A hybrid PSO–BFO evolutionary algorithm for optimization of fused deposition modelling process parameters

  • Maraboina Raju
  • Munish Kumar GuptaEmail author
  • Neeraj Bhanot
  • Vishal S. Sharma


Fused deposition modeling (FDM), a well known 3D printing technology is widely used in various sorts of industrial applications because of its ability to manufacture complex objects in the stipulated time. However, the proper selection of input process parameters in FDM is a tedious task that directly affects the part performance. Here, in this work, the research efforts have been made to optimize the FDM process parameters in order to find out the best parameter setting as per the mechanical and surface quality perspectives by using hybrid particle swarm and bacterial foraging optimization (PSO–BFO) evolutionary algorithm. Taguchi L18 orthogonal array was used for the development of acro-nitrile butadiene styrene based 3D components by considering layer thickness, support material, model interior and orientation as a process parameters. Further, the relationships among selected FDM process parameters and output responses such as hardness, flexural modulus, tensile strength and surface roughness were established by using linear multiple regression. Then, the effects of individual process parameters on selected response parameters were examined by signal to noise ratio plots. Finally, a multi-objective optimization of process parameters has been performed with hybrid PSO–BFO, general PSO and BFO algorithm, respectively. The overall results reveal that the layer thickness of 0.007 mm, support material type sparse, part orientation of 60\({^\circ }\) and model interior of high density helps in achieving desired performance level.


Evolutionary algorithm Mechanical properties Optimization Surface roughness Rapid prototyping 



Fused deposition modeling


Bacterial foraging optimization


Signal to noise


Flexural modulus


Surface roughness


Model interior


Support material


No. of bacteria in population


No. of reproduction steps


No. of swim


Particle best position (PSO)


Maximum inertia weight (PSO)


Current iteration (PSO)


Length of unit walk (BFO)

\(Jcc \left( \theta ,P\left( {j,k,l} \right) \right) \)

Cost function value (BFO)


Particle swarm optimization


Acro-nitrile butadiene styrene




Tensile strength


Layer thickness


Part orientation


Additive manufacturing


No. of elimination–dispersion


No. of chemo-tactic steps


Dispersion probability


Global best position (PSO)

\(w_{min} \)

Minimum inertia weight (PSO)


Total number of iteration (PSO)

\(\phi \left( i \right) \)

Direction angle of the jth step (BFO)



The authors acknowledge the “Institute for Auto Parts and Hand Tools Technology, Ludhiana” and “Central Institute of Plastics Engineering and Technology, Amritsar” for helping in carrying out the experiments.

