A modified optimization method for optimal control problems of continuous stirred tank reactor

[1] SA. Ravichandran, J.J. Krist, D. Edwards, S. Delagah and J. Pellegrino, Measuring sparingly-soluble, aqueous salt crystallization kinetics using CSTRs-in-series: Methodology development and CaCO3 studies, Sep. Purif. Technol. 211 (2019) 408–420.

[2] A. Regalado-Mendez, RR. Romero, RN. Rangel and S. Skogestad, Biodiesel production in stirred tank chemical reactors: A numerical simulation, In New Trends in Networking, Computing, E-learning, Systems Sciences, and Engineering, pp. 109–116, Springer, Cham, 2015.

[3] Z. Cao, Q. Wu, H. Zhou, P. Chen and F. You, Dynamic modeling, systematic analysis, and operation optimization for shell entrained-flow heavy residue gasifier, Energy 197 (2020)  117220.

[4] T.M. Braden, M.D. Johnson, M.E. Kopach, J. McClary Groh, R.D. Spencer, J. Lewis and J..J. Adler, Development of a commercial flow Barbier process for a pharmaceutical intermediate, Org. Process. Res. Dev. 21(3) (2017)317–326.

[5] D. Gola, P. Chawla, A. Malik and S.Z. Ahammad, Development and performance evaluation of native microbial consortium for multi metal removal in lab scale aerobic and anaerobic bioreactor, Environ. Technol. Innov. (2020)100714.

[6] I. Malinen, J. Kangas, J. Ahola and J. Tanskanen, A new homotopy-based strategy for the robust determination of all the feasible solutions for CSTR systems, Period. Polytech. Chem. 60(1) (2016) 8–23.

[7] A. Uppal, W.H. Ray and A.B. Poore, On the dynamic behavior of continuous stirred tank reactors, Chem. Eng. Sci. 29(4) (1974) 967–985.

[8] K. Pathak, A. Markana, N. Parikh, Optimal control of CSTR, Nirma Univ. J. Eng. Technol. 1(2) (2010) 56–60.

[9] Z.S. Abo Hammour, A.G. Asasfeh, A.M. Al-Smadi, and O.M. Alsmadi, A novel continuous genetic algorithm for the solution of optimal control problems, Optim. Contr. Appl. Met. 32(4) (2011) 414–432.

[10] A. Uppal, W.H. Ray and A.B. Poore, The classification of the dynamic behavior of continuous stirred tank reactors influence of reactor residence time, Chem. Eng. Sci. 31(3) (1976) 205–214.

[11] M.M. Ali, C. Storey and A. T¨orn, Application of stochastic global optimization algorithms to practical problems, J. Optimiz. Theory. Appl. 95(3) (1997) 545–563.

[12] C.A. Floudas, P.M. Pardalos, C.S. Adjimann, W.R. Esposito, Z.H. Gumus, S.T. Harding and CA. Schweiger, Handbook of Test Problems in Local and Global Optimization, 1999.

[13] L. Lapidus and R. Luus, Optimal Control of Engineering Processes, Blaisdell Pub. Co., 1967.

[14] M. Salimi, A.H. Borzabadi, H.H. Mehne and A. Heydari, The hub location’s method for solving optimal control problems, Evol. Intel. (2020) 1–20

[15] E.Z. Serper and S.A. Alumur, The design of capacitated intermodal hub networks with different vehicle types, Transport. Res. Part B: Methodol. 86 (2016) 51–65.

[16] S. Alumur and B.Y. Kara, Network hub location problems: The state of the art, Eur. J. Oper. Res. 190(1) (2008) 1–21.

[17] R.Z. Farahani, M. Hekmatfar, A.B. Arabani, E. Nikbakhsh, Hub location problems: A review of models, classification, solution techniques, and applications, Comput. Ind. Eng. 64(4) (2013) 1096–1109.

[18] J.F. Campbell, Hub location and the p-hub median problem Oper. Res. 44(6) (1996) 923–935.

[19] J. Kratica, Z. Stanimirovic, D. Tosic and V. Filipovic, Two genetic algorithms for solving the uncapacitated single allocation p-hub median problem, Eur. J. Oper. Res. 182(1) (2007) 15–28.

[20] Z. Stanimirovic, A genetic algorithm approach for the capacitated single allocation p-hub median problem, Comput. Inf. 29 (1) (2010) 117–132.

[21] J. Rieck, C. Ehrenberg and J. Zimmermann, Many-to-many location-routing with inter-hub transport and multicommodity pickup-and-delivery, Eur. J. Oper. Res. 236(3) (2014) 863–878.

[22] H. Karimi and M. Setak, Proprietor and customer costs in the incomplete hub location-routing network topology, Appl. Math. Model. 38(3) (2014) 1011–1023.

[23] AT. Ernst and M. Krishnamoorthy, Efficient algorithms for the uncapacitated single allocation p-hub median problem, Location Sci. 4(3) (1996) 139–154.

