Multi-objective process parameter optimization using a hybrid reinforcement/machine learning model in metal additive manufacturing

Abstract

Additive manufacturing enables the production of complex geometries and lightweight structures. However, producing defect-free components fundamentally depends on the careful optimization of process parameters that influence critical factors, such as melt pool depth, in laser powder bed fusion (L-PBF), an important class of metal additive manufacturing methods. Hence, for the first time, this paper presents a novel data-driven framework that integrates machine learning (ML) with reinforcement learning (RL) to optimize process parameters, ensuring the desired melt pool characteristics while meeting multi-objective design criteria. Experimental data from the literature were extracted to train several ML models, with Gaussian process regression (GPR) featuring a Matérn kernel proved to be the most accurate predictor. This model served as the digital twin of the L-PBF process and was integrated with a Q-learning-based RL agent to derive the optimal process parameters. The GPR model achieved a high prediction accuracy (root mean squared error (RMSE): 34 µm, the coefficient of determination R²: 96.05%) for L-PBF Ti6Al4V alloy using minimal training data. Integrating a Q-learning framework with ML demonstrated superior performance in deriving process parameters that achieved the target melt pool depth while minimizing the normalized enthalpy, directly impacting the formation of the keyhole defect.

Keywords

Metal additive manufacturing / Laser powder bed fusion (L-PBF) / Machine learning (ML) / Q-learning / Normalized enthalpy / Keyhole

References

[1] DebRoy T, Mukherjee T, Milewski JOet al. . Scientific, technological and economic issues in metal printing and their solutions. Nat Mater. 2019, 18(10): 1026-1032.

[2] Saboori A, Aversa A, Marchese Get al. . Application of directed energy deposition-based additive manufacturing in repair. Appl Sci. 2019, 9(16): 3316.

[3] Frazier WE. Metal additive manufacturing: a review. J Mater Eng Perform. 2014, 2361917-1928.

[4] Mosallanejad MH, Abdi A, Karpasand et al (2023) Additive manufacturing of titanium alloys: processability, properties, and applications. Adv Eng Mater 25:2301122. https://doi.org/10.1002/adem.202301122

[5] King WE, Anderson AT, Ferencz RMet al. . Laser powder bed fusion additive manufacturing of metals; physics, computational, and materials challenges. Appl Phys Rev. 2015, 2(4. 041304

[6] Wei HL, Mukherjee T, Zhang Wet al. . Mechanistic models for additive manufacturing of metallic components. Prog Mater Sci. 2021, 116. 100703

[7] Mosallanejad MH, Niroumand B, Aversa Aet al. . In-situ alloying in laser-based additive manufacturing processes: a critical review. J Alloys Compd. 2021, 872. 159567

[8] Dadkhah M, Tulliani JM, Saboori A et al (2023) Additive manufacturing of ceramics: advances, challenges, and outlook. J Eur Ceram Soc 43(15):6635–6664. https://doi.org/10.1016/j.jeurceramsoc.2023.07.033

[9] Behjat A, Shamanian M, Sadeghi Fet al. . Additive manufacturing of a novel in-situ alloyed AISI316L-Cu stainless steel: microstructure and antibacterial properties. Mater Lett. 2024, 355. 135363

[10] Dadkhah M, Mosallanejad MH, Iuliano Let al. . A comprehensive overview on the latest progress in the additive manufacturing of metal matrix composites: potential, challenges, and feasible solutions. Acta Metall Sin (Eng Lett). 2021, 349): 1173-1200.

[11] Galati M, Defanti S, Saboori Aet al. . An investigation on the processing conditions of Ti-6Al-2Sn-4Zr-2Mo by electron beam powder bed fusion: microstructure, defect distribution, mechanical properties and dimensional accuracy. Addit Manuf. 2022, 50. 102564

[12] Zhang Y, Wu L, Guo Xet al. . Additive manufacturing of metallic materials: a review. J Mater Eng Perform. 2018, 27(1): 1-13.