Author Contributions

The contributions of all authors are equivalent in this paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. Anguluri, R., Abraham, A., & Snasel, V. (2011). A hybrid bacterial foraging—PSO algorithm based tuning of optimal FOPI speed controller. Acta Montanistica Slovaca, 16(1), 55–65. Scholar
  2. Balogun, V. A., Kirkwood, N. D., & Mativenga, P. T. (2014). Direct electrical energy demand in fused deposition modelling. Procedia CIRP, 15, 38–43.CrossRefGoogle Scholar
  3. Bikas, H., Stavropoulos, P., & Chryssolouris, G. (2015). Additive manufacturing methods and modelling approaches?: A critical review. International Journal of Advanced Manufacturing Technology,. Scholar
  4. Biswas, A., Dasgupta, S., Das, S., & Abraham, A. (2007). Synergy of PSO and bacterial foraging optimization—A comparative study on numerical benchmarks. In E. Corchado, J. M. Corchado, & A. Abraham (Eds.), Innovations in hybrid intelligent systems (pp. 255–263). Berlin: Springer. Scholar
  5. Chen, C., Su, M., Lin, C., & Lin, C. (2014). A hybrid of bacterial foraging optimization and particle swarm optimization for evolutionary neural fuzzy classifier. International Journal of Fuzzy Systems, 16(3), 422–433.Google Scholar
  6. El-Wakeel, A. S., Ellissy, A. E.-E. K. M., & Abdel-hamed, A. M. (2015). A hybrid bacterial foraging–particle swarm optimization technique for optimal tuning of proportional–integral–derivative controller of a permanent magnet brushless DC motor. Electric Power Components and Systems, 43(3), 309–319. Scholar
  7. Elazim, S. M. A., & Ali, E. S. (2015). A hybrid particle swarm optimization and bacterial foraging for power system stability enhancement. Wiley Periodicals, 21(2), 245–255. Scholar
  8. Filipovic, V., Nedic, N., & Stojanovic, V. (2011). Robust identification of pneumatic servo actuators in the real situations. Forschung im Ingenieurwesen, 75(4), 183–196. Scholar
  9. Galantucci, L. M., Lavecchia, F., & Percoco, G. (2009). Experimental study aiming to enhance the surface finish of fused deposition modeled parts. CIRP Annals—Manufacturing Technology, 58, 189–192. Scholar
  10. Garg, A., Tai, K., Lee, C. H., & Savalani, M. M. (2013). A hybrid M5–Genetic programming approach for ensuring greater trustworthiness of prediction ability in modelling of FDM process. Journal of Intelligent Manufacturing.
  11. Garg, S., Patra, K., & Pal, S. K. (2014). Particle swarm optimization of a neural network model. Sadhana, 39, 533–548.CrossRefGoogle Scholar
  12. Güler, T., Demirci, E., Yıldız, A. R., & Yavuz, U. (2018). Lightweight design of an automobile hinge component using glass fiber polyamide composites. Materials Testing, 60(3), 306–310. Scholar
  13. Gupta, M. K., Singh, G., & Sood, P. K. (2015). Modelling and optimization of tool wear in machining of EN24 steel using taguchi approach. Journal of The Institution of Engineers (India): Series C, 96, 269–277. Scholar
  14. Gupta, M. K., & Sood, P. (2017). Machining comparison of aerospace materials considering minimum quantity cutting fluid: A clean and green approach. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 231(8), 1445–1464. Scholar
  15. Gupta, M. K., Sood, P. K., & Sharma, V. S. (2016a). Machining parameters optimization of titanium alloy using response surface methodology and particle swarm optimization under minimum quantity lubrication environment. Materials and Manufacturing Processes, 31, 1671–1682. Scholar
  16. Gupta, M. K., Sood, P. K., & Sharma, V. S. (2016b). Optimization of machining parameters and cutting fluids during nano-fluid based minimum quantity lubrication turning of titanium alloy by using evolutionary techniques. Journal of Cleaner Production, 135, 1276–1288. Scholar
  17. Gurrala, P. K., & Regalla, S. P. (2014). DOE based parametric study of volumetric change of FDM parts. Procedia Materials Science, 6, 354–360.CrossRefGoogle Scholar
  18. Homami, R. M., Tehrani, A. F., Mirzadeh, H., Movahedi, B., & Azimifar, F. (2014). Optimization of turning process using artificial intelligence technology. The International Journal of Advanced Manufacturing Technology, 70(5–8), 1205–1217. Scholar
