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A nonlinear goal-programming-based DE and ANN approach to grade optimization in iron mining

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Abstract

This study proposes a combined ‘nonlinear goal-programming’-based ‘differential evolution’ (DE) and ‘artificial neural networks’ (ANN) methodology for grade optimization in iron mining production processes. The nonlinear goal-programming model has decision variables of ‘cutoff grade,’ ‘dressing grade’ and ‘concentrate grade,’ with the goals being ‘concentrate output,’ ‘resource utilization rate’ and ‘economic benefit (profit).’ The model, which contains three unknown functions, the ‘loss rate,’ the ‘ore-dressing metal recovery rate’ and the ‘total cost,’ is subsequently converted into an unconstrained optimization problem, to be solved by our integrated DE–ANN approach. DE is used to search for the optimum combination of the cutoff, dressing and concentrate grades, with the crossover rate in the DE analysis being dynamically adjusted within the evolutionary process. The loss rate is calculated by a regression model, whilst the ore-dressing metal recovery rate and the total cost functions are, respectively, calculated using ‘back-propagation’ and ‘radial basis function’ neural networks. We subsequently go on to analyze a case study of the Daye iron mine in China to demonstrate the reliability and efficiency of our proposed approach. Our study provides a novel approach for decision makers to guide production and management in iron mining.

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References

  1. Osanloo M, Ataei M (2003) Using equivalent grade factors to find the optimum cut-off grades of multiple metal deposits. Miner Eng 16(8):771–776

    Article  Google Scholar 

  2. Bascetin A, Nieto A (2007) Determination of optimal cut-off grade policy to optimize NPV using a new approach with optimization factor. J S Afr Inst Min Metall 107(2):87–94

    Google Scholar 

  3. Asad MWA, Topal E (2011) Net present value maximization model for optimum cut-off grade policy of open pit mining operations. J S Afr Inst Min Metall 111(11):741–750

    Google Scholar 

  4. Li K, Liu B, Zhang W (1997) General system for determining rational dressing grade. J Beijing Univ Sci Technol 19(5):425–428

    Google Scholar 

  5. Yuan H, Liu B, Li K (2002) Study on dynamic optimization of the dressing grade. J Beijing Univ Sci Technol 24(3):239–242

    Google Scholar 

  6. Jiang A, Zhao D, Sun H (2003) The development of a decision support system for optimizing the dressing grade. Min Res Devel 23(4):43–45

    Google Scholar 

  7. Shi Y, Mai X, Cao J, Yu Y (2003) Optimization of multi-objects for iron concentrate grade. Min Metall Eng 23(2):46–48

    Google Scholar 

  8. Li K, Qin Y, Liu B, Yuan H (2005) General optimization system of iron concentrate grade. J Beijing Univ Sci Technol 27(1):114–118

    Google Scholar 

  9. Reddick JF, Hesketh AH, Morar SH, Bradshaw DJ (2009) An evaluation of factors affecting the robustness of colour measurement and its potential to predict the grade of flotation concentrate. Miner Eng 22(1):64–69

    Article  Google Scholar 

  10. Charnes A, Cooper WW (1957) Management models and industrial applications of linear programming. Manag Sci 4(1):38–91

    Article  MathSciNet  MATH  Google Scholar 

  11. Ijiri Y (1996) Management goals and accounting for control. North-Holland Publishing Company, Amsterdam

    Google Scholar 

  12. Lee SM (1972) Goal programming for decision analysis. Auerbach, Philadelphia

    Google Scholar 

  13. Ignizio JP (1976) Goal programming and extensions. Lexington Books, Lexington

    Google Scholar 

  14. Ignizio JP (1978) A review of goal programming: a tool for multi-objective analysis. J Oper Res Soc 29(11):1109–1119

    Article  MATH  Google Scholar 

  15. Romero C (1986) A survey of generalized goal programming (1970–1982). Eur J Oper Res 25(2):183–191

    Article  MathSciNet  MATH  Google Scholar 

  16. Tamiz M, Jones DF, El-Darzi E (1995) A review of goal programming and its applications. Ann Oper Res 58(1):39–53

    Article  MathSciNet  MATH  Google Scholar 

  17. Tyagi S, Yang K, Tyagi A, Verma A (2012) A fuzzy goal programming approach for optimal product family design of mobile phones and multiple-platform architecture. IEEE Trans Syst Man Cybern Part C Appl Rev 42(6):1519–1530

    Article  Google Scholar 

  18. Kaveh KD, Soheil SN, Madjid T (2013) Solving multi-period project selection problems with fuzzy goal programming based on TOPSIS and a fuzzy preference relation. Inf Sci 252(10):42–61

    MathSciNet  MATH  Google Scholar 

  19. Parisa SS, Reza TM, Hamed K (2013) Solving a multi-objective multi-skilled manpower scheduling model by a fuzzy goal programming approach. Appl Math Model 37(7):5424–5443

