Abstract
The copper removal process (CRP) is an indispensable step for the purification of zinc sulfate solution by adding powdered zinc to a series of reactors in zinc hydrometallurgy. The selection of optimal amount of zinc powder is a complicated task because of the complex reaction mechanism, resulting in the fluctuation of copper ion concentration and the waste of zinc powder in the actual process. In this paper, we formulate a dynamic optimization problem (DOP) for the control of the zinc powder in CRP, aiming at reducing production costs and improving product quality simultaneously. A novel dynamic optimization method based on the state transition algorithm (STA) is investigated for solving this problem, and to improve the performance of STA, an adaptive strategy is adopted by its transformation operators. Simulation results from some classical DOPs show that the proposed method can optimize effectively and efficiently. The proposed approach is successfully applied to solve the DOP arising in CRP and the simulation results show that zinc powder consumption is considerably reduced under the assumption of an acceptable copper ion concentration.






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Balarini JC, de Oliveira Polli L, Miranda TLS, de Castro RMZ, Salum A (2008) Importance of roasted sulphide concentrates characterization in the hydrometallurgical extraction of zinc. Miner Eng 21(1):100–110
Laatikainen K, Lahtinen M, Laatikainen M, Paatero E (2010) Copper removal by chelating adsorption in solution purification of hydrometallurgical zinc production. Hydrometallurgy 104(1):14–19
Srinivasan B, Palanki S, Bonvin D (2003) Dynamic optimization of batch processes: I. Characterization of the nominal solution. Comput Chem Eng 27(1):1–26
Açıkmeşe B, Blackmore L (2011) Lossless convexification of a class of optimal control problems with non-convex control constraints. Automatica 47(2):341–347
Wongrat W, Younes A, Elkamel A, Douglas PL, Lohi A (2011) Control vector optimization and genetic algorithms for mixed-integer dynamic optimization in the synthesis of rice drying processes. J Frankl Inst 348(7):1318–1338
Angira R, Santosh A (2007) Optimization of dynamic systems: a trigonometric differential evolution approach. Comput Chem Eng 31(9):1055–1063
Biegler LT, Grossmann IE (2004) Retrospective on optimization. Comput Chem Eng 28(8):1169–1192
Biegler LT (2007) An overview of simultaneous strategies for dynamic optimization. Chem Eng Process 46(11):1043–1053
Schlegel M, Stockmann K, Binder T, Marquardt W (2005) Dynamic optimization using adaptive control vector parameterization. Comput Chem Eng 29(8):1731–1751
Lin Q, Loxton R, Teo KL (2014) The control parameterization method for nonlinear optimal control: a survey. J Ind Manag Optim 10(1):275–309
Sarkar D, Modak JM (2003) Optimisation of fed-batch bioreactors using genetic algorithms. Chem Eng Sci 58(11):2283–2296
Chen X, Du W, Tianfield H, Qi R, He W, Qian F (2014) Dynamic optimization of industrial processes with nonuniform discretization-based control vector parameterization. IEEE Trans Autom Sci Eng 11(4):1289–1299
Cruz IL, Van Willigenburg L, Van Straten G (2003) Efficient differential evolution algorithms for multimodal optimal control problems. Appl Soft Comput 3(2):97–122
Zhang H, Cao X, Ho JK, Chow TW (2017) Object-level video advertising: an optimization framework. IEEE Trans Ind Inf 13(2):520–531
Zhou X, Yang C, Gui W (2012) State transition algorithm. J Ind Manag Optim 8(4):1039–1056
Zhou X, Shi P, Lim CC, Yang C, Gui W (2017) A dynamic state transition algorithm with application to sensor network localization. Neurocomputing. doi:10.1016/j.neucom.2017.08.010
Han J, Yang C, Zhou X, Gui W (2017) A new multi-threshold image segmentation approach using state transition algorithm. Appl Math Model 44:588–601
