A hierarchical decoupling framework and hybrid adaptive genetic algorithm for multimachine dual-arm PCB placement scheduling

Chang Kou; Mingze Sun; Ting Song; Jihong Shen; Chang Kou; Mingze Sun; Ting Song; Jihong Shen

doi:10.3934/nhm.2026047

Networks and Heterogeneous Media

2026, Volume 21, Issue 4: 1172-1196. doi: 10.3934/nhm.2026047

Previous Article Next Article

Research article Special Issues

A hierarchical decoupling framework and hybrid adaptive genetic algorithm for multimachine dual-arm PCB placement scheduling

1.
Dalian Rijia Co., Ltd., Dalian 116600, China
2.
College of Mathematical Sciences, Harbin Engineering University, Harbin 150000, China

Received: 18 March 2026 Revised: 05 May 2026 Accepted: 05 June 2026 Published: 10 June 2026

Printed circuit boards (PCBs) are an indispensable part of electronic products. As the consumer electronics market continues to expand, the PCB assembly rate has become a key factor limiting production line efficiency. PCB placement scheduling is a highly complex, multivariable combinatorial optimization problem characterized by nonlinearity and high coupling. From a system perspective, this scheduling problem is modeled as a complex network optimization, wherein the intricate coupling of resources, time, and processes parallels the node interdependencies and information propagation mechanisms inherent in complex system architectures. Given its nondeterministic polynomial-time (NP)-hard nature and the dynamic constraints of the production environment, this study develops a rigorous mathematical model based on motion trajectory analysis and proposes a three-stage hierarchical decoupling framework. This decomposition transforms the high-dimensional network complexity into manageable subtasks while preserving essential variable interdependencies. To solve this complex network optimization, the framework integrates a hybrid adaptive genetic algorithm (HAGA) implemented through a three-level strategy.Initially, an improved adaptive genetic algorithm (IAGA) handles global load balancing; subsequently, an improved spectral clustering algorithm groups components to minimize tool-changing overhead; finally, a hybrid genetic algorithm and ant colony optimization (GA-ACO) optimizes synchronized intramachine paths. Unlike partial-stage methods, this holistic approach ensures synergistic optimization from global network equilibrium to local machine precision. Numerical experiments using real-world data from Dalian Rijia Co., Ltd. demonstrate that HAGA achieves at least a 10% reduction in the production cycle. This research proves that the hierarchical strategy effectively balances computational efficiency with global optimization performance.
Citation: Chang Kou, Mingze Sun, Ting Song, Jihong Shen. A hierarchical decoupling framework and hybrid adaptive genetic algorithm for multimachine dual-arm PCB placement scheduling[J]. Networks and Heterogeneous Media, 2026, 21(4): 1172-1196. doi: 10.3934/nhm.2026047

Related Papers:

Abstract

Printed circuit boards (PCBs) are an indispensable part of electronic products. As the consumer electronics market continues to expand, the PCB assembly rate has become a key factor limiting production line efficiency. PCB placement scheduling is a highly complex, multivariable combinatorial optimization problem characterized by nonlinearity and high coupling. From a system perspective, this scheduling problem is modeled as a complex network optimization, wherein the intricate coupling of resources, time, and processes parallels the node interdependencies and information propagation mechanisms inherent in complex system architectures. Given its nondeterministic polynomial-time (NP)-hard nature and the dynamic constraints of the production environment, this study develops a rigorous mathematical model based on motion trajectory analysis and proposes a three-stage hierarchical decoupling framework. This decomposition transforms the high-dimensional network complexity into manageable subtasks while preserving essential variable interdependencies. To solve this complex network optimization, the framework integrates a hybrid adaptive genetic algorithm (HAGA) implemented through a three-level strategy.Initially, an improved adaptive genetic algorithm (IAGA) handles global load balancing; subsequently, an improved spectral clustering algorithm groups components to minimize tool-changing overhead; finally, a hybrid genetic algorithm and ant colony optimization (GA-ACO) optimizes synchronized intramachine paths. Unlike partial-stage methods, this holistic approach ensures synergistic optimization from global network equilibrium to local machine precision. Numerical experiments using real-world data from Dalian Rijia Co., Ltd. demonstrate that HAGA achieves at least a 10% reduction in the production cycle. This research proves that the hierarchical strategy effectively balances computational efficiency with global optimization performance.