[13] Behjat A, Shamanian M, Taherizadeh Aet al. . Enhanced surface properties and bioactivity of additively manufactured 316L stainless steel using different post-treatments. Mater Today Proc. 2022, 70: 188-194.

[14] Khairallah SA, Anderson AT, Rubenchik A et al (2016) Laser powder-bed fusion additive manufacturing: physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Mater 108:36-45. https://doi.org/10.1016/j.actamat.2016.02.014

[15] King WE, Barth HD, Castillo VMet al. . Observation of keyhole-mode laser melting in laser powder-bed fusion additive manufacturing. J Mater Process Technol. 2014, 214(12): 2915-2925.

[16] Gong H, Rafi K, Gu Het al. . Analysis of defect generation in Ti-6Al-4V parts made using powder bed fusion additive manufacturing processes. Addit Manuf. 2014, 1: 87-98.

[17] Mower TM, Long MJ. Mechanical behavior of additive manufactured, powder-bed laser-fused materials. Mater Sci Eng A. 2016, 651: 198-213.

[18] Sames WJ, List FA, Pannala Set al. . The metallurgy and processing science of metal additive manufacturing. Int Mater Rev. 2016, 61(5): 315-360.

[19] Viale V, Stavridis J, Salmi Aet al. . Optimisation of downskin parameters to produce metallic parts via laser powder bed fusion process: an overview. Int J Adv Manuf Technol. 2022, 123(7): 2159-2182.

[20] Taghian M, Mosallanejad MH, Lannunziata Eet al. . Laser powder bed fusion of metallic components: latest progress in productivity, quality, and cost perspectives. J Mater Res Technol. 2023, 27: 6484-6500.

[21] Marler RT, Arora JS. Survey of multi-objective optimization methods for engineering. Struct Multidiscip Optim. 2004, 26(6): 369-395.

[22] Deb K, Jain H. An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans Evol Comput. 2013, 18(4): 577-601.

[23] Chia HY, Wu J, Wang X et al (2022) Process parameter optimization of metal additive manufacturing: a review and outlook. J Mater Inform 2:16. https://doi.org/10.20517/jmi.2022.18

[24] Moradi A, Tajalli S, Mosallanejad MHet al. . Intelligent laser-based metal additive manufacturing: a review on machine learning for process optimization and property prediction. Int J Adv Manuf Technol. 2025, 136(2): 527-560.

[25] Schleder GR, Padilha AC, Acosta CMet al. . From DFT to machine learning: recent approaches to materials science—a review. J Phys Mater. 2019, 2(3. 032001

[26] Kamath C. Data mining and statistical inference in selective laser melting. Int J Adv Manuf Technol. 2016, 865): 1659-1677.

[27] Mosallanejad MH, Gashmard H, Javanbakht Met al. . A novel feature engineering approach for predicting melt pool depth during LPBF by machine learning models. Addit Manuf Lett. 2024, 10. 100214

[28] Wang C, Tan XP, Tor SBet al. . Machine learning in additive manufacturing: state-of-the-art and perspectives. Addit Manuf. 2020, 36. 101538

[29] DebRoy T, Mukherjee T, Wei HLet al. . Metallurgy, mechanistic models and machine learning in metal printing. Nat Rev Mater. 2021, 6(1): 48-68.

[30] Meng L, McWilliams B, Jarosinski Wet al. . Machine learning in additive manufacturing: a review. JOM. 2020, 72(6): 2363-2377.

[31] Himanen L, Geurts A, Foster ASet al. . Data-driven materials science: status, challenges, and perspectives. Adv Sci. 2019, 6(21): 1900808.

[32] Wang AYT, Murdock RJ, Kauwe SKet al. . Machine learning for materials scientists: an introductory guide toward best practices. Chem Mater. 2020, 32124954-4965.

