摘要
作业车间调度问题(JSSP)是经典的离线组合优化问题,广泛应用于工厂排产,物流配送等领域。作为NP-hard问题,其求解复杂度随作业和机器数量呈指数级增长。然而,传统的精确算法难以应对大规模实例,而现有的启发式和深度学习方法大多未能充分挖掘问题的全局信息,且通常仅能提供单一分布的解,难以满足组合优化问题的多解性。针对这一局限,提出了一种基于扩散概率模型的全局信息预测方法。首先,结合作业车间调度问题的特征和求解约束对扩散概率模型进行迁移,以预测表征最优解分布的概率图。随后,基于概率图的引导进行约束求解与局部搜索优化,充分发挥扩散概率模型的多模态生成优势与对全局信息的编码能力,从而获得符合问题约束的高质量调度方案。为进一步提升算法的求解效率,在国产深度学习框架Jittor上进行了迁移与重构,基于Jittor构建出一套高效的作业车间调度问题求解管线,并在网络推理速度上相较于Pytorch实现了最高40%的推理速度提升。在主流数据集上的实验结果表明,该方法在各类问题规模下均表现优异,取得了最佳的求解质量。据悉,这是首个基于扩散概率模型的作业车间调度问题求解器。
The job-shop scheduling problem(JSSP)is a classic NP-hard combinatorial optimization problem with broad applications in manufacturing,logistics,and related domains.Due to its exponential computational complexity with increasing jobs and machines,traditional exact algorithms struggle with large-scale instances,while existing heuristic and deep learning-based methods often inadequately exploit global information.Furthermore,these approaches typically generate solutions from a single distribution,failing to capture the inherent multi-modality of combinatorial optimization problems.To address these limitations,we propose a novel global information prediction method based on diffusion probabilistic models.Our approach adapts the diffusion model to the structural constraints of JSSP,predicting a heatmap that represents the distribution of optimal solutions.Leveraging this heatmap,we perform constrained optimization and local search,effectively harnessing the model’s multi-modal generation capability and global information encoding.This results in high-quality,constraint-satisfying scheduling solutions.For enhanced computational efficiency,we implement our framework on the domestic deep learning platform Jittor,developing an optimized JSSP solving pipeline that achieves up to 40%faster inference than PyTorch.Extensive experiments on mainstream benchmarks demonstrate that our method outperforms existing approaches across varying problem scales,delivering state-of-the-art solution quality.To the best of our knowledge,this work presents the first diffusion-based solver for JSSP.
作者
余克雄
何鸿君
易任娇
赵航
徐凯
朱晨阳
YU Kexiong;HE Hongjun;YI Renjiao;ZHAO Hang;XU Kai;ZHU Chenyang(School of Computer Science,National University of Defense Technology,Changsha Hunan 410000,China)
出处
《图学学报》
北大核心
2025年第5期1144-1151,共8页
Journal of Graphics
基金
国家自然科学基金(62325221,62132021,62372457)
湖南省自然科学基金(2021RC3071,2022RC1104)
国防科技大学研究资助项目(ZK22-52)。
关键词
作业车间调度问题
扩散概率模型
图神经网络
组合优化
Jittor
Job-shop scheduling problem
diffusion probabilistic model
graph neural network
combinatorial optimization
Jittor
作者简介
第一作者:余克雄(2000-),男,硕士研究生。主要研究方向为基于神经网络的组合优化。E-mail:yukexiong18@nudt.edu.cn;通信作者:朱晨阳(1990-),男,副教授,博士。主要研究方向为计算机图形学、计算机视觉等。E-mail:zhuchenyang07@nudt.edu.cn。
