Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

RBF and NSGA-II based EDM process parameters optimization with multiple constraints

1 Henan Key Laboratory of Mechanical Equipment Intelligent Manufacturing, School of Mechanical and Electrical Engineering, Zhengzhou University of Light Industry, Zhengzhou, MO 450002, China
2 College of Mechanical Engineering, Donghua University, Shanghai, MO 201620, China

Special Issues: Artificial Intelligence and Optimization in Sustainable Manufacturing

In this study, the radial basis function (RBF) which has good performance for nonlinear problem is introduced to approximate the implicit relationships between EDM parameters and performance responses for 304 steel. The fitting precision of RBF is compared with the second order polynomial response surface (PRS), support vector regression (SVR) and Kriging model (KRG) using the multiple correlation coefficient (R2) based cross validation error method. Then the RBF model is called to conduct multi-objective optimization using non-dominated sorting genetic algorithm II (NSGA-II) method. The energy consumption index unit energy consumption (UEC) and the air-pollution indices PM2.5 and PM10 are considered in proposed multi-objective optimization model. UEC is considered as the objective function to reduce the machining cost and the PM indices are termed as the constraints to protect the operators’ health. The pulse current, time period and duty cycle are considered as the main factors affecting the EDM responses. According to the Pareto plots of multi-objective optimization model, conclusion can be drawn that SR and PM10 play significant roles in multi-optimization and PM2.5 has less influence on optimization results. The results of the present study reveal that using maximum material removal rate (MRR) and minimum UEC as objective and using surface roughness (SR), PM2.5 and PM10 as constraints can be an effective method to provide appropriate process parameters reference for EDM machining.
  Article Metrics

Keywords EDM; process parameter optimization; RBF; NSGA-II

Citation: Xiaoke Li, Fuhong Yan, Jun Ma, Zhenzhong Chen, Xiaoyu Wen, Yang Cao. RBF and NSGA-II based EDM process parameters optimization with multiple constraints. Mathematical Biosciences and Engineering, 2019, 16(5): 5788-5803. doi: 10.3934/mbe.2019289