[33] He P, Liu Q, Kruzic JJet al. . Machine-learning assisted additive manufacturing of a TiCN reinforced AlSi10Mg composite with tailorable mechanical properties. Mater Lett. 2022, 307. 131018

[34] Barrionuevo GO, Walczak M, Ramos-Grez Jet al. . Microhardness and wear resistance in materials manufactured by laser powder bed fusion: machine learning approach for property prediction. CIRP J Manuf Sci Technol. 2023, 43: 106-114.

[35] Minkowitz L, Arneitz S, Effertz PSet al. . Laser-powder bed fusion process optimisation of AlSi10Mg using extra trees regression. Mater Des. 2023, 227. 111718

[36] Theeda S, Jagdale SH, Ravichander BBet al. . Optimization of process parameters in laser powder bed fusion of SS 316L parts using artificial neural networks. Metals. 2023, 13(5): 842.

[37] Hassanin H, Zweiri Y, Finet Let al. . Laser powder bed fusion of Ti-6Al-2Sn-4Zr-6Mo alloy and properties prediction using deep learning approaches. Mater. 2021, 14: 2056.

[38] Eshkabilov S, Ara I, Azarmi F. A comprehensive investigation on application of machine learning for optimization of process parameters of laser powder bed fusion-processed 316L stainless steel. Int J Adv Manuf Technol. 2022, 12372733-2756.

[39] Muhammad W, Kang J, Ibragimova Oet al. . Experimental investigation and development of a deep learning framework to predict process-induced surface roughness in additively manufactured aluminum alloys. Weld World. 2023, 674897-921.

[40] Lee CH, Kühn U, Lee SCet al. . Optimizing laser powder bed fusion of Ti-5Al-5V-5Mo-3Cr by artificial intelligence. J Alloys Compd. 2021, 862. 158018

[41] Chen C, Wong SJL, Raghavan Set al. . Design of experiments informed deep learning for modeling of directed energy deposition process with a small-size experimental dataset. Mater Des. 2022, 222. 111098

[42] Zhu X, Jiang F, Guo Cet al. . Prediction of melt pool shape in additive manufacturing based on machine learning methods. Opt Laser Technol. 2023, 159. 108964

[43] Akbari P, Ogoke F, Kao NYet al. . MeltpoolNet: melt pool characteristic prediction in metal additive manufacturing using machine learning. Addit Manuf. 2022, 55. 102817

[44] Kaelbling LP, Littman ML, Moore AW. Reinforcement learning: a survey. J Artif Intell Res. 1996, 4: 237-285.

[45] Sousa J, Brandau B, Darabi Ret al. . Artificial intelligence for control in laser-based additive manufacturing: a systematic review. IEEE Access. 2025, 13: 30845-30860.

[46] Mattera G, Caggiano A, Nele L. Optimal data-driven control of manufacturing processes using reinforcement learning: an application to wire arc additive manufacturing. J Intell Manuf. 2025, 36(2): 1291-1310.

[47] Knaak C, Masseling L, Duong Eet al. . Improving build quality in laser powder bed fusion using high dynamic range imaging and model-based reinforcement learning. IEEE access. 2021, 9: 55214-55231.

[48] Wu H, Bordatchev E, Tutunea-Fatan OR. Training reinforcement learning-based controller using performance simulation of the laser remelting process. Procedia Comput Sci. 2024, 232: 1849-1858.

[49] Petrik J, Bambach M. RLTube: reinforcement learning based deposition path planner for thin-walled bent tubes with optionally varying diameter manufactured by wire-arc additive manufacturing. Manuf Lett. 2024, 40: 31-36.

[50] Petrik J, Bambach M. Reinforcement learning and optimization based path planning for thin-walled structures in wire arc additive manufacturing. J Manuf Process. 2023, 93: 75-89.

