Multi-objective optimization of multipass turning processes

  • N. R. Abburi
  • U. S. DixitEmail author


In this paper, a methodology is proposed for the multi-objective optimization of a multipass turning process. A real-parameter genetic algorithm (RGA) is used for minimizing the production time, which provides a nearly optimum solution. This solution is taken as the initial guess for a sequential quadratic programming (SQP) code, which further improves the solution. Thereafter, the Pareto-optimal solutions are generated without using the cost data. For any Pareto-optimal solution, the cost of production can be calculated at a higher level for known cost data. An objective method based on the linear programming model is proposed for choosing the best among the Pareto-optimal solutions. The entire methodology is demonstrated with the help of an example. The optimization is carried out with equal depths of cut for roughing passes. A simple numerical method has been suggested for estimating the expected improvement in the optimum solution if an unequal depth of cut strategy would have been employed.


Turning process Multi-objective optimization Real-parameter genetic algorithm Sequential quadratic programming Linear programming Lagrange multiplier 



Constant in extended Taylor’s tool life equation


Operating cost ($/min)


Tool cost ($)


Depth of cut (mm)


Depth of cut for the finishing pass (mm)


Depth of cut for the roughing pass (mm)


Final diameter of the work piece (mm)


Initial work piece diameter (mm)


Feed for the finishing pass (mm/rev)


Feed for the roughing pass (mm/rev)


Total production cost per piece ($)


Cutting force (kgf)


Fraction of tool consumed per piece

k, α, β

Constants used in the empirical relation for cutting force


Length of machining (mm)


Number of roughing passes


Exponent of extended Taylor’s tool life equation

p, q, r

Exponents of speed, feed, and depth of cut in tool life equation

pc, pm

Crossover and mutation probabilities


Maximum power (kW)

ri, ui

Random numbers between 0 and 1


Nose radius of cutting tool (mm)

\(R_{{t_{{\max }} }} \)

Peak-to-valley height of surface roughness for finishing pass


Tool change time (min)


Tool setting time per pass (min)


Total tool setting time (min)


Tool life for the finishing pass (min)


Loading/unloading time per component (min)

Tmax, Tmin

Maximum and minimum allowed values of tool life


Total production time per component (min)


Tool life for the roughing pass (min)


Total cutting time for finishing pass (min)


Total cutting time for roughing passes (min)


Cutting speed for the finishing pass (m/min)


Cutting speed for the roughing pass(m/min)


