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Deep Learning for Unrelated-Machines Scheduling: Handling Variable Dimensions

Diego Hitzges, Guillaume Sagnol

TL;DR

This work tackles offline deterministic scheduling on unrelated parallel machines by introducing an NLP-inspired neural architecture capable of processing variable numbers of jobs and machines. By formulating the problem as a deterministic MDP and training via supervised learning on small instances, the model learns a policy that can generate complete schedules from the full input, generalizing well to larger problem sizes. Empirically, it achieves near-optimal performance on 8J/4M (about 2.5% above optimum) and consistently outperforms a sophisticated dispatching rule across configurations up to 100J/10M, with significant gains in many settings. The approach offers fast retraining, adaptability to different objectives, and potential as a standard methodology for learning-based scheduling in unrelated-machine environments.

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.

Deep Learning for Unrelated-Machines Scheduling: Handling Variable Dimensions

TL;DR

This work tackles offline deterministic scheduling on unrelated parallel machines by introducing an NLP-inspired neural architecture capable of processing variable numbers of jobs and machines. By formulating the problem as a deterministic MDP and training via supervised learning on small instances, the model learns a policy that can generate complete schedules from the full input, generalizing well to larger problem sizes. Empirically, it achieves near-optimal performance on 8J/4M (about 2.5% above optimum) and consistently outperforms a sophisticated dispatching rule across configurations up to 100J/10M, with significant gains in many settings. The approach offers fast retraining, adaptability to different objectives, and potential as a standard methodology for learning-based scheduling in unrelated-machine environments.

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.
Paper Structure (20 sections, 12 equations, 4 figures, 3 tables)

This paper contains 20 sections, 12 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Our Approach
  4. Related Work
  5. Methodology
  6. States as Inputs
  7. Action Values as Targets
  8. Neural Network as Policy
  9. Data Simulation and Supervised Training
  10. Learning Based versus Heuristic Scheduling
  11. Network Architecture
  12. Data Preprocessing
  13. Sequential Embedding
  14. Transformer Encoder
  15. Action-Pointer Decoder
  16. ...and 5 more sections

Figures (4)

  • Figure 1: State information to data
  • Figure 2: Embedding machine data into job representations of static dimension
  • Figure 3: Contextualizing urgencies of jobs
  • Figure 4: The modified Action-Pointer decoder outputs an attention distribution over all feasible actions: assigning the associated pending job to the currently free machine ($\hat{a}_1, \ldots, \hat{a}_J$) or deactivating the machine ($\hat{a}_{J+1}$).