[51] Vagenas S, Al-Saadi T, Panoutsos G (2026) Multi-layer process control in selective laser melting: a reinforcement learning approach. J Intell Manuf 37:281–298. https://doi.org/10.1007/s10845-024-02548-3

[52] Dharmadhikari S, Menon N, Basak A. A reinforcement learning approach for process parameter optimization in additive manufacturing. Addit Manuf. 2023, 71. 103556

[53] Watkins CJCH, Dayan P. Technical note: Q-learning. Mach Learn. 1992, 8: 279-292.

[54] Vaghefi E, Hosseini S, Afsharinejad AHet al. . Additive manufacturing process parameter design for variable component geometries using reinforcement learning. Addit Manuf. 2024, 84. 104121

[55] Haarnoja T, Zhou A, Abbeel P et al (2018) Soft actor-critic: off-policy maximum entropy deep reinforcement learning with a stochastic actor. https://doi.org/10.48550/arXiv.1801.01290

[56] Sousa J, Darabi R, Sousa A et al (2023) Enhancing sample efficiency for temperature control in DED with reinforcement learning and MOOSE framework. In: proceedings of ASME 2023 international mechanical engineering congress and exposition. October 29–November 2, 2023, New Orleans, US. https://doi.org/10.1115/IMECE2023-113629

[57] Shi S, Liu X, Wang Zet al. . An intelligent process parameters optimization approach for directed energy deposition of nickel-based alloys using deep reinforcement learning. J Manuf Process. 2024, 120: 1130-1140.

[58] Liu S, Shin YC. Additive manufacturing of Ti6Al4V alloy: a review. Mater Des. 2019, 164. 107552

[59] Dilip JJS, Zhang S, Teng Cet al. . Influence of processing parameters on the evolution of melt pool, porosity, and microstructures in Ti-6Al-4V alloy parts fabricated by selective laser melting. Prog Addit Manuf. 2017, 2(3): 157-167.

[60] Ye J, Khairallah SA, Rubenchik AMet al. . Energy coupling mechanisms and scaling behavior associated with laser powder bed fusion additive manufacturing. Adv Eng Mater. 2019, 21(7): 1900185.

[61] Yang J, Han J, Yu Het al. . Role of molten pool mode on formability, microstructure and mechanical properties of selective laser melted Ti-6Al-4V alloy. Mater Des. 2016, 110: 558-570.

[62] Vaglio E, Totis G, Lanzutti Aet al. . A novel thermo-geometrical model for accurate keyhole porosity prediction in laser powder-bed fusion. Prog Addit Manuf. 2024, 92247-261.

[63] Rafi HK, Karthik NV, Gong Het al. . Microstructures and mechanical properties of Ti6Al4V parts fabricated by selective laser melting and electron beam melting. J Mater Eng Perform. 2013, 22(12): 3872-3883.

[64] Cortes C, Vapnik V. Support-vector networks. Mach Learn. 1995, 20(3): 273-297.

[65] Rasmussen CE (2004) Gaussian processes in machine learning. In: Bousquet O, von Luxburg U, Rätsch G (eds) Advanced lectures on machine learning. ML 2003. Lecture Notes in Computer Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28650-9_4

[66] Breiman L. Random forests. Mach Learn. 2001, 45(1): 5-32.

[67] Friedman JH (2001) Greedy function approximation: a gradient boosting machine. Ann Stat 1189–1232. https://doi.org/10.1214/AOS/1013203451

[68] Chen T, Guestrin C (2016) XGBoost: a scalable tree boosting system. In: proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, 13–17 August, San Francisco. 785–794. https://doi.org/10.1145/2939672.2939785

[69] Pedregosa F, Varoquaux G, Gramfort Aet al. . Scikit-learn: machine learning in Python. J Mach Learn Res. 2011, 12: 2825-2830

[70] Brockman G, Cheung V, Pettersson L et al (2016) Openai gym. https://doi.org/10.48550/arXiv.1606.01540

Funding

Politecnico di Torino

RIGHTS & PERMISSIONS

The Author(s)