  • 1. A. M. Nikalje, A. Kumar and S. K. V. Sai, Influence of parameters and optimization of EDM performance measures on MDN 300 steel using Taguchi method, Int. J. Adv. Manuf. Tech., 69 (2013), 41–49.
  • 2. X. P. Dang, Constrained multi-objective optimization of EDM process parameters using kriging model and particle swarm algorithm, Mater. Manuf. Process., 33 (2018), 397–404.
  • 3. G. D'Urso, C. Giardini, G. Maccarini, et al., Analysis of the surface quality of steel and ceramic materials machined by micro-EDM, European Society for Precision Engineering and Nanotechnology, Conference Proceedings-18th International Conference and Exhibition, EUSPEN 2018, 431–432.
  • 4. G. D'Urso, C. Giardini and M. Quarto, Characterization of surfaces obtained by micro-EDM milling on steel and ceramic components, Int. J. Adv. Manuf. Tech., 97 (2018), 2077–2085.
  • 5. S. Gopalakannan, T. Senthilvelan and S. Ranganathan, Modeling and Optimization of EDM Process Parameters on Machining of Al 7075-B 4 C MMC Using RSM, Procedia Eng., 38 (2012), 685–690.
  • 6. H. Mohammadjifar, L. Q. Bui and C. T. Ngyen, Experimental investigation of the effects of tool initial surface roughness on the electrical discharge machining (EDM) performance, Int. J. Adv. Manuf. Tech., 95 (2018), 2093–2104.
  • 7. J. L. Lin, K. S. Wang, B. H. Yan, et al., Optimization of the electrical discharge machining process based on the Taguchi method with fuzzy logics, J. Mater. Process. Tech., 102 (2000), 48–55.
  • 8. K. P. Somashekhar, N. Ramachandran and J. Mathew, Optimization of material removal rate in micro-EDM using artificial neural network and genetic algorithms, Mater. Manuf. Process., 25 (2010), 467–475.
  • 9. M. Arindam, Process parameter optimization during EDM of AISI 316 LN stainless steel by using fuzzy based multi-objective PSO, J. Mech. Sci. Tech., 27 (2013), 2143–2151.
  • 10. G. D'Urso, C. Giardini, M. Quarto, et al., Cost index model for the process performance optimization of micro-EDM drilling on tungsten carbide, Micromach., 8 (2017), 251.
  • 11. S. Parsana, N. Radadia, M. Sheth, et al., Machining parameter optimization for EDM machining of Mg–RE–Zn–Zr alloy using multi-objective Passing Vehicle Search algorithm, Arch. Civ. Mech. Eng., 18 (2018), 799–817.
  • 12. G. Rajyalakshmi and P. V. Ramaiah, Multiple process parameter optimization of wire electrical discharge;machining on Inconel 825 using Taguchi grey relational analysis, Int. J. Adv. Manuf. Tech., 69 (2013), 1249–1262.
  • 13. R. Świercz, D. Oniszczuk-Świercz and T. Chmielewski, Multi-Response Optimization of Electrical Discharge Machining Using the Desirability Function, Micromach., 10 (2019), 72.
  • 14. P. S. Bharti, S. Maheshwari and C. Sharma, Multi-objective optimization of electric-discharge machining process using controlled elitist NSGA-II, J. Mech. Sci. Tech., 26 (2012), 1875–1883.
  • 15. D. Kanagarajan, R. Karthikeyan, K. Palanikumar, et al., Optimization of electrical discharge machining characteristics of WC/Co composites using non-dominated sorting genetic algorithm (NSGA-II), Int. J. Adv. Manuf. Tech., 36 (2008), 1124–1132.
  • 16. C. Ulas and H. Ahmet, Modeling and analysis of electrode wear and white layer thickness in die-sinking EDM process through response surface methodology, Int. J. Adv. Manuf. Tech., 38 (2008), 1148–1156.
  • 17. A. Majumder, P. K. Das, A. Majumber, et al., An approach to optimize the EDM process parameters using desirability-based multi-objective PSO, Prod. Manuf. Res., 2 (2014), 228–240.
  • 18. F. G. Cao and D. Y. Yang, The study of high efficiency and intelligent optimization system in EDM sinking process, J. Mater. Process. Tech., 49 (2004), 83–87.
  • 19. G. K. M. Rao, G. Rangajanardhaa, D. H. Rao, et al., Development of hybrid model and optimization of surface roughness in electric discharge machining using artificial neural networks and genetic algorithm, J. Mater. Process. Tech., 209 (2009), 1512–1520.
  • 20. G. Rajyalakshmi and P. V. Ramaiah, Multiple process parameter optimization of wire electrical discharge machining on Inconel 825 using Taguchi grey relational analysis, Int. J. Adv. Manuf. Tech., 69 (2013), 1249–1262.