  19. Karagoz, S., & Yildiz, A. R. (2017). A comparison of recent metaheuristic algorithms for crashworthiness optimisation of vehicle thin-walled tubes considering sheet metal forming effects. International Journal of Vehicle Design, 73(1–3, SI), 179–188. Scholar
  20. Kiani, M., & Yildiz, A. R. (2016). A comparative study of non-traditional methods for vehicle crashworthiness and NVH optimization. Archives of Computational Methods in Engineering, 23(4), 723–734. Scholar
  21. Kora, P., & Kalva, S. R. (2015). Hybrid bacterial foraging and particle swarm optimization for detecting bundle branch block. SpringerPlus,. Scholar
  22. Kumar, A., Ohdar, R. K., & Mahapatra, S. S. (2009). Improving dimensional accuracy of fused deposition modelling processed part using grey taguchi method. Materials and Design, 30(10), 4243–4252. Scholar
  23. Mohamed, O. A., Masood, S. H., & Bhowmik, J. L. (2016). Mathematical modeling and FDM process parameters optimization using response surface methodology based on Q-optimal design. Applied Mathematical Modelling, 40(23), 10057–10073.Google Scholar
  24. Nedić, N., Pršić, D., Fragassa, C., Stojanović, V., & Pavlovic, A. (2017). Simulation of hydraulic check valve for forestry equipment. International Journal of Heavy Vehicle Systems, 24(3), 260–276.CrossRefGoogle Scholar
  25. Nuñez, P. J., Rivas, A., García-Plaza, E., Beamud, E., & Sanz-Lobera, A. (2015). Dimensional and surface texture characterization in fused deposition modelling (FDM) with ABS plus. Procedia Engineering, 132, 856–863.CrossRefGoogle Scholar
  26. Onuh, S. O. Y., & Yusuf, Y. Y. (1999). Rapid prototyping technology?: Applications and benefits for rapid product development. Journal of Intelligent Manufacturing, 10, 301–311.CrossRefGoogle Scholar
  27. Panda, B., Akhil, K. S., & Savalani, G. M. M. (2016). Evaluation of genetic programming-based models for simulating bead dimensions in wire and arc additive manufacturing. Journal of Intelligent Manufacturing,. Scholar
  28. Peng, A., Xiao, X., & Yue, R. (2014). Process parameter optimization for fused deposition modeling using response surface methodology combined with fuzzy inference system. International Journal of Advanced Manufacturing Technology, 73(1–4), 87–100.CrossRefGoogle Scholar
  29. Phatak, A. M., & Pande, S. S. (2012). Optimum part orientation in rapid prototyping using genetic algorithm. Journal of manufacturing systems, 31(4), 395–402.CrossRefGoogle Scholar
  30. Phokane, T., Gupta, K., & Gupta, M. K. (2017). Investigations on surface roughness and tribology of miniature brass gears manufactured by abrasive water jet machining. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science.
  31. Pholdee, N., Bureerat, S., & Yildiz, A. R. (2017). Hybrid real-code population-based incremental learning and differential evolution for many-objective optimisation of an automotive floor-frame. International Journal of Vehicle Design, 73(1), 20–53. Scholar
  32. Pršić, D., Nedić, N., & Stojanović, V. (2017). A nature inspired optimal control of pneumatic-driven parallel robot platform. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 231(1), 59–71. Scholar
  33. Rao, R. V., & Kalyankar, V. D. (2013). Experimental investigation on submerged arc welding of Cr–Mo–V steel. The International Journal of Advanced Manufacturing Technology, 69(1–4), 93–106. Scholar
  34. Reeves, P. E., & Cobb, R. C. (1995). Surface deviation modelling of LMT process—A comparative analysis. In Fifth European conference on rapid prototyping and manufaturing, University of Nottingham, U.K. (pp. 59–77).Google Scholar
  35. Singh, R., & Gupta, M. K. (2017). Experimental investigations for modelling hardness of ABS replica based investment castings. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 10, 100. Scholar
  36. Singh, R., Singh, S., Singh, I. P., Fabbrocino, F., & Fraternali, F. (2017). Investigation for surface finish improvement of FDM parts by vapor smoothing process. Composites Part B: Engineering, 111, 228–234.CrossRefGoogle Scholar