[24] D. Skorin-Kapov and J. Skorin-Kapov, On tabu search for the location of interacting hub facilities, Eur. J. Oper. Res. 73(3) (1994) 502–509.

[25] M.P. Perez, F.A. Rodrıguez and J.M.M. Vega, On the use of path relinking for the ρ–hub median problem, Eur. Conf. Evol. Comput. Combin. Optim., 2004, pp.155–164.

[26] P. Hansen, N. Mladenovic and J.A.M. Perez, Variable neighborhood search: Methods and applications, 4OR 6(4) (2008) 319-360.

[27] P. Hansen, N. Mladenovic and D. Urosevic, Variable neighborhood search and local branching, Comput. Oper. Res. 33(10) (2006) 3034–3045.

[28] W.E. Costa, MC. Goldbarg and E.G. Goldbarg, New VNS heuristic for total flowtime flow shop scheduling problem, Expert. Syst. Appl. 39(9) (2012) 8149–8161.

[29] N. Mladenovic, D. Urosevic and A. Ilic, A general variable neighborhood search for the one-commodity pickup and delivery travelling salesman problem, Eur. J. Oper. Res. 220(1) (2012) 270–285.

[30] N. Mladenovic, M. Drazic, V. Kovacevic-Vujcic and M. Cangalovic, General variable neighborhood search for the continuous optimization, Eur. J. Oper. Res. 191(3) (2008) 753–770.

[31] A. Ilic, D. Urosevic, J. Brimberg and N. Mladenovic, A general variable neighborhood search for solving the uncapacitated single allocation p-hub median problem, Eur. J. Oper. Res. 206(2) (2010) 289–300.

[32] N. Mladenovic and P. Hansen, Variable neighborhood search, Comput. Oper. Res. 24(11) (1997) 1097–1100.

[33] S. Wolf and P. Merz, Evolutionary local search for the super-peer selection problem and the p-hub median problem, In International Workshop on Hybrid Metaheuristics, Springer, Berlin, Heidelberg, 2007, pp.1–15.

[34] P. Hansen and N. Mladenovic, Developments of variable neighborhood search, In Essays and surveys in metaheuristics, Springer, Boston, MA., 2002, pp. 415–439,

[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.

[37] X. Wu, B. Lei, K. Zhang and M. Cheng, Hybrid stochastic optimization method for optimal control problems of chemical processes, Chem. Eng. Res. Des. 126 (2017) 297–310.

[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.

[39] E. Lazutkin, A. Geletu, S. Hopfgarten, and P. Li, An analytical hessian and parallel-computing approach for efficient dynamic optimization based on control-variable correlation analysis, Ind. Eng. Chem. Res. 54(48) (2015)12086–12095.

[40] A.M. Johnson and S.H. Jacobson, On the convergence of generalized hill climbing algorithms, Discrete. Appl. Math. 119(1-2) (2002) 37–57.

[41] H. Muhlenbein and J. Zimmermann, Size of neighborhood more important than temperature for stochastic local search, Proc. Congress on Evolutionary Computation, (Cat. No. 00TH8512), IEEE, 2000, pp.1017–1024.

[42] J. Brimberg, P. Hansen and N. Mladenovic, Attraction probabilities in variable neighborhood search, 4OR 8(2) (2010) 181–194.

[43] R. Aris and N.R. Amundson, An analysis of chemical reactor stability and control—III: The principles of programming reactor calculations, Some extensions, Chem. Eng. Sci. 7(3) (1958) 148–155.

[44] R. Luus and D.E. Cormack, Multiplicity of solutions resulting from the use of variational methods in optimal control problems, Can. J. Chem. Eng. 50(2) (1972) 309–311.

[45] L. Bayon, J.M. Grau, M.M. Ruiz and P.M. Suarez, Initial guess of the solution of dynamic optimization of chemical processes, J. Math. Chem. 48(1) (2010) 28–37.

46] H. Modares and M.B.N. Sistani, Solving nonlinear optimal control problems using a hybrid IPSO–SQP algorithm, Eng. Appl. Artif. Intel. 24(3) (2011) 476–484.

[47] H.H. 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] I.L. Cruz, L.G. Van Willigenburg and G. Van Straten, Efficient differential evolution algorithms for multimodal optimal control problems, Appl. Soft. Comput. 3(2) (2003) 97–122.

[49] S.A. Dadebo and K.B. 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, H.S. Kusumakar, V.K. Jayaraman and B.D. Kulkarni, Dynamic optimization of chemical processes using ant colony framework, Comput. Chem. 25(6) (2001) 583–595.

[53] S.N. 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] T.B. 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] M.P. Perez, F.A. Rodrıguez and JM. Moreno-Vega, A hybrid VNS–path relinking for the p-hub median problem, IMA. J. Manag. Math. 18(2) (2007) 157–171.