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Multi-criteria optimization of the part build orientation (PBO) through a combined meta-modeling/NSGAII/TOPSIS method for additive manufacturing processes


Additive manufacturing (AM), is a new technology for the manufacturing of the physical parts through an additive manner. In the AM process, the orientation pattern of the part is an important variable that significantly influences the product properties such as the build time, the surface roughness, the mechanical strength, the wrinkling, and the amount of support material. The build time and the surface roughness are the more important criteria than others that can be considered to find the optimum orientation of parts. The designers and manufacturing engineers usually attempt to find an optimum solution to reach the product with high quality at the minimum time. Determining the optimum build orientation of the virtual model in the design stage for the additive manufacturing to reach a real production with higher quality at the lower time can be an effective strategy to success in the competitive environment of manufacturing firms. In this paper, a new combined meta-modeling/NSGA II/TOPSIS approach is introduced to search the accurate optimum PBO in the AM based on the multi-criteria optimization formulation. In order to reach this aim, first, a new formulation is proposed to model the build time with respect to the PBO in AM processes. Then, a proper formulation is developed to estimate the mean surface roughness based on the part orientations. By utilizing Kriging method as a powerful meta-modeling approach, the build time and the surface roughness as the objective functions are modeled in the explicit form in terms of the part orientation. Then, the non-dominated sorting genetic algorithm II (NSGA-II) is utilized to solve the multi-criteria optimization problem with the build time and the surface roughness as the objective functions. Consequently, Pareto-optimum solutions are obtained from the optimization problem-solving. The TOPSIS method is employed to rank all obtained optimum solutions for selecting the best solution. The proposed approach aims to precisely find the optimum PBO for the several AM processes under the low computational time. Finally, to illustrate and validate the efficiency and accuracy of the proposed approach two case studies are considered and the obtained results are compared and discussed.

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  1. 1.


  2. 2.

    Selective Laser Sintering.

  3. 3.

    Selective Laser Melting.


  1. 1.

    Ma, W., He, P.: An adaptive slicing and selective hatching strategy for layered manufacturing. J. Mater. Process. Technol. 89, 191–197 (1999)

    Article  Google Scholar 

  2. 2.

    Kumke, M., Watschke, H., Hartogh, P., Bavendiek, A.K., Vietor, T.: Methods and tools for identifying and leveraging additive manufacturing design potentials. Int. J. Interact. Des. Manuf. 1–13 (2017).

  3. 3.

    Barone, S., Casinelli, M., Frascaria, M., Paoli, A., Razionale, A.V.: Interactive design of dental implant placements through CAD–CAM technologies: from 3D imaging to additive manufacturing. Int. J. Interact. Des. Manuf. 10(2), 105–117 (2016)

    Article  Google Scholar 

  4. 4.

    Paul, R., Anand, S.: Optimal part orientation in Rapid Manufacturing process for achieving geometric tolerances. J. Manuf. Syst. 30(4), 214–222 (2011)

    MathSciNet  Article  Google Scholar 

  5. 5.

    Bikas, H., Stavropoulos, P., Chryssolouris, G.: Additive manufacturing methods and modelling approaches: a critical review. Int. J. Adv. Manuf. Technol. 83(1–4), 389–405 (2016)

    Article  Google Scholar 

  6. 6.

    Yan, C., Shi, Y., Yang, J., Liu, J.: Investigation into the selective laser sintering of styrene–acrylonitrile copolymer and postprocessing. Int. J. Adv. Manuf. Technol. 51(9), 973–982 (2010)

    Article  Google Scholar 

  7. 7.

    Pandey, P.M., Reddy, N.V., Dhande, S.G.: Part deposition orientation studies in layered manufacturing. J. Mater. Process. Technol. 185(1), 125–131 (2007)

    Article  Google Scholar 

  8. 8.

    Hanzl, P., Zetek, M., Bakša, T., Kroupa, T.: The influence of processing parameters on the mechanical properties of SLM parts. Procedia Eng. 100, 1405–1413 (2015)

    Article  Google Scholar 

  9. 9.

    Todai, M., Nakano, T., Liu, T., Yasuda, H.Y., Hagihara, K., Cho, K., Takeyama, M.: Effect of building direction on the microstructure and tensile properties of Ti–48Al–2Cr–2Nb alloy additively manufactured by electron beam melting. Addit. Manuf. 13, 61–70 (2017)

    Article  Google Scholar 

  10. 10.