    Article  MathSciNet  Google Scholar 

  20. Chen VYX (1994) A 0–1 goal programming model for scheduling multiple maintenance projects at a copper mine. Eur J Oper Res 76(1):176–191

    Article  MATH  Google Scholar 

  21. Chanda EKC, Dagdelen K (1995) Optimal blending of mine production using goal programming and interactive graphics systems. Int J Surf Min Reclam Environ 9(4):203–208

    Article  Google Scholar 

  22. Mukherjee K, Bera A (1995) Application of goal programming in project selection decisions: a case study from the Indian coal mining industry. Eur J Oper Res 82(1):18–25

    Article  MATH  Google Scholar 

  23. Saber HM, Ravindran A (1996) A partitioning gradient-based (PGB) algorithm for solving non-linear goal-programming problems. Comput Oper Res 23(2):141–152

    Article  MathSciNet  MATH  Google Scholar 

  24. Zheng DW, Gen M, Ida K (1996) Evolution program for non-linear goal programming. Comput Ind Eng 31(3–4):907–911

    Article  Google Scholar 

  25. Gen M, Ida K, Lee J, Kim J (1997) Fuzzy non-linear goal programming using genetic algorithms. Comput Ind Eng 33(1–2):39–42

    Article  Google Scholar 

  26. Deb K (2001) Non-linear goal programming using multi-objective genetic algorithms. J Oper Res Soc 52(3):291–302

    Article  MathSciNet  MATH  Google Scholar 

  27. Jana RK, Biswal MP (2006) Genetic-based fuzzy goal programming for multi-objective chance-constrained programming problems with continuous random variables. Int J Comput Math 83(2):171–179

    Article  MathSciNet  MATH  Google Scholar 

  28. Sharma DK, Jana RK (2009) Fuzzy goal programming-based genetic algorithm approach to nutrient management for rice crop planning. Intern J Product Econ 121(1):224–232

    Article  Google Scholar 

  29. Pal BB, Chakraborti D, Biswas P, Mukhopadhyay A (2012) An application of genetic algorithm method for solving patrol manpower deployment problems through fuzzy goal programming in a traffic management system: a case study. Int J Bio-inspired Comput 4(1):47–60

    Article  Google Scholar 

  30. Chen KH, Su CT (2010) Activity assigning of fourth party logistics by particle swarm optimization-based preemptive fuzzy integer goal programming. Expert Syst Appl 37(5):3630–3637

    Article  Google Scholar 

  31. Tyagi SK, Yang K, Tyagi A, Dwivedi SN (2011) Development of a fuzzy goal programming model for optimization of lead time and cost in an overlapped product development project using a Gaussian adaptive particle swarm optimization-based approach. Eng Appl Artif Intell 24(5):866–879

    Article  Google Scholar 

  32. Jeroen CJHA, Marjan VH, Theodor JS (2003) Using simulated annealing and spatial goal programming for solving a multi-site land use allocation problem. Lect Notes Comput Sci 2632:448–463

    Article  MATH  Google Scholar 

  33. Mishraa S, Prakash B, Tiwaria MK, Lashkaric RS (2006) A fuzzy goal-programming model of machine tool selection and operation allocation problem in FMS: a quick converging simulated annealing-based approach. Int J Product Res 44(1):43–76

    Article  Google Scholar 

  34. Storn R, Price K (1997) Differential evolution: a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    Article  MathSciNet  MATH  Google Scholar 

  35. Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Syst Man Cybern Part B Cybern 15(1):4–31

    Google Scholar 

  36. Hwang CL, Masud A (1979) Multiple objective decision making methods and applications: a state-of-the-art survey. Springer, Berlin

    Book  MATH  Google Scholar 

  37. Masud A, Hwang CL (1981) Interactive sequential goal programming. J Oper Res Soc 32(5):391–400

    MathSciNet  MATH  Google Scholar 

  38. Weistroffer HR (1983) An interactive goal programming method for non- linear multiple-criteria decision-making problems. Comput Oper Res 10(4):311–320

    Article  MathSciNet  Google Scholar 

  39. Saber HM, Ravindran A (1993) Non-linear goal programming theory and practice: a survey. Comput Oper Res 20(3):275–291

    Article  MathSciNet  MATH  Google Scholar 

  40. Jiménez M, Arenas M, Bilbao A, Rodríguez Uría MV (2005) Approximate resolution of an imprecise goal programming model with nonlinear membership functions. Fuzzy Sets Syst 150(1):129–145

    Article  MathSciNet  MATH  Google Scholar 

  41. Dhahri I, Chabchoub H (2007) Nonlinear goal programming models quantifying the bullwhip effect in supply chain based on ARIMA parameters. Eur J Oper Res 117(3):1800–1810