  • 21. R. Maneswar and P. P. Kumar, Parametric optimization for selective surface modification in EDM using Taguchi analysis, Mater. Manuf. Process., 31 (2016), 422–431.
  • 22. J. L. Lin and C. L. Lin, The use of the orthogonal array with grey relational analysis to optimize the electrical discharge machining process with multiple performance characteristics, Int. J. Mach. Tool. Manuf., 42 (2002), 237–244.
  • 23. P. Sathiya, S. Aravindan and A. N. Haq, Mechanical and metallurgical properties of friction welded AISI 304 austenitic stainless steel, Int. J. Adv. Manuf. Tech., 26 (2005), 505–511.
  • 24. Z. Zhang, X. Q. Yang and H. Ma, Optimization of Enzymatic Hydrolysis of Tilapia Waste by Plackett-Burman Design and Central Composite Design, Food Sci., 32 (2011), 1–5.
  • 25. X. Li, C. Gong, L. Gu, et al., A reliability-based optimization method using sequential surrogate model and Monte Carlo simulation, Struct. Multidiscip. O., (2018), 1–22.
  • 26. F. Biancofiore, M. Busilacchio, M. Verdecchia, et al., Recursive neural network model for analysis and forecast of PM10 and PM2.5, Atmo. Pollut. Res., 8 (2017), 652–659.
  • 27. Q. Zhou, H. Jiang, J. Wang, et al., A hybrid model for PM 2.5 forecasting based on ensemble empirical mode decomposition and a general regression neural network, Sci. Total Environ., 496 (2014), 264–274.
  • 28. K. Deb, A. Pratap, S. Agarwal, et al., A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE T. Evolut. Comput., 6 (2002), 182–197.
  • 29. H. Li and Q. F. Zhang, Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II, IEEE T. Evolut. Comput., 13 (2009), 284–302.
  • 30. S. Mardle and K. M. Miettinen, Nonlinear multiobjective optimization, J. Oper. Res. Soc., 51 (2000), 246.
  • 31. R. Gudolph, On a multi-objective evolutionary algorithm and its convergence to the Pareto set, IEEE International Conference on Evolutionary Computation, IEEE ICEC 1998, 511–516.
  • 32. S. Chaki, N. B. Rani, S. Ghosal, et al., Multi-objective optimisation of pulsed Nd:YAG laser cutting process using integrated ANN–NSGAII model, J. Intell. Manuf., 29 (2018), 175–190.
  • 33. T. Chang, J. Q. Lu, A. X. Shen, et al., Simulation and optimization of the post plasma-catalytic system for toluene degradation by a hybrid ANN and NSGA-II method, Appl. Catal. B-Environ., 244 (2019), 107–119.
  • 34. A. Adel, Y. Kai and M. Alper, ASRSM: A sequential experimental design for response surface optimization, Qual. Reliab. Eng. Int., 29 (2013), 241–258.
  • 35. W. Chen, M. H. Nguyen, W. H. Chiu, et al., Optimization of the plastic injection molding process using the Taguchi method, RSM, and hybrid GA-PSO, Int. J. Adv. Manuf. Tech., 83 (2016), 1873–1886.
  • 36. S. J. An, W. Q. Liu and S. Venkatesh, Fast cross-validation algorithms for least squares support vector machine and kernel ridge regression, Pattern Recogn., 40 (2005), 2154–2162.
  • 37. T. Chen and S. J. Lu, Accurate and efficient traffic sign detection using discriminative adaboost and support vector regression, IEEE T. Veh. Tech., 65 (2016), 4006–4015.
  • 38. X. K. Li, H. B. Qiu, Z. Z. Chen, et al., A local Kriging approximation method using MPP for reliability-based design optimization, Comput. Struct., 162 (2016), 102–115.
  • 39. X. K. Li, H. B. Qiu, Z. Z. Chen, et al., A local sampling method with variable radius for RBDO using Kriging, Eng. Computation., 32 (2015), 1908–1933.
  • 40. G. Shieh, Improved shrinkage estimation of squared multiple correlation coefficient and squared cross-validity coefficient, Organ. Res. Meth., 11 (2008), 387–407.
  • 41. H. Wang, S. Shan, G. G. Wang, et al., Integrating least square support vector regression and mode pursuing sampling optimization for crashworthiness design, J. Mech. Design, 133 (2011), 041002.


This article has been cited by

  • 1. Alaa M. Ubaid, Shukry H. Aghdeab, Ahmed Ghazi Abdulameer, Laith Abdullah Al-Juboori, Fikri T. Dweiri, Multidimensional optimization of electrical discharge machining for high speed steel (AISI M2) using Taguchi-fuzzy approach, International Journal of System Assurance Engineering and Management, 2020, 10.1007/s13198-020-00951-6

Reader Comments

your name: *   your email: *  

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved