochastic Orienteering](https://mlsanity.com/paper/2606.18514/) (2026)

## Abstract (arXiv)

Neural combinatorial optimization (NCO) has gained significant attention due to the potential of deep learning to efficiently solve combinatorial optimization problems. NCO has been widely applied to job shop scheduling problems (JSPs) with the current focus predominantly on deterministic problems. In this paper, we propose a novel attention-based scenario processing module (SPM) to extend NCO methods for solving stochastic JSPs. Our approach explicitly incorporates stochastic information by an attention mechanism that captures the embedding of sampled scenarios (i.e., an approximation of stochasticity). Fed with the embedding, the base neural network is intervened by the attended scenarios, which accordingly learns an effective policy under stochasticity. We also propose a training paradigm that works harmoniously with either the expected makespan or Value-at-Risk objective. Results demonstrate that our approach outperforms existing learning and non-learning methods for the flexible JSP problem with stochastic processing times on a variety of instances. In addition, our approach holds significant generalizability to varied numbers of scenarios and disparate distributions.