    Frank, D., Fadel, G.: Expert system-based selection of the preferred direction of build for rapid prototyping processes. J. Intell. Manuf. 6(5), 339–345 (1995)

    Article  Google Scholar 

  11. 11.

    Cheng, W., Fuh, J.Y.H., Nee, A.Y.C., Wong, Y.S., Loh, H.T., Miyazawa, T.: Multi-objective optimization of part-building orientation in stereolithography. Rapid Prototyp. J. 1(4), 12–23 (1995)

    Article  Google Scholar 

  12. 12.

    Lan, P.T., Chou, S.Y., Chen, L.L., Gemmill, D.: Determining fabrication orientations for rapid prototyping with stereolithography apparatus. Comput. Aided Des. 29(1), 53–62 (1997)

    Article  Google Scholar 

  13. 13.

    Padhye, N., Deb, K.: Multi-objective optimisation and multi-criteria decision making in SLS using evolutionary approaches. Rapid Prototyp. J. 17(6), 458–478 (2011)

    Article  Google Scholar 

  14. 14.

    Alexander, P., Allen, S., Dutta, D.: Part orientation and build cost determination in layered manufacturing. Comput. Aided Des. 30(5), 343–356 (1998)

    Article  Google Scholar 

  15. 15.

    Moroni, G., Syam, W.P., Petrò, S.: Functionality-based part orientation for additive manufacturing. Procedia CIRP 36, 217–222 (2015)

    Article  Google Scholar 

  16. 16.

    Phatak, A.M., Pande, S.S.: Optimum part orientation in rapid prototyping using genetic algorithm. J. Manuf. Syst. 31(4), 395–402 (2012)

    Article  Google Scholar 

  17. 17.

    Giannatsis, J., Dedoussis, V., Laios, L.: A study of the build-time estimation problem for stereolithography systems. Robot. Comput. Integr. Manuf. 17(4), 295–304 (2001)

    Article  Google Scholar 

  18. 18.

    Nezhad, A.S., Vatani, M., Barazandeh, F., Rahimi, A.: Build time estimator for determining optimal part orientation. Proc. Inst. Mech. Eng. B J. Eng. Manuf. 224(12), 1905–1913 (2010)

    Article  Google Scholar 

  19. 19.

    Pandey, P.M., Thrimurthulu, K., Reddy, N.V.: Optimal part deposition orientation in FDM by using a multicriteria genetic algorithm. Int. J. Prod. Res. 42(19), 4069–4089 (2004)

    Article  MATH  Google Scholar 

  20. 20.

    Chen, C.C., Sullivan, P.A.: Predicting total build-time and the resultant cure depth of the 3D stereolithography process. Rapid Prototyp. J. 2(4), 27–40 (1996)

    Article  Google Scholar 

  21. 21.

    Campbell, I., Combrinck, J., de Beer, D., Barnard, L.: Stereolithography build time estimation based on volumetric calculations. Rapid Prototyp. J. 14(5), 271–279 (2008)

    Article  Google Scholar 

  22. 22.

    Zhang, Y., Bernard, A., Valenzuela, J.M., Karunakaran, K.P.: Fast adaptive modeling method for build time estimation in additive manufacturing. CIRP J. Manuf. Sci. Technol. 10, 49–60 (2015)

    Article  Google Scholar 

  23. 23.

    Choi, S.H., Samavedam, S.: Modelling and optimisation of rapid prototyping. Comput. Ind. 47(1), 39–53 (2002)

    Article  Google Scholar 

  24. 24.

    Kim, H.C., Lee, S.H.: Reduction of post-processing for stereolithography systems by fabrication-direction optimization. Comput. Aided Des. 37(7), 711–725 (2005)

    Article  Google Scholar 

  25. 25.

    Reeves, P.E., Cobb, R.C.: Reducing the surface deviation of stereolithography using an alternative building strategy. In: Proceedings of Solid Freeform Fabrication Symposium, pp. 193–203 (1998)

  26. 26.

    Ordaz-Hernandez, K., Fischer, X., Bennis, F.: Granular modelling for virtual prototyping in interactive design. Virtual Phys. Prototyp. 2(2), 111–126 (2007)

    Article  Google Scholar 

  27. 27.

