Multi-objective flexible job-shop scheduling via graph attention network and reinforcement learning

In real-world production scheduling, it is crucial to quickly create a plan while also achieving various objectives. Consequently, addressing the multi-objective flexible job-shop scheduling problem (MOFJSP) is both complex and challenging. Previous methods utilizing meta-heuristic approaches have made significant strides in approximating high-quality Pareto front. However, they have not adequately addressed the issue of prolonged computation times. This paper introduces an end-to-end approach to solving the MOFJSP that leverages graph attention networks (GATs) and reinforcement learning, which we term as multi-objective graph attention reinforcement learning scheduler. The GAT effectively captures the machine and operation features within heterogeneous graphs. We employ a weighted-sum method to decompose the problem into smaller optimization tasks, thereby balancing three scheduling objectives: minimizing makespan, maximum machine load, and total machine load. Experimental results demonstrate that the proposed method outperforms five commonly used multi-objective evolutionary algorithms on synthetic instances, with a more pronounced performance advantage observed in larger instances. Furthermore, results from solving public instances with model trained on the smallest synthetic instance (10x5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10\times 5$$\end{document}) indicate that the proposed method can rapidly approximate the Pareto front, yielding high-quality solutions and effectively addressing unseen instances.