All You Need is an Improving Column: Enhancing Column Generation for Parallel Machine Scheduling via Transformers

TL;DR

This paper introduces a neural network-enhanced column generation method using transformers to significantly speed up parallel machine scheduling, maintaining optimality guarantees and demonstrating strong generalization and scalability.

Contribution

It develops a novel transformer-based neural network approach to predict negative reduced cost columns, improving computational efficiency in column generation for scheduling.

Findings

45% average reduction in computation time for small to medium instances

80% improvement in objective value for large instances within 500 seconds

Method generalizes well to unseen larger and different distribution instances

Abstract

We present a neural network-enhanced column generation (CG) approach for a parallel machine scheduling problem. The proposed approach utilizes an encoder-decoder attention model, namely the transformer and pointer architectures, to develop job sequences with negative reduced cost and thus generate columns to add to the master problem. By training the neural network offline and using it in inference mode to predict negative reduced costs columns, we achieve significant computational time savings compared to dynamic programming (DP). Since the exact DP procedure is used to verify that no further columns with negative reduced cost can be identified at termination, the optimality guarantee of the original CG procedure is preserved. For small to medium-sized instances, our approach achieves an average 45% reduction in computation time compared to solving the subproblems with DP. Furthermore, the model generalizes not only to unseen, larger problem instances from the same probability distribution but also to instances from different probability distributions than those presented at training time. For large-sized instances, the proposed approach achieves an 80% improvement in the objective value in under 500 seconds, demonstrating both its scalability and efficiency.