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Graph-Enhanced Deep Reinforcement Learning for Multi-Objective Unrelated Parallel Machine Scheduling

Bulent Soykan, Sean Mondesire, Ghaith Rabadi, Grace Bochenek

TL;DR

A Deep Reinforcement Learning framework using Proximal Policy Optimization (PPO) and a Graph Neural Network (GNN), allowing the PPO agent to learn a direct scheduling policy and provides a robust and scalable solution for complex manufacturing scheduling.

Abstract

The Unrelated Parallel Machine Scheduling Problem (UPMSP) with release dates, setups, and eligibility constraints presents a significant multi-objective challenge. Traditional methods struggle to balance minimizing Total Weighted Tardiness (TWT) and Total Setup Time (TST). This paper proposes a Deep Reinforcement Learning framework using Proximal Policy Optimization (PPO) and a Graph Neural Network (GNN). The GNN effectively represents the complex state of jobs, machines, and setups, allowing the PPO agent to learn a direct scheduling policy. Guided by a multi-objective reward function, the agent simultaneously minimizes TWT and TST. Experimental results on benchmark instances demonstrate that our PPO-GNN agent significantly outperforms a standard dispatching rule and a metaheuristic, achieving a superior trade-off between both objectives. This provides a robust and scalable solution for complex manufacturing scheduling.

Graph-Enhanced Deep Reinforcement Learning for Multi-Objective Unrelated Parallel Machine Scheduling

TL;DR

A Deep Reinforcement Learning framework using Proximal Policy Optimization (PPO) and a Graph Neural Network (GNN), allowing the PPO agent to learn a direct scheduling policy and provides a robust and scalable solution for complex manufacturing scheduling.

Abstract

The Unrelated Parallel Machine Scheduling Problem (UPMSP) with release dates, setups, and eligibility constraints presents a significant multi-objective challenge. Traditional methods struggle to balance minimizing Total Weighted Tardiness (TWT) and Total Setup Time (TST). This paper proposes a Deep Reinforcement Learning framework using Proximal Policy Optimization (PPO) and a Graph Neural Network (GNN). The GNN effectively represents the complex state of jobs, machines, and setups, allowing the PPO agent to learn a direct scheduling policy. Guided by a multi-objective reward function, the agent simultaneously minimizes TWT and TST. Experimental results on benchmark instances demonstrate that our PPO-GNN agent significantly outperforms a standard dispatching rule and a metaheuristic, achieving a superior trade-off between both objectives. This provides a robust and scalable solution for complex manufacturing scheduling.
Paper Structure (23 sections, 2 figures, 1 table)

This paper contains 23 sections, 2 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. Related Work
  3. Parallel Machine Scheduling Problem (PMSP)
  4. Deep Reinforcement Learning in Scheduling
  5. Graph Neural Networks in Combinatorial Optimization
  6. Problem Formulation
  7. Formal Definition
  8. Decision Variables
  9. Constraints
  10. Objective Functions
  11. Methodology: PPO-GNN for Multi-Objective UPMSP
  12. Markov Decision Process (MDP) Formulation
  13. State Representation ($s_t \in \mathcal{S}$)
  14. Action Space ($a_t \in \mathcal{A}$)
  15. Reward Function ($r_t = \mathcal{R}(s_t, a_t, s_{t+1})$)
  16. ...and 8 more sections

Figures (2)

  • Figure 1: Overview of the DRL framework for UPMSP scheduling.
  • Figure 2: Comparison of scheduling methods across different problem sizes (n jobs, m machines).