Abstract
Injection molding is a widely used manufacturing technology for the mass production of plastic parts. Despite the importance of process optimization for achieving high quality at a low cost, process conditions have often been heuristically sought by field engineers. Here, we propose two systematic data-driven optimization frameworks for the injection molding process based on a multi-objective Bayesian optimization (MBO) framework and a constrained generative inverse design network (CGIDN) framework. MBO, an extension of Bayesian optimization, uses Gaussian process regression adopting a multidimensional acquisition function based on the concepts of hypervolume and Pareto front. The CGIDN, which is an improved version of the original generative inverse design network (GIDN), uses backpropagation to calculate the analytical gradients of the objective function with respect to design variables. Both methods can be used for multi-objective optimization with trade-off relationships, for example, between the cycle time and deflection after extraction. We demonstrate the applicability of the optimization methods utilizing simulation data from Moldflow software for the manufacturing process of a door trim part. We showed that the optimal process parameters which simultaneously minimized deflection and cycle time were obtained with a relatively small dataset. We expect that in a realistic manufacturing facility, the optimal conditions found from simulations can guide the process design of the injection molding machine, or the proposed methods can be directly utilized because they do not require a very large dataset. We also note that the proposed optimization schemes are readily applicable to the optimization of other types of plastic manufacturing processes.










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References
Altan, M. (2010). Reducing shrinkage in injection moldings via the Taguchi, ANOVA and neural network methods. Materials & Design, 31(1), 599–604.
Ashhab, M. D. S., Breitsprecher, T., & Wartzack, S. (2014). Neural network based modeling and optimization of deep drawing–extrusion combined process. Journal of Intelligent Manufacturing, 25(1), 77–84.
AUTODESK. (2021). Moldflow insight manual. https://help.autodesk.com/view/MFIA/2021/ENU/
Blum, M., & Riedmiller, M. A. (2013). Optimization of Gaussian process hyperparameters using Rprop. ESANN.
Chen, C. T., & Gu, G. X. (2020). Generative deep neural networks for inverse materials design using backpropagation and active learning. Advanced Science, 7(5), 1902607.
Chen, W.-C., Liou, P.-H., & Chou, S.-C. (2014). An integrated parameter optimization system for MIMO plastic injection molding using soft computing. The International Journal of Advanced Manufacturing Technology, 73(9), 1465–1474.
Cheng, J., Liu, Z., & Tan, J. (2013). Multiobjective optimization of injection molding parameters based on soft computing and variable complexity method. The International Journal of Advanced Manufacturing Technology, 66(5–8), 907–916.
Daulton, S., Balandat, M., & Bakshy, E. (2020). Differentiable expected hypervolume improvement for parallel multi-objective Bayesian optimization. arXiv:2006.05078
Denzel, A., & Kästner, J. (2018). Gaussian process regression for geometry optimization. The Journal of Chemical Physics, 148(9), 094114.
Du, K.-L., & Swamy, M. (2016). Particle swarm optimization. In Search and optimization by metaheuristics (pp. 153–173). Springer.
Emmerich, M. (2005). Single-and multi-objective evolutionary design optimization assisted by gaussian random field metamodels. Dissertation, Universität Dortmund.
Emmerich, M., Yang, K., Deutz, A., Wang, H., & Fonseca, C. M. (2016). A multicriteria generalization of bayesian global optimization. In Advances in stochastic and deterministic global optimization (pp. 229–242). Springer.
Emmerich, M. T., Giannakoglou, K. C., & Naujoks, B. (2006). Single-and multiobjective evolutionary optimization assisted by Gaussian random field metamodels. IEEE Transactions on Evolutionary Computation, 10(4), 421–439.
Feng, Z., Zhang, Q., Zhang, Q., Tang, Q., Yang, T., & Ma, Y. (2015). A multiobjective optimization based framework to balance the global exploration and local exploitation in expensive optimization. Journal of Global Optimization, 61(4), 677–694.
Gao, Y., & Wang, X. (2009). Surrogate-based process optimization for reducing warpage in injection molding. Journal of Materials Processing Technology, 209(3), 1302–1309.