Machine efficiency


Crossover index


Mutation index


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  1. 1.
    Gilbert WW (1950) Economics of machining. Machining theory and practice. American Society of Metals, Cleveland, Ohio, pp 465–485Google Scholar
  2. 2.
    Ermer DS (1971) Optimization of the constrained machining economics problem by geometric programming. J Eng Ind 93:1067–1072Google Scholar
  3. 3.
    Petropoulos PG (1973) Optimal selection of machining rate variables by geometric programming. Int J Prod Res 11(4):305–314Google Scholar
  4. 4.
    Lambert BK, Walvekar AG (1978). Optimization of multipass machining operations. Int J Prod Res 16(4):259–265Google Scholar
  5. 5.
    Shin YC, Joo YS (1992) Optimization of machining conditions with practical constraints. Int J Prod Res 30(12):2907–2919Google Scholar
  6. 6.
    Gupta R, Batra JL, Lal GK (1995) Determination of optimal subdivision of depth of cut in multipass turning with constraints. Int J Prod Res 33(9):2555–2565zbMATHGoogle Scholar
  7. 7.
    Yeo SH (1995) A multipass optimization strategy for CNC lathe operations. Int J Prod Econ 40(2–3):209–218CrossRefGoogle Scholar
  8. 8.
    Lee BY, Tarng YS (2000) Cutting parameter selection for maximizing production rate or minimizing production cost in multistage turning operations. J Mater Process Technol 105:61–66CrossRefGoogle Scholar
  9. 9.
    Wang J (1998) Computer-aided economic optimization of end-milling operations. Int J Prod Econ 54(3):307–320CrossRefGoogle Scholar
  10. 10.
    Shabtay D, Kaspi M (2002) Optimization of the machining economics problem under the failure replacement strategy. Int J Prod Econ 80(3):213–230CrossRefGoogle Scholar
  11. 11.
    Abuelnaga AM, El-Dardiry EA (1984) Optimization methods for metal cutting. Int J Mach Tool Des Res 24(1):11–18CrossRefGoogle Scholar
  12. 12.
    Chen MC, Tsai DM (1996) A simulated annealing approach for optimization of multipass turning operations. Int J Prod Res 34(10):2803–2825zbMATHGoogle Scholar
  13. 13.
    Onwubolu GC, Kumalo T (2001) Optimization of multipass turning operations with genetic algorithms. Int J Prod Res 39(16):3727–3745zbMATHCrossRefGoogle Scholar
  14. 14.
    Amiolemhen PE, Ibhadode AOA (2004) Application of genetic algorithms—determination of the optimal machining parameters in the conversion of a cylindrical bar stock into a continuous finished profile. Int J Mach Tools Manuf 44:1403–1412CrossRefGoogle Scholar
  15. 15.
    Shunmugam MS, Reddy SVB, Narendran TT (2000) Selection of optimal conditions in multi-pass face-milling using genetic algorithm. Int J Mach Tools Manuf 40:401–414CrossRefGoogle Scholar
  16. 16.
    Saravanan R, Ashokan P, Vijaykumar K (2003) Machining parameters optimisation for turning cylindrical stock into a continuous finished profile using genetic algorithm (GA) and simulated annealing (SA). Int J Adv Manuf Technol 21(1):1–9CrossRefGoogle Scholar
  17. 17.
    Davim JP, Antonio CAC (2001) Optimization of cutting conditions in machining of aluminium matrix composites using a numerical and experimental model. J Mater Process Technol 112:78–82CrossRefGoogle Scholar
  18. 18.
    Saravanan R, Sachithanandam M (2001) Genetic algorithm (GA) for multivariable surface grinding process optimization using a multi-objective function model. Int J Adv Manuf Technol 17(5):330–338CrossRefGoogle Scholar
  19. 19.
    Baskar N, Saravanan R, Ashokan P, Prabhaharan G (2004) Ants colony algorithm approach for multi-objective optimisation of surface grinding operations. Int J Adv Manuf Technol 23:311–317CrossRefGoogle Scholar
  20. 20.
    Tosun N, Ozler L (2004) Optimisation of hot turning operations with multiple performance characteristics. Int J Adv Manuf Technol 23(11–12):777–782Google Scholar
  21. 21.
    Cauchick-Miguel PA, Coppini NL (1996) Cost per piece determination in machining process: an alternative approach. Int J Mach Tools Manuf 36(8):939–946CrossRefGoogle Scholar
  22. 22.
    Arora JS (1989) Introduction to optimum design. McGraw-Hill, New YorkGoogle Scholar
  23. 23.
    Rao SS (1984) Optimization: theory and applications, 2nd edn. Wiley, New YorkzbMATHGoogle Scholar
  24. 24.
    Deb K (2001) Multiobjective optimization using evolutionary algorithms. Wiley, SingaporeGoogle Scholar
  25. 25.
    Kohli A, Dixit US (2004) A neural network based methodology for prediction of surface roughness in turning process. Int J Adv Manuf Technol 25(1–2):118–129Google Scholar
  26. 26.
    Ojha DK, Dixit US (2005) An economic and reliable tool life estimation procedure for turning. Int J Adv Manuf Technol 26(7–8):726–732CrossRefGoogle Scholar

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© Springer-Verlag London Limited 2006

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of TechnologyGuwahatiIndia

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