考虑多材料和二维装箱的3D打印调度问题研究*

doi:10.16731/j.cnki.1671-3133.2026.05.004

现代制造工程 ›› 2026, Vol. 548 ›› Issue (5): 31-46.doi: 10.16731/j.cnki.1671-3133.2026.05.004

考虑多材料和二维装箱的3D打印调度问题研究^*

宋朋朋¹, 傅广^2,3, 张涛², 肖晓民¹, 张凯飞⁴, 张正文²

1 贵州大学省部共建公共大数据国家重点实验室,贵阳 550025;
2 贵州大学机械工程学院,贵阳 550025;
3 贵州省核能部件及材料制造技术全省重点实验室,遵义 563000;
4 重庆理工大学机械工程学院,重庆 400054

收稿日期:2025-05-12 出版日期:2026-05-18 发布日期:2026-06-04
通讯作者: 傅广,博士,副教授,主要研究方向为增材制造、智能优化算法。E-mail:gfu@gzu.edu.cn
作者简介:宋朋朋,硕士研究生,主要研究方向为增材制造、智能优化算法。E-mail:1391929640@qq.com
基金资助:
^*贵州省科技计划项目(黔科合基础ZD[2025]083,黔科合支撑[2025]一般041,黔科合平台人才-BQW[2024]011);贵州大学基础研究项目(贵大基础[2024]14号,贵大领军合字[2024]03号)

Research on 3D printing scheduling problem considering multi-material and 2D packing

SONG Pengpeng¹, FU Guang^2,3, ZHANG Tao², XIAO Xiaomin¹, ZHANG Kaifei⁴, ZHANG Zhengwen²

1 State Key Laboratory of Public Big Data,Guizhou University,Guiyang 550025,China;
2 School of Mechanical Engineering,Guizhou University,Guiyang 550025,China;
3 Guizhou Provincial Key Laboratory of Nuclear Components and Materials Manufacturing Technology,Zunyi 563000,China;
4 School of Mechanical Engineering,Chongqing University of Technology,Chongqing 400054,China

Received:2025-05-12 Online:2026-05-18 Published:2026-06-04

摘要/Abstract

摘要： 随着3D打印技术向多材料方向的发展,衍生出材料转换与构建平台二维空间优化的双重约束,显著增加了生产调度的复杂性。为应对这一挑战,以最小化所有零件总延迟时间为优化目标,结合多材料及二维装箱约束条件建立数学模型,并提出一种改进的遗传算法进行求解。其中,新设计了相应的编码和初始化方法,以支持在复杂约束下生成高质量的可行解;在左下启发式算法中考虑零件的水平旋转,以探讨二维装箱子问题;集成精英主义选择和玻尔兹曼选择设计了新的混合选择策略。此外,还设计了新的交叉和变异策略,以平衡算法的探索和开发能力。最后,试验结果表明,所提算法在不同规模的试验中均能有效且稳健地获得高质量的解,并且与其他遗传算法相比较也展现出卓越的性能。

关键词: 3D打印, 遗传算法, 混合整数线性规划, 批次调度, 二维装箱

Abstract: With the development of 3D printing technology in the direction of multi-material,the dual constraints of material conversion and 2D space optimization of the build platform are derived,which significantly increase the complexity of production scheduling. In order to meet this challenge,with the optimization objective of minimizing the total latency time of all parts,a mathematical model was established by combining the multi-material and 2D packing constraints,and an improved genetic algorithm was proposed to solve it. In particular, it newly designed the corresponding coding and initialization methods to support the generation of high-quality feasible solutions under complex constraints. Moreover,it considered the horizontal rotation of the part in the bottom-left heuristic algorithm in order to explore the 2D packing problem. It also integrated elitism method and Boltzmann selection to design a new hybrid selection strategy. Additionally, new crossover and mutation strategies were constructed to balance the exploration and exploitation capabilities of the algorithm. Finally,the experimental results show that the proposed algorithm is effective and robust in obtaining high-quality solutions in different sizes of experiments,and also exhibits excellent performance in comparison with other genetic algorithms.

Key words: 3D printing, genetic algorithm, mixed integer linear programming, batch scheduling, 2D packing

中图分类号:

TP391.73

宋朋朋, 傅广, 张涛, 肖晓民, 张凯飞, 张正文. 考虑多材料和二维装箱的3D打印调度问题研究^*[J]. 现代制造工程, 2026, 548(5): 31-46.

SONG Pengpeng, FU Guang, ZHANG Tao, XIAO Xiaomin, ZHANG Kaifei, ZHANG Zhengwen. Research on 3D printing scheduling problem considering multi-material and 2D packing[J]. Modern Manufacturing Engineering, 2026, 548(5): 31-46.

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考虑多材料和二维装箱的3D打印调度问题研究^*

Research on 3D printing scheduling problem considering multi-material and 2D packing

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