Gardner, J. R., Kusner, M. J., Xu, Z. E., Weinberger, K. Q., & Cunningham, J. P. (2014). Bayesian optimization with inequality constraints. ICML.
Haklı, H., & Uğuz, H. (2014). A novel particle swarm optimization algorithm with Levy flight. Applied Soft Computing, 23, 333–345.
Hwang, S.-F., & He, R.-S. (2006). A hybrid real-parameter genetic algorithm for function optimization. Advanced Engineering Informatics, 20(1), 7–21.
Jiang, Z., Jiang, Y., Wang, Y., Zhang, H., Cao, H., & Tian, G. (2019). A hybrid approach of rough set and case-based reasoning to remanufacturing process planning. Journal of Intelligent Manufacturing, 30(1), 19–32.
Jung, J., Kim, Y., Park, J., & Ryu, S. (2022). Transfer learning for enhancing the homogenization-theory-based prediction of elasto-plastic response of particle/short fiber-reinforced composites. Composite Structures, 115210.
Khosravani, M. R., & Nasiri, S. (2020). Injection molding manufacturing process: Review of case-based reasoning applications. Journal of Intelligent Manufacturing, 31(4), 847–864.
Kim, Y., Kim, Y., Yang, C., Park, K., Gu, G. X., & Ryu, S. (2021). Deep learning framework for material design space exploration using active transfer learning and data augmentation. NPJ Computational Materials, 7(1), 1–7.
Kingma, D. P., & Ba, J. (2014). Adam: A method for stochastic optimization. arXiv:1412.6980
Kurtaran, H., Ozcelik, B., & Erzurumlu, T. (2005). Warpage optimization of a bus ceiling lamp base using neural network model and genetic algorithm. Journal of Materials Processing Technology, 169(2), 314–319.
Li, K., Yan, S., Zhong, Y., Pan, W., & Zhao, G. (2019). Multi-objective optimization of the fiber-reinforced composite injection molding process using Taguchi method, RSM, and NSGA-II. Simulation Modelling Practice and Theory, 91, 69–82.
Lizotte, D., Wang, T., Bowling, M., & Schuurmansdepartment, D. (2005). Gaussian process regression for optimization. NIPS Workshop on Value of Information.
Ma, H., Liu, W., Zhou, X., Niu, Q., & Kong, C. (2020). An effective and automatic approach for parameters optimization of complex end milling process based on virtual machining. Journal of Intelligent Manufacturing, 31(4), 967–984.
Oktem, H., Erzurumlu, T., & Uzman, I. (2007). Application of Taguchi optimization technique in determining plastic injection molding process parameters for a thin-shell part. Materials & Design, 28(4), 1271–1278.
Ozcelik, B., & Erzurumlu, T. (2005). Determination of effecting dimensional parameters on warpage of thin shell plastic parts using integrated response surface method and genetic algorithm. International Communications in Heat and Mass Transfer, 32(8), 1085–1094.
Park, H. S., Nguyen, D. S., Le-Hong, T., & Van Tran, X. (2022). Machine learning-based optimization of process parameters in selective laser melting for biomedical applications. Journal of Intelligent Manufacturing, 33(6), 1843–1858.
Pelikan, M., & Goldberg, D. E. (2006). Hierarchical Bayesian optimization algorithm. In Scalable optimization via probabilistic modeling (pp. 63–90). Springer.
Pongcharoen, P., Hicks, C., Braiden, P., & Stewardson, D. (2002). Determining optimum genetic algorithm parameters for scheduling the manufacturing and assembly of complex products. International Journal of Production Economics, 78(3), 311–322.
SheffieldML. (2012). GPy: A Gaussian process framework in python. http://github.com/SheffieldML/GPy.
Shen, C., Wang, L., & Li, Q. (2007). Optimization of injection molding process parameters using combination of artificial neural network and genetic algorithm method. Journal of Materials Processing Technology, 183(2–3), 412–418.
Sibalija, T. V., & Majstorovic, V. D. (2012). An integrated approach to optimise parameter design of multi-response processes based on Taguchi method and artificial intelligence. Journal of Intelligent Manufacturing, 23(5), 1511–1528.
Snoek, J., Larochelle, H., & Adams, R. P. (2012). Practical bayesian optimization of machine learning algorithms. Advances in neural information processing systems, 25.