Han J, Yang C, Zhou X, Gui W (2017) Dynamic multi-objective optimization arising in iron precipitation of zinc hydrometallurgy. Hydrometallurgy 173:134–148
Han J, Yang C, Zhou X, Gui W (2017) A two-stage state transition algorithm for constrained engineering optimization problems. Int J Control Autom Syst (in press)
Zhou X, Gao DY, Simpson AR (2016) Optimal design of water distribution networks by a discrete state transition algorithm. Eng Optim 48(4):603–628
Zhou X, Gao DY, Yang C, Gui W (2016) Discrete state transition algorithm for unconstrained integer optimization problems. Neurocomputing 173:864–874
Zhang F, Yang C, Zhou X, Gui W (2016) Fractional-order PID controller tuning using continuous state transition algorithm. Neural Comput Appl. doi:10.1007/s00521-016-2605-0
Näsi J (2004) Statistical analysis of cobalt removal from zinc electrolyte using the arsenic-activated process. Hydrometallurgy 73(1):123–132
Li YG, Gui WH, Teo KL, Zhu HQ, Chai QQ (2012) Optimal control for zinc solution purification based on interacting CSTR models. J Process Control 22(10):1878–1889
Zhang B, Yang C, Zhu H, Li Y, Gui W (2013) Kinetic modeling and parameter estimation for competing reactions in copper removal process from zinc sulfate solution. Ind Eng Chem Res 52(48):17074–17086
Irizarry R (2005) A generalized framework for solving dynamic optimization problems using the artificial chemical process paradigm: applications to particulate processes and discrete dynamic systems. Chem Eng Sci 60(21):5663–5681
Han J, Dong T, Zhou X, Yang C, Gui W (2014) State transition algorithm for constrained optimization problems. In: the 33rd Chinese control conference (CCC). IEEE, pp 7543–7548
Zhou X, Hanoun S, Gao DY, Nahavandi S (2015) A multiobjective state transition algorithm for single machine scheduling. In: Gao D, Ruan N, Xing W (eds) Advances in global optimization, vol 95. Springer, Cham, pp 79–88
Zhou X, Yang C, Gui W (2014) Nonlinear system identification and control using state transition algorithm. Appl Math Comput 226:169–179
Zhou X, Yang C, Gui W (2016) A matlab toolbox for continuous state transition algorithm. In: 2016 35th Chinese control conference (CCC). IEEE, pp 9172–9177
Tran T-D, Jin G-G (2010) Real-coded genetic algorithm benchmarked on noiseless black-box optimization testbed. In: Proceedings of the 12th annual conference companion on genetic and evolutionary computation. ACM, pp 1731–1738
Karaboga D, Ozturk C (2011) A novel clustering approach: artificial bee colony (abc) algorithm. Appl Soft Comput 11(1):652–657
Iadevaia S, Lu Y, Morales FC, Mills GB, Ram PT (2010) Identification of optimal drug combinations targeting cellular networks: integrating phospho-proteomics and computational network analysis. Cancer Res 70(17):6704–6714
Senthilnath J, Das V, Omkar SN, Mani V (2013) Clustering using levy flight cuckoo search. In: Bansal J, Singh P, Deep K, Pant M, Nagar A (eds) Proceedings of Seventh International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA 2012), vol 202. Springer, India
Dadebo S, McAuley K (1995) Dynamic optimization of constrained chemical engineering problems using dynamic programming. Comput Chem Eng 19(5):513–525
Acknowledgements
Authors thank the National Natural Science Foundation of China (Grant Nos. 61503416, 61533020, 61533021, 61590921), the 111 Project (Grant No. B17048), National Priority Research Project NPRP 8-274-2-107, funded by Qatar National Research Fund and the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 2017zzts487) for the funding support.
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Huang, M., Zhou, X., Huang, T. et al. Dynamic optimization based on state transition algorithm for copper removal process. Neural Comput & Applic 31, 2827–2839 (2019). https://doi.org/10.1007/s00521-017-3232-0
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DOI: https://doi.org/10.1007/s00521-017-3232-0