    Article  MATH  Google Scholar 

  42. Brest J, Greiner S, Boskovic B, Mernik M, Zumer V (2006) Self- adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evolut Comput 10(6):646–657

    Article  Google Scholar 

  43. Guo H, Li Y, Li J, Sun H, Wang D, Chen X (2014) Differential evolution improved with self-adaptive control parameters based on simulated annealing. Swarm Evolut Comput 19:52–67

    Article  Google Scholar 

  44. Gandomia AH, Yang X, Talatahari S, Deb S (2012) Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization. Comput Math Appl 63(1):191–200

    Article  MathSciNet  MATH  Google Scholar 

  45. Guo H, Diao F, Zhu K, Li J (2008) A new method of soft computing to estimate the economic contribution rate of education in China. Appl Soft Comput 8(1):499–506

    Article  Google Scholar 

  46. Panahi PN, Niaei A, Tseng H, Salari D, Mousavi SM (2015) Modeling of catalyst composition–activity relationship of supported catalysts in NH3–NO–SCR process using artificial neural network. Neural Comput Appl. (in press). doi:10.1007/s00521-014-1781-z

  47. Cevik HH, Cunkas M (2015) Short-term load forecasting using fuzzy logic and ANFIS. Neural Comput Appl (in press). doi:10.1007/s00521-014-1809-4

  48. Vundavilli PR, Kumar JP, Priyatham CS, Parappagoudar MB (2015) Neural network-based expert system for modeling of tube spinning process. Neural Comput Appl (in press). doi:10.1007/s00521-015-1820-4

  49. McClelland JL, Rumelhart DE (1989) Explorations in parallel distributed processing, a handbook of models, programs and exercises. MIT Press, Cambridge

    Google Scholar 

  50. Rumelhart DE, Hinton GE, Williams RJ (1986) Learning representations by back-propagating errors. Nature 323(9):533–536

    Article  Google Scholar 

  51. Hornik K, Stinchcombe M, White H (1989) Multi-layer feed forward networks are universal approximators. Neural Netw 2(5):359–366

    Article  Google Scholar 

  52. Broomhead DS, Lowe D (1988) Multi-variable functional interpolation and adaptive networks. Complex Syst 2:321–355

    MathSciNet  MATH  Google Scholar 

  53. Moody J, Darken C (1989) Fast learning in networks of locally-tuned processing units. Neural Comput 1(2):281–294

    Article  Google Scholar 

  54. Light WA (1992) Some aspects of radial basis function approximation. Approx Theory Spline Funct Appl 356:163–190

    Article  MathSciNet  MATH  Google Scholar 

  55. Yu S, Zhu K, Diao F (2008) A dynamic all-parameters-adaptive BP neural network model and its application on oil reservoir prediction. Appl Math Comput 195(1):66–75

    MathSciNet  MATH  Google Scholar 

  56. Kuo R, Hong S, Huang Y (2010) Integration of a particle swarm optimization-based fuzzy neural network and artificial neural network for supplier selection. Appl Math Model 34(12):3976–3990

    Article  MATH  Google Scholar 

  57. Yu S, Zhu K, Gao S (2009) A hybrid MPSO-BP structure-adaptive algorithm for RBFNs. Neural Comput Appl 18(7):769–779

    Article  Google Scholar 

  58. Yu S, Wei YM, Wang K (2012) China’s primary energy demands in 2020: predictions from an MPSO-RBF estimation model. Energy Conversion and Management 61:59–66

    Article  Google Scholar 

  59. Gan M, Peng H, Dong X (2012) A hybrid algorithm to optimize RBF network architecture and parameters for non-linear time-series prediction. Appl Math Model 36(7):2911–2919

    Article  MathSciNet  MATH  Google Scholar 

  60. He Y, Zhu K, Gao S, Liu T, Li Y (2009) Theory and method of genetic-neural optimizing cut-off grade and grade of crude ore. Expert Syst Appl 36(4):7617–7623

    Article  Google Scholar 

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Acknowledgments

The authors would like to express their gratitude for the support for this work provided by The National Natural Science Foundation of China (under Grant Numbers 71303061 and 71301030), by The Humanities and Social Science Foundation at the Ministry of Education of China (under Grant Number 11YJCZH057) and by The College Humanities and Social Science Project of Guangdong Province (under Grant Number 12ZS0080).

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Authors and Affiliations

  1. School of Management, Guangdong University of Technology, Guangzhou, 510520, People’s Republic of China

    Yong He, Nuo Liao & Hongwei Liu

  2. School of Business, Eastern Kentucky University, Richmond, KY, 40475, USA

    Siwei Gao

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  1. Yong He
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Correspondence to Yong He.

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He, Y., Gao, S., Liao, N. et al. A nonlinear goal-programming-based DE and ANN approach to grade optimization in iron mining. Neural Comput & Applic 27, 2065–2081 (2016). https://doi.org/10.1007/s00521-015-2006-9

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