References

[1]	M. O. Ball, M. J. Magazine, Sequencing of insertions in printed circuit board assembly, Oper. Res., 36 (1988), 192–201. https://doi.org/10.1287/opre.36.2.192 doi: 10.1287/opre.36.2.192
[2]	G. Y. Zhu, W. B. Zhang, An improved shuffled frog-leaping algorithm to optimize component pick-and-place sequencing optimization problem, Expert Syst. Appl., 41 (2014), 6818–6829. https://doi.org/10.1016/j.eswa.2014.04.038 doi: 10.1016/j.eswa.2014.04.038
[3]	D. Li, S. W. Yoon, PCB assembly optimization in a single gantry high-speed rotary-head collect-and-place machine, Int. J. Adv. Manuf. Technol., 88 (2017), 2819–2834. https://doi.org/10.1007/s00170-016-8942-4 doi: 10.1007/s00170-016-8942-4
[4]	H. Y. Lin, C. J. Lin, M. L. Huang, Optimization of printed circuit board component placement using an efficient hybrid genetic algorithm, Appl. Intell., 45 (2016), 622–637. https://doi.org/10.1007/s10489-016-0775-1 doi: 10.1007/s10489-016-0775-1
[5]	H. P. Hsu, Solving feeder assignment and component sequencing problems for printed circuit board assembly using particle swarm optimization, IEEE Trans. Autom. Sci. Eng., 14 (2017), 881–893. https://doi.org/10.1109/TASE.2016.2622253 doi: 10.1109/TASE.2016.2622253
[6]	A. R. Alazzam, Using BUA algorithm to solve a sequential pick and place problem, in 2018 International Conference on Information and Computer Technologies (ICICT), DeKalb, IL, USA, 144–149. https://doi.org/10.1109/INFOCT.2018.8356858
[7]	J. Mumtaz, Z. Guan, L. Yue, L. Zhang, C. He, Hybrid spider monkey optimization algorithm for multi-level planning and scheduling problems of assembly lines, Int. J. Prod. Res., 58 (2020), 6252–6267. https://doi.org/10.1080/00207543.2019.1675917 doi: 10.1080/00207543.2019.1675917
[8]	C. J. Lin, C. H. Lin, Component placement process optimization for multi-head surface mounting machine using a hybrid algorithm, Sens. Mater., 33 (2021), 3529–3545. https://doi.org/10.18494/SAM.2021.3579 doi: 10.18494/SAM.2021.3579
[9]	Z. Li, X. Yu, J. Qiu, H. Gao, Cell division genetic algorithm for component allocation optimization in multifunctional placers, IEEE Trans. Ind. Inf., 18 (2022), 559–570. https://doi.org/10.1109/TII.2021.3069459 doi: 10.1109/TII.2021.3069459
[10]	Z. Li, H. Sun, X. Yu, S. Wei, Heuristic sequencing hopfield neural network for pick-and-place location routing in multi-functional placers, Neurocomputing, 472 (2022), 35–44. https://doi.org/10.1016/j.neucom.2021.11.040 doi: 10.1016/j.neucom.2021.11.040
[11]	T. He, D. B. Li, S. W. Yoon, A multi-phase planning heuristic for a dual-delivery SMT placement machine optimization, Robot. Comput.-Integr. Manuf., 47 (2017), 85–94. https://doi.org/10.1016/j.rcim.2016.11.006 doi: 10.1016/j.rcim.2016.11.006
[12]	T. He, D. Li, S. W. Yoon, An adaptive clustering-based genetic algorithm for the dual-gantry pick-and-place machine optimization, Adv. Eng. Inf., 37 (2018), 66–78. https://doi.org/10.1016/j.aei.2018.04.007 doi: 10.1016/j.aei.2018.04.007
[13]	D. Li, R. Qiang, S. W. Yoon, Balanced adaptive tabu search algorithm to optimize dual-gantry pick-and-place assembly, Procedia Manuf., 11 (2017), 1892–1899. https://doi.org/10.1016/j.promfg.2017.07.331 doi: 10.1016/j.promfg.2017.07.331
[14]	D. S. Sun, T. E. Lee, K. H. Kim, Component allocation and feeder arrangement for a dual-gantry multi-head surface mounting placement tool, Int. J. Prod. Econ., 95 (2005), 245–264. https://doi.org/10.1016/j.ijpe.2004.01.003 doi: 10.1016/j.ijpe.2004.01.003
[15]	A. Tóth, T. Knuutila, O. S. Nevalainen, Machine configuration and workload balancing of modular placement machines in multi-product PCB assembly, Int. J. Comput. Integr. Manuf., 31 (2018), 815–830. https://doi.org/10.1080/0951192X.2018.1429667 doi: 10.1080/0951192X.2018.1429667
[16]	Y. Crama, J. Klundert, F. C. R. Spieksma, Production planning problems in printed circuit board assembly, Discrete Appl. Math., 123 (2002), 339–361. https://doi.org/10.1016/S0166-218X(01)00345-6 doi: 10.1016/S0166-218X(01)00345-6
[17]	P. Ji, Y. F. Wan, Planning for printed circuit board assembly: The state-of-the-art review, Int. J. Comput. Appl. Technol., 14 (2001), 136–144. https://doi.org/10.1504/IJCAT.2001.000268 doi: 10.1504/IJCAT.2001.000268
[18]	P. Rogers, R. Warrington, Production planning for surface mount technology lines, Int. J. Prod. Res., 42 (2004), 2693–2718. https://doi.org/10.1080/00207540410001671697 doi: 10.1080/00207540410001671697