  37. Sood, A. K., Ohdar, R. K., & Mahapatra, S. S. (2012). Experimental investigation and empirical modelling of FDM process for compressive strength improvement. Journal of Advanced Research, 3(1), 81–90.CrossRefGoogle Scholar
  38. Stojanovic, V., & Filipovic, V. (2014). Adaptive input design for identification of output error model with constrained output. Circuits, Systems, and Signal Processing, 33(1), 97–113. Scholar
  39. Stojanovic, V., & Nedic, N. (2016). Robust identification of OE model with constrained output using optimal input design. Journal of the Franklin Institute, 353(2), 576–593. Scholar
  40. Stojanovic, V., Nedic, N., Prsic, D., Dubonjic, L., & Djordjevic, V. (2016). Application of cuckoo search algorithm to constrained control problem of a parallel robot platform. International Journal of Advanced Manufacturing Technology, 87(9–12), 2497–2507. Scholar
  41. Vladimir, S., & Novak, N. (2016). Identification of time-varying OE models in presence of non-Gaussian noise: Application to pneumatic servo drives. International Journal of Robust and Nonlinear Control, 26(18), 3974–3995. Scholar
  42. Wang, W. L., Conley, J. G., Yan, Y. N., & Fuh, J. Y. H. (2000). Towards intelligent setting of process parameters for layered manufacturing. Journal of Intelligent Manufacturing, 11, 65–74.CrossRefGoogle Scholar
  43. Xiaolong, L., Rongjun, L., & Ping, Y. (2010). A bacterial foraging global optimization algorithm based on the particle swarm optimization. In 2010 IEEE international conference on intelligent computings and intellignet systems (pp. 22–27).Google Scholar
  44. Yildiz, A. R. (2012). A comparative study of population-based optimization algorithms for turning operations. Information Sciences, 210, 81–88. Scholar
  45. Yildiz, A. R. (2013). Comparison of evolutionary-based optimization algorithms for structural design optimization. Engineering Applications of Artificial Intelligence, 26(1), 327–333. Scholar
  46. Yildiz, A. R., & Öztürk, F. (2010). Hybrid taguchi–harmony search approach for shape optimization. In Z. W. Geem (Ed.), Recent Advances in Harmony Search Algorithm (pp. 89–98). Berlin: Springer. Scholar
  47. Yildiz, A. R., & Saitou, K. (2011). Topology synthesis of multicomponent structural assemblies in continuum domains. Journal of Mechanical Design, 133(1), 11008. Scholar
  48. Yıldız, B. S. (2017). A comparative investigation of eight recent population-based optimisation algorithms for mechanical and structural design problems. International Journal of Vehicle Design, 73(1/2/3), 208. Scholar
  49. Yıldız, B. S., & Lekesiz, H. (2017). Fatigue-based structural optimisation of vehicle components. International Journal of Vehicle Design, 73(1/2/3), 54. Scholar
  50. Yildiz, B. S., Lekesiz, H., & Yildiz, A. R. (2016). Structural design of vehicle components using gravitational search and charged system search algorithms. Materials Testing, 58(1), 79–81. Scholar
  51. Yıldız, B. S., & Yıldız, A. R. (2017). Optimization of thin-wall structures using hybrid gravitational search and Nelder–Mead algorithm. Materials Testing, 58(1), 75–78. Scholar
  52. Yıldız, B. S., & Yıldız, A. R. (2018). Comparison of grey wolf, whale, water cycle, ant lion and sine–cosine algorithms for the optimization of a vehicle engine connecting rod. Materials Testing, 60(3), 311–315. Scholar
  53. Zhang, Y., Bernard, A., Harik, R., & Karunakaran, K. P. (2015). Build orientation optimization for multi-part production in additive manufacturing. Journal of Intelligent Manufacturing,. Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Maraboina Raju
    • 1
  • Munish Kumar Gupta
    • 2
    Email author
  • Neeraj Bhanot
    • 3
  • Vishal S. Sharma
    • 1
  1. 1.I & P DepartmentDr. B. R. Ambedkar NIT JalandharJalandharIndia
  2. 2.MEDNITHamirpurIndia
  3. 3.Department of Quantitative methods and Operation ManagementIndian Institute of ManagementAmritsarIndia

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