A Three-section Algorithm of Dynamic Programming Based on Three-stage Decomposition System Model for Grade Transition Trajectory Optimization Problems

doi:10.1016/j.cjche.2014.09.002

›› 2014, Vol. 22 ›› Issue (10): 1122-1130.DOI: 10.1016/j.cjche.2014.09.002

• 过程系统工程与过程安全 • 上一篇下一篇

A Three-section Algorithm of Dynamic Programming Based on Three-stage Decomposition System Model for Grade Transition Trajectory Optimization Problems

Yujie Wei, Yongheng Jiang, Dexian Huang

National Laboratory for Information Science and Technology, Department of Automation, Tsinghua University, Beijing 100084, China

收稿日期:2013-01-29 修回日期:2013-06-30 出版日期:2014-10-28 发布日期:2014-12-01
通讯作者: Dexian Huang
基金资助:
Supported by the National Basic Research Program of China (2012CB720500) and the NationalHigh Technology Research andDevelopment Programof China (2013AA040702).

A Three-section Algorithm of Dynamic Programming Based on Three-stage Decomposition System Model for Grade Transition Trajectory Optimization Problems

Yujie Wei, Yongheng Jiang, Dexian Huang

National Laboratory for Information Science and Technology, Department of Automation, Tsinghua University, Beijing 100084, China

Received:2013-01-29 Revised:2013-06-30 Online:2014-10-28 Published:2014-12-01
Supported by:
Supported by the National Basic Research Program of China (2012CB720500) and the NationalHigh Technology Research andDevelopment Programof China (2013AA040702).

摘要/Abstract

摘要： This paper introduces a practical solving scheme of gradetransition trajectory optimization (GTTO) problems under typical certificate-checking-updating framework. Due to complicated kinetics of polymerization, differential/algebraic equations (DAEs) always cause great computational burden and system non-linearity usually makes GTTO non-convex bearing multiple optima. Therefore, coupled with the three-stage decomposition model, a three-section algorithm of dynamic programming (TSDP) is proposed based on the general iteration mechanism of iterative programming (IDP) and incorporated with adaptivegrid allocation scheme and heuristic modifications. The algorithm iteratively performs dynamic programming with heuristic modifications under constant calculation loads and adaptively allocates the valued computational resources to the regions that can further improve the optimality under the guidance of local error estimates. TSDP is finally compared with IDP and interior point method (IP) to verify its efficiency of computation.

关键词: Gradetransition trajectory optimization, Adaptivegrid allocation, Heuristic modifications, Three-section dynamic programming, Three-stage decomposition model

Abstract: This paper introduces a practical solving scheme of gradetransition trajectory optimization (GTTO) problems under typical certificate-checking-updating framework. Due to complicated kinetics of polymerization, differential/algebraic equations (DAEs) always cause great computational burden and system non-linearity usually makes GTTO non-convex bearing multiple optima. Therefore, coupled with the three-stage decomposition model, a three-section algorithm of dynamic programming (TSDP) is proposed based on the general iteration mechanism of iterative programming (IDP) and incorporated with adaptivegrid allocation scheme and heuristic modifications. The algorithm iteratively performs dynamic programming with heuristic modifications under constant calculation loads and adaptively allocates the valued computational resources to the regions that can further improve the optimality under the guidance of local error estimates. TSDP is finally compared with IDP and interior point method (IP) to verify its efficiency of computation.

Key words: Gradetransition trajectory optimization, Adaptivegrid allocation, Heuristic modifications, Three-section dynamic programming, Three-stage decomposition model

Yujie Wei, Yongheng Jiang, Dexian Huang. A Three-section Algorithm of Dynamic Programming Based on Three-stage Decomposition System Model for Grade Transition Trajectory Optimization Problems[J]. , 2014, 22(10): 1122-1130.