    Nadeau, J.P., Fischer, X.: Research in Interactive Design: Virtual, Interactive and Integrated Product Design and Manufacturing for Industrial Innovation. Springer, Berlin (2010)

    Google Scholar 

  28. 28.

    Dolenc, A., Mäkelä, I.: Rapid prototyping from a computer scientist’s point of view. Rapid Prototyp. J. 2(2), 18–25 (1996)

    Article  Google Scholar 

  29. 29.

    Mohan Pandey, P., Venkata Reddy, N., Dhande, S.G.: Slicing procedures in layered manufacturing: a review. Rapid prototyp. J. 9(5), 274–288 (2003)

    Article  Google Scholar 

  30. 30.

    He, Y., Zhang, F., Saleh, E., Vaithilingam, J., Aboulkhair, N., Begines, B., Wildman, R.D.: A tripropylene glycol diacrylate-based polymeric support ink for material jetting. Addit. Manuf. 16, 153–161 (2017).

  31. 31.

    Strano, G., Hao, L., Everson, R.M., Evans, K.E.: A new approach to the design and optimisation of support structures in additive manufacturing. Int. J. Adv. Manuf. Technol. 66, 1–8 (2013)

    Article  Google Scholar 

  32. 32.

    Barnett, E., Gosselin, C.: Weak support material techniques for alternative additive manufacturing materials. Addit. Manuf. 8, 95–104 (2015)

    Article  Google Scholar 

  33. 33.

    Campbell, R.I., Martorelli, M., Lee, H.S.: Surface roughness visualisation for rapid prototyping models. Comput. Aided Des. 34(10), 717–725 (2002)

    Article  Google Scholar 

  34. 34.

    McClurkin, J.E., Rosen, D.W.: Computer-aided build style decision support for stereolithography. Rapid Prototyp. J. 4(1), 4–13 (1998)

    Article  Google Scholar 

  35. 35.

    Bacchewar, P.B., Singhal, S.K., Pandey, P.M.: Statistical modelling and optimization of surface roughness in the selective laser sintering process. Proc. Inst. Mech. Eng. B J. Eng. Manuf. 221(1), 35–52 (2007)

    Article  Google Scholar 

  36. 36.

    Ahn, D., Kim, H., Lee, S.: Surface roughness prediction using measured data and interpolation in layered manufacturing. J. Mater. Process. Technol. 209(2), 664–671 (2009)

    Article  Google Scholar 

  37. 37.

    McKay, M.D., Beckman, R.J., Conover, W.J.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 42(1), 55–61 (2000)

    Article  MATH  Google Scholar 

  38. 38.

    Leary, S., Bhaskar, A., Keane, A.: Optimal orthogonal-array-based latin hypercubes. J. Appl. Stat. 30(5), 585–598 (2003)

    MathSciNet  Article  MATH  Google Scholar 

  39. 39.

    Angeles, J.: The role of the rotation matrix in the teaching of planar kinematics. Mech. Mach. Theory 89, 28–37 (2015)

    Article  Google Scholar 

  40. 40.

    Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments. Stat. Sci. 4, 409–423 (1989)

    MathSciNet  Article  MATH  Google Scholar 

  41. 41.

    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.A.M.T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  42. 42.

    Hwang, C.L., Masud, A.S.M.: Multiple Objective Decision Making—Methods and Applications: A State-of-the-Art Survey, vol. 164. Springer, Berlin (2012)

    Google Scholar 

  43. 43.

    Thrimurthulu, K.P.P.M., Pandey, P.M., Reddy, N.V.: Optimum part deposition orientation in fused deposition modeling. Int. J. Mach. Tools Manuf. 44(6), 585–594 (2004)

    Article  Google Scholar 

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Correspondence to S. Khodaygan.

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Khodaygan, S., Golmohammadi, A.H. Multi-criteria optimization of the part build orientation (PBO) through a combined meta-modeling/NSGAII/TOPSIS method for additive manufacturing processes. Int J Interact Des Manuf 12, 1071–1085 (2018).

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  • Additive manufacturing
  • Multi-criteria optimization
  • Part build orientation
  • Build time
  • Surface roughness