Deep Learning for Unrelated-Machines Scheduling: Handling Variable Dimensions

TL;DR

This paper introduces a neural network architecture for offline scheduling on unrelated machines with variable job and machine counts, achieving near-optimal solutions and outperforming traditional dispatching rules.

Contribution

The work presents a novel NLP-inspired neural network architecture capable of handling arbitrary sizes and feature dimensions in unrelated-machine scheduling, with strong generalization to larger instances.

Findings

Cost only 2.51% above optimal on small instances

Outperformed dispatching rule by 22.22% on larger instances

Fast retraining and adaptation demonstrated

Abstract

Deep learning has been effectively applied to many discrete optimization problems. However, learning-based scheduling on unrelated parallel machines remains particularly difficult to design. Not only do the numbers of jobs and machines vary, but each job-machine pair has a unique processing time, dynamically altering feature dimensions. We propose a novel approach with a neural network tailored for offline deterministic scheduling of arbitrary sizes on unrelated machines. The goal is to minimize a complex objective function that includes the makespan and the weighted tardiness of jobs and machines. Unlike existing online approaches, which process jobs sequentially, our method generates a complete schedule considering the entire input at once. The key contribution of this work lies in the sophisticated architecture of our model. By leveraging various NLP-inspired architectures, it effectively processes any number of jobs and machines with varying feature dimensions imposed by unrelated processing times. Our approach enables supervised training on small problem instances while demonstrating strong generalization to much larger scheduling environments. Trained and tested on instances with 8 jobs and 4 machines, costs were only 2.51% above optimal. Across all tested configurations of up to 100 jobs and 10 machines, our network consistently outperformed an advanced dispatching rule, which incurred 22.22% higher costs on average. As our method allows fast retraining with simulated data and adaptation to various scheduling conditions, we believe it has the potential to become a standard approach for learning-based scheduling on unrelated machines and similar problem environments.