[19]	S. Emet, T. Knuutila, E. Alhoniemi, M. Maier, M. Johnsson, O. S. Nevalainen, Workload balancing in printed circuit board assembly, Int. J. Adv. Manuf. Technol., 50 (2010), 1175–1182. https://doi.org/10.1007/s00170-010-2558-x doi: 10.1007/s00170-010-2558-x
[20]	S. Rajakumar, V. P. Arunachalam, V. Selladurai, Workflow balancing in parallel machines through genetic algorithm, Int. J. Adv. Manuf. Technol., 33 (2007), 1212–1221. https://doi.org/10.1007/s00170-006-0553-z doi: 10.1007/s00170-006-0553-z
[21]	M. T. Sze, P. Ji, W. B. Lee, Modeling the component assignment problem in PCB assembly, Assem. Autom., 21 (2001), 55–60. https://doi.org/10.1108/01445150110381745 doi: 10.1108/01445150110381745
[22]	L. P. Khoo, D. Alisantoso, Line balancing of PCB assembly line using immune algorithms, Eng. Comput., 19 (2003), 92–100. https://doi.org/10.1007/s00366-003-0256-0 doi: 10.1007/s00366-003-0256-0
[23]	G. Zhang, Z. Li, X. Du, A hybrid genetic algorithm to optimize the printed circuit board assembly process, in International Conference on Logistics Systems and Intelligent Management, 2010,563–567. https://doi.org/10.1109/ICLSIM.2010.5461358
[24]	Y. Wu, P. Ji, A solution method for the component allocation problem in printed circuit board assembly, Assem. Autom., 30 (2010), 155–163. https://doi.org/10.1108/01445151011029790 doi: 10.1108/01445151011029790
[25]	A. Rong, A. Tóth, O. S. Nevalainen, T. Knuutila, R. Lahdelma, Modeling the machine configuration and line-balancing problem of a PCB assembly line with modular placement machines, Int. J. Adv. Manuf. Technol., 54 (2011), 349–360. https://doi.org/10.1007/s00170-010-2920-z doi: 10.1007/s00170-010-2920-z
[26]	T. He, D. B. Li, S. W. Yoon, A heuristic algorithm to balance workloads of high-speed SMT machines in a PCB assembly line, Procedia Manuf., 11 (2017), 1790–1797. https://doi.org/10.1016/j.promfg.2017.07.316 doi: 10.1016/j.promfg.2017.07.316
[27]	J. Mumtaz, Z. Guan, L. Yue, Z. Wang, S. Ullah, M. Rauf, Multi-level planning and scheduling for parallel PCB assembly lines using hybrid spider monkey optimization approach, IEEE Access, 7 (2019), 18685–18700. https://doi.org/10.1109/ACCESS.2019.2895954 doi: 10.1109/ACCESS.2019.2895954
[28]	X. Yan, H. Zuo, C. Hu, W. Gong, V. S. Sheng, Load optimization scheduling of chip mounter based on hybrid adaptive optimization algorithm, Complex Syst. Model. Simul., 3 (2023), 1–11. https://doi.org/10.23919/CSMS.2022.0026 doi: 10.23919/CSMS.2022.0026
[29]	T. L. Chen, J. C. Chen, Y. J. Chang, The optimal configuration for various placement machines in PCB assembly lines, Ann. Oper. Res., 349 (2025), 365–-396. https://doi.org/10.1007/s10479-024-05828-6 doi: 10.1007/s10479-024-05828-6
[30]	J. P. Huang, Q. K. Pan, P. N. Suganthan, Effective constructive and composite heuristics for grouping printed circuit boards in the electronic assembly industry, Eng. Optim., 54 (2022), 1722–1758. https://doi.org/10.1080/0305215X.2021.1983806 doi: 10.1080/0305215X.2021.1983806
[31]	Y. Chen, J. Zhong, J. Mumtaz, S. Zhou, L. Zhu, An improved spider monkey optimization algorithm for multi-objective planning and scheduling problems of PCB assembly lines, Expert Syst. Appl., 229 (2023), 120600 https://doi.org/10.1016/j.eswa.2023.120600 doi: 10.1016/j.eswa.2023.120600
[32]	H. Gao, Z. Li, X. Yu, J. Qiu, Hierarchical multi-objective heuristic for PCB assembly optimization in a beam-head surface mounter, IEEE Trans. Cybern., 52 (2021), 6911–6924. https://doi.org/10.1109/TCYB.2020.3040788 doi: 10.1109/TCYB.2020.3040788
[33]	J. Zhong, Y. Chen, J. Mumtaz, A multi-objective scheduling optimization method for PCB assembly lines based on the improved spider monkey algorithm, Eng. Proc., 23 (2022), 15. https://doi.org/10.3390/engproc2022023015 doi: 10.3390/engproc2022023015
[34]	J. Du, J. Mumtaz, W. Zhao, J. Huang, Flexsim-simulated PCB assembly line optimization using deep Q-network, Eng. Proc., 75 (2024), 34. https://doi.org/10.3390/engproc2024075034 doi: 10.3390/engproc2024075034
[35]	A. Tóth, T. Knuutila, O. S. Nevalainen, A divide and combine method for machine configuration and workload balancing problem in multiple product PCB assembly, Int. J. Adv. Manuf. Technol., 120 (2022), 4079–4095. https://doi.org/10.1007/s00170-022-08819-8 doi: 10.1007/s00170-022-08819-8

Reader Comments

Your name:*

Email:*
© 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)