参考文献

[1] G. Dunnebier, D. van Hessem, J.V. Kadam, K.U. Klatt, M. Schlegel, Optimization and control of polymerization processes, Chem. Eng. Technol. 28 (5) (2005) 575-580.
[2] P.O. Larsson, J. Akesson, N. Carlsson, N. Andersson, Model-based optimization of economical grade changes for the Borealis Borstar (R) polyethylene plant, Comput. Chem. Eng. 46 (2012) 153-166.
[3] C. Chatzidoukas, S. Pistikopoulos, C. Kiparissides, A hierarchical optimization approach to optimal production scheduling in an industrial continuous olefin polymerization reactor, Macromol. React. Eng. 3 (1) (2009) 36-46.
[4] K.B.McAuley, J.F.MacGregor, On-line inference of polymer properties in an industrial polyethylene reactor, AICHE J. 37 (6) (1991) 825-835.
[5] B. Kou, K.B. McAuley, J.C.C. Hsu, D.W. Bacon, Mathematical model and parameter estimation for gas-phase ethylene/hexene copolymerization with metallocene catalyst, Macromol. Mater. Eng. 290 (6) (2005) 537-557.
[6] J.D. Wang, Y.R. Yang, Study on optimal strategy of grade transition in industrial fluidized bed gas-phase polyethylene production process, Chin. J. Chem. Eng. 11 (1) (2003) 1-8.
[7] K.B. McAuley, J.F. MacGregor, Optimal grade transitions in a gas phase polyethylene reactor, AICHE J. 38 (10) (1992) 1564-1576.
[8] M. Takeda, W.H. Ray, Optimal-grade transition strategies for multistage polyolefin reactors, AICHE J. 45 (8) (1999) 1776-1793.
[9] A. Prata, J. Oldenburg, A. Kroll, W. Marquardt, Integrated scheduling and dynamic optimization of grade transitions for a continuous polymerization reactor, Comput. Chem. Eng. 32 (3) (2008) 463-476.
[10] D. HE, T. ZOU, L. YU, Receding horizon control for grade transition of large-scale polypropylene production plants, Chin. J. Chem. Eng. 024 (2010).
[11] Z.S. Fei, B. Hu, L.B. Ye, J. Liang, ARX-NNPLSmodel based optimization strategy and its application in polymer grade transition process, Chin. J. Chem. Eng. 20 (5) (2012) 971-979.
[12] M.H. Lee, C. Han, K.S. Chang, Hierarchical time-optimal control of a continuous copolymerization reactor during start-up or grade change operation using genetic algorithms, Comput. Chem. Eng. 21 (1997) S1037-S1042 (Suppl.).
[13] M.H. Lee, C. Han, K.S. Chang, Dynamic optimization of a continuous polymer reactor using a modified differential evolution algorithm, Ind. Eng. Chem. Res. 38 (12) (1999) 4825-4831.
[14] L.T. Biegler, V.M. Zavala, Large-scale nonlinear programming using IPOPT: an integrating framework for enterprise-wide dynamic optimization, Comput. Chem. Eng. 33 (3SI) (2009) 575-582.
[15] A.M. Cervantes, S. Tonelli, A. Brandolin, J.A. Bandoni, L.T. Biegler, Large-scale dynamic optimization for grade transitions in a low density polyethylene plant, Comput. Chem. Eng. 26 (2) (2002) 227-237.
[16] N. Padhiyar, S. Bhartiya, R.D. Gudi, Optimal grade transition in polymerization reactors: a comparative case study, Ind. Eng. Chem. Res. 45 (10) (2006) 3583-3592.
[17] H. Pakravesh, A. Shojaei, Optimization of industrial CSTR for vinyl acetate polymerization using novel shuffled frog leaping based hybrid algorithms and dynamic modeling, Comput. Chem. Eng. 35 (11) (2011) 2351-2365.
[18] A. Flores-Tlacuahuac, L.T. Biegler, E. Saldivar-Guerra, Dynamic optimization of HIPS open-loop unstable polymerization reactors, Ind. Eng. Chem. Res. 44 (8) (2005) 2659-2674.
[19] A. Flores-Tlacuahuac, L.T. Biegler, E. Saldivar-Guerra, Optimal grade transitions in the high-impact polystyrene polymerization process, Ind. Eng. Chem. Res. 45 (18) (2006) 6175-6189.
[20] Y.Wei, Y. Jiang, F. Yang, D. Huang, Three-stage Decomposition Modeling for Quality of Polymerization Processes Based on Adaptive Hinging Hyperplanes and Impulse Response Template, Ind. Eng. Chem. Res. 52 (16) (2013) 5747-5756.
[21] W.B. Powell, A. George, B. Bouzaiene-Ayari, H.P. Simao, Approximate dynamic programming for high dimensional resource allocation problems, Proceedings of the International Joint Conference onNeuralNetworks (IJCNN) 1-5 (2005) 2989-2994.
[22] R. Luus, Iterative Dynamic Programming, Chapman & Hall/CRC Press, New York, 2000.
[23] M.H. Chang, Y.C. Park, T. Lee, Iterative dynamic programming