Song, Z., Liu, S., Wang, X., & Hu, Z. (2020). Optimization and prediction of volume shrinkage and warpage of injection-molded thin-walled parts based on neural network. The International Journal of Advanced Manufacturing Technology, 109(3), 755–769.
Steadman, S., & Pell, K. M. (1995). Expert systems in engineering design: An application for injection molding of plastic parts. Journal of Intelligent Manufacturing, 6(5), 347–353.
Tsai, K.-M., & Luo, H.-J. (2017). An inverse model for injection molding of optical lens using artificial neural network coupled with genetic algorithm. Journal of Intelligent Manufacturing, 28(2), 473–487.
Wagner, T., Emmerich, M., Deutz, A., & Ponweiser, W. (2010). On expected-improvement criteria for model-based multi-objective optimization. International Conference on Parallel Problem Solving from Nature.
Williams, C., & Rasmussen, C. (1995). Gaussian processes for regression. Advances in neural information processing systems, 8.
Xu, G., & Yang, Z. (2015). Multiobjective optimization of process parameters for plastic injection molding via soft computing and grey correlation analysis. The International Journal of Advanced Manufacturing Technology, 78(1–4), 525–536.
Xu, Y., Zhang, Q., Zhang, W., & Zhang, P. (2015). Optimization of injection molding process parameters to improve the mechanical performance of polymer product against impact. The International Journal of Advanced Manufacturing Technology, 76(9), 2199–2208.
Yang, K., Emmerich, M., Deutz, A., & Bäck, T. (2019). Multi-objective Bayesian global optimization using expected hypervolume improvement gradient. Swarm and Evolutionary Computation, 44, 945–956.
Yilmaz, A. (2021). A door trim part example. GRABCAD library. https://grabcad.com/library/trim-part-1
Yin, F., Mao, H., & Hua, L. (2011). A hybrid of back propagation neural network and genetic algorithm for optimization of injection molding process parameters. Materials & Design, 32(6), 3457–3464.
Yu, S., Zhang, T., Zhang, Y., Huang, Z., Gao, H., Han, W., Turng, L.-S., & Zhou, H. (2020). Intelligent setting of process parameters for injection molding based on case-based reasoning of molding features. Journal of Intelligent Manufacturing, 1–13.
Zhang, J., Wang, J., Lin, J., Guo, Q., Chen, K., & Ma, L. (2016). Multiobjective optimization of injection molding process parameters based on Opt LHD, EBFNN, and MOPSO. The International Journal of Advanced Manufacturing Technology, 85(9), 2857–2872.
Zhao, D., Ivanov, M., Wang, Y., Liang, D., & Du, W. (2021). Multi-objective optimization of the resistance spot welding process using a hybrid approach. Journal of Intelligent Manufacturing, 32(8), 2219–2234.
Zhao, J., Cheng, G., Ruan, S., & Li, Z. (2015). Multi-objective optimization design of injection molding process parameters based on the improved efficient global optimization algorithm and non-dominated sorting-based genetic algorithm. The International Journal of Advanced Manufacturing Technology, 78(9), 1813–1826.
Zhou, J., & Turng, L. S. (2007). Adaptive multiobjective optimization of process conditions for injection molding using a Gaussian process approach. Advances in Polymer Technology, 26(2), 71–85.
Acknowledgements
This research was supported by project for materials, parts and equipment strategic cooperation R&D funded Korea Ministry of SMEs and Startups in 2021 (S3207585), Basic Science Research Program (2022R1A2B5B02002365) funded by the National Research Foundation of Korea, and Global Singularity Program (1711100689 and N10220003) funded by KAIST. We would like to acknowledge the generous support of Mr. Daewook Kim, Product Specialist Sales Exec. at Autodesk Korea Ltd. and Mr. Jinsung Son, Executive Director at Hankook Delcam Ltd.
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Jung, J., Park, K., Cho, B. et al. Optimization of injection molding process using multi-objective bayesian optimization and constrained generative inverse design networks. J Intell Manuf 34, 3623–3636 (2023). https://doi.org/10.1007/s10845-022-02018-8
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DOI: https://doi.org/10.1007/s10845-022-02018-8