International Journal of Nonlinear Analysis and Applications
A modified optimization method for optimal control problems of continuous stirred tank reactor
Document Type : Research Paper
Authors
1 Department of Mathematics, Payame Noor University, Tehran, P.O. Box. 19395-3697, Iran
2 Department of Applied Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran
3 Department of Avionics, Aerospace Research Institute, Tehran, 14665-834, Iran
4 Department of Mathematics, Payame Noor University, Tehran, P.O. Box. 19395-3697, Iran
Abstract
Continuous stirred tank reactor (CSTR) is an important and constructive part in various chemical and process industries and therefore it is necessary to control the process in optimal temperature and concentration conditions. Because of the nonlinear nature and limits of the control input, solving this problem is very difficult. To achieve a sub-optimal control policy for chemical processes, we focused on a new construction model. Then, a two-phase algorithm, denoted as modified sequential general variable neighborhood search (MSGVNS) algorithm based on three local searches that use efficient neighborhood interchange has been employed to solve CSTR problems numerically. The results of the proposed method show that its convergence to the exact solution is achieved by the accuracy comparable to other numerical algorithms in few times.
Keywords
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[27] P. Hansen, N. Mladenovi´c and D. Uroˇsevi´c, Variable neighborhood search and local branching, Comput. Oper. Res. 33(10) (2006) 3034–3045.
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[29] N. Mladenovi´c, D. Uroˇsevi´c and A. Ili´c, A general variable neighborhood search for the one-commodity pickupand delivery travelling salesman problem, Eur. J. Oper. Res. 220(1) (2012) 270–285.
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[35] S. Nezhadhosein, A. Heydari and R. Ghanbari, A modified hybrid genetic algorithm for solving nonlinear optimal control problems, Math. Probl. Eng. (2015), 1–21.
[36] R. Luus, Iterative Dynamic Programming, CRC Press, 2000.
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[38] S. Nezhadhosein, A. Heydari and R. Ghanbari, Integrating Differential Evolution Algorithm with Modified Hybrid GA for Solving Nonlinear Optimal Control Problems, Iran. J. Math. Sci. Inf. 12(1) (2017) 47–67.
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[47] HH. Mehne and S. Mirjalili, A parallel numerical method for solving optimal control problems based on whale optimization algorithm, Knowl-Based. Syst. 151 (2018) 114–123.
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[45] L. Bay´on, JM. Grau, M.M. Ruiz and PM. Su´arez, Initial guess of the solution of dynamic optimization of chemical processes, J. Math. Chem. 48(1) (2010) 28–37.
[46] H. Modares and MBN. Sistani, Solving nonlinear optimal control problems using a hybrid IPSO–SQP algorithm, Eng. Appl. Artif. Intel. 24(3) (2011) 476–484.
[47] HH. Mehne and S. Mirjalili, A parallel numerical method for solving optimal control problems based on whale optimization algorithm, Knowl-Based. Syst. 151 (2018) 114–123.
[48] IL. Cruz, LG. Van Willigenburg and G. Van Straten, Efficient differential evolution algorithms for multimodal optimal control problems, Appl. Soft. Comput. 3(2) (2003) 97–122.
[49] SA. Dadebo and KB. McAuley Dynamic optimization of constrained chemical engineering problems using dynamic programming, Comput. Chem. Eng. 19(5) (1995) 513–525.
[50] B. Zhang, D. Chen and W. Zhao, Iterative ant-colony algorithm and its application to dynamic optimization of chemical process, Comput. Chem. Eng. 29(10) (2005) 2078–2086.
[51] S. Fan, D. Wenli, Q. Rongbin, Q.Feng and W. ZHONG, A hybrid improved genetic algorithm and its application in dynamic optimization problems of chemical processes, Chinese. J. Chem. Eng. 21(2) (2013) 144–154.
[52] J. Rajesh, K. Gupta, HS. Kusumakar, VK. Jayaraman and BD. Kulkarni, Dynamic optimization of chemical processes using ant colony framework, Comput. Chem. 25(6) (2001) 583–595.
[53] SN. Rao and R. Luus, Evaluation and improvement of control vector iteration procedures for optimal control, Can. J. Chem. Eng. 50(6) (1972) 777–784.
[54] TB. Jensen, Dynamic control of large dimension nonlinear chemical processes, Doctoral dissertation, Princeton University, (1965).
[55] X. Chen, W. Du, R. Qi, F. Qian and H. Tianfield, Hybrid gradient particle swarm optimization for dynamic optimization problems of chemical processes, Asia. Pac. J. Chem. Eng. 8(5) (2013) 708–720.
[56] MP. P´erez, FA. Rodr´ıguez and JM. Moreno-Vega, A hybrid VNS–path relinking for the p-hub median problem, IMA. J. Manag. Math. 18(2) (2007) 157–171.
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Volume 12, Issue 1
May 2021Pages 445-459
- Receive Date: 19 July 2020
- Revise Date: 23 September 2020
- Accept Date: 29 September 2020
- First Publish Date: 02 February 2021