Abstract
An intelligent integrated method is proposed for optimizing the head grade and dressing grade in the mining and ore-dressing management of metal mines, beginning with the establishment of a nonlinear constrained optimization model with the objective function of economic benefit, two constraints comprising of the resource utilization rate and the output of concentrate, along with head grade and dressing grade as the decision variables. Particle swarm optimization (PSO) algorithm is then integrated with artificial neural networks to create a PSO–ANN algorithm capable of identifying the optimal grade combination. The outer layer of PSO–ANN uses the PSO algorithm to carry out a global search, with the head grade and dressing grade being combined as swarm particles for evolutionary computation. The constraint handling techniques of feasibility-based rules are used to update the historical best location of each particle (pbest) and the global best location of the swarm (gbest) to guide the particles toward the optimum. The inner layer uses regression model, BPNN and RBFNN to calculate the loss rate, ore-dressing metal recovery rate and costs, respectively, to facilitate the further calculation of the resource utilization rate, the concentrate output and the economic benefit of each particle. Finally, the proposed method is tested by carrying out a case study based upon Daye Iron Mine to indicate its effectiveness and reliability.
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Ali MM, Bagdadi Z (2009) A local exploration-based differential evolution algorithm for constrained global optimization. Appl Math Comput 208:31–48
Asad MWA (2007) Optimum cut-off grade policy for open pit mining operations through net present value algorithm considering metal price and cost escalation. Eng Comput 24(7):723–736
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
Ataei M, Osanloo M (2003) Using a combination of genetic algorithm and the grid search method to determine optimum cutoff grades of multiple metal deposits. Int J Surf Min Reclam Environ 18(1):60–78
Azimi Y, Osanloo M (2011) Determination of open pit mining cut-off grade strategy using combination of nonlinear programming and genetic algorithm. Arch Min Sci 56(2):189–212
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
Broomhead DS, Lowe D (1988) Multivariable functional interpolation and adaptive networks. Complex Syst 2:321–355
Cetin E, Dowd PA (2002) The use of genetic algorithms for multiple cut-off grade optimization. In: Proceedings of the 30th international symposium on the application of computers and operations research in the mineral industry, pp. 769–780
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
Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186:311–338
He Q, Wang L (2007) A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization. Appl Math Comput 186(2):1407–1422
Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor
Homaifar A, Lai SHY, Qi X (1994) Constrained optimization via genetic algorithms. Simulation 62(4):242–254
Hornik K, Stinchcombe M, White H (1989) Multilayer feed forward networks are universal approximators. Neural Netw 2:359–366
Hu XH, Eberhart RC (2002) Solving constrained nonlinear optimization problems with particle swarm optimization. In: Proceedings of the sixth world multi conference on systematics, cybernetics and informatics, Orlando, FL, pp 203–206
Huang F, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186:340–356
Jang JSR, Sun CT (1993) Functional equivalence between radial basis function networks and fuzzy inference system. IEEE Trans Neural Netw 4(1):156–159
Jiang A, Zhao D, Sun H (2003) The development of decision support system for optimizing the dressing-grade. Min Res Dev 23(4):43–45 (in Chinese)
Kennedy J, Eberhart RC, Shi Y (2001) Swarm intelligence. Morgan Kaufman Publishers, San Francisco
Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, pp. 1942–1948
Kirkpatrick S, Gelatt CD Jr, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680
Kirkpatrick S (1984) Optimization by simulated annealing: quantitative studies. J Stat Phys 34(5):975–986
Kou X, Liu S, Zhang J, Zheng W (2009) Co-evolutionary particle swarm optimization to solve constrained optimization problems. Comput Math Appl 57:1776–1784
Krohling RA, dos Santos Coelho L (2006) Co-evolutionary particle swarm optimization using Gaussian distribution for solving constrained optimization problems. IEEE Trans Syst Man Cybern Part B Cybern 36(6):1407–1416
Lane KF (1964) Choosing the optimum cut-off grade. Colo Sch Mines Q 59:485–492
Lane KF (1988) The economic definition of ore, cut-off grade in theory and practice. Mining Journal Books, London
Li K, Liu B, Zhang W (1997) General system for determining rational dressing-grade. J Univ Sci Technol Beijing 19(5):425–428 (in Chinese)
Light WA (1992) Some aspects of radial basis function approximation. Approx Theory Spline Funct Appl 356:163–190
Liu H, Cai Z, Wang Y (2010) Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization. Appl Soft Comput 10:629–640
McClelland JL, Rumelhart DE (1989) Explorations in parallel distributed processing, programs and exercises, a handbook of models. MIT Press, Cambridge
Michalewicz Z, Schoenauer M (1996) Evolutionary algorithm for constrained parameter optimization problems. Evol Comput 4(1):1–32
Minnitt RCA (2004) Cut-off grade determination for the maximum value of a small Wits-type gold mining operation. J S Afr Inst Min Metall 6:277–283
Mohamed AW, Sabry HZ (2012) Constrained optimization based on modified differential evolution algorithm. Inf Sci 194:171–208
Moody J, Darken C (1989) Fast learning in networks of locally-tuned processing units. Neural Comput 1(2):281–294
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
Pedamallu CS, Ozdamar L (2008) Investigating a hybrid simulated annealing and local search algorithm for constrained optimization. Eur J Oper Res 185:1230–1245
Pulido GT, Coello CAC (2004) A constraint-handling mechanism for particle swarm optimization. In Proceedings of the 2004 congress on evolutionary computation, pp 1396–1403
Rumelhart DE, Hinton GE, Williams RJ (1986) Learning representations by back-propagating errors. Nature 323(9):533–536
Singh HK, Ray T, Smith W (2011) C-PSA: constrained Pareto simulated annealing for constrained multi-objective optimization. Inf Sci 181:1153–1163
Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359
Sun C, Zeng J, Pan J (2011) An improved vector particle swarm optimization for constrained optimization problems. Inf Sci 181:1153–1163
Tsoulos IG (2009) Solving constrained optimization problems using a novel genetic algorithm. Appl Math Comput 208:273–283
Wang YJ, Zhang JS (2007) Global optimization by an improved differential evolutionary algorithm. Appl Math Comput 186:669–680
Yuan H, Liu B, Li K (2002) Study on dynamic optimization of the dressing-grade. J Univ Sci Technol Beijing 24(3):239–242 (in Chinese)
Yu W, Liu A (2004) Study on dynamic optimization of dressing-grade of metal mines. China Tungsten Ind 19(3):27–30 (in Chinese)
Zhu H, Wang Y, Wang K, Chen Y (2011) Particle swarm optimization (PSO) for the constrained portfolio optimization problem. Expert Syst Appl 38:10161–10169
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This study was funded by National Natural Science Foundation of China (Grant 71303061 and 71301030), and Humanities and Social Science Foundation, Ministry of Education of China (Grant Number 11YJCZH057).
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Communicated by V. Loia.
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He, Y., Liao, N. & Bi, J. Intelligent integrated optimization of mining and ore-dressing grades in metal mines. Soft Comput 22, 283–299 (2018). https://doi.org/10.1007/s00500-016-2333-5
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DOI: https://doi.org/10.1007/s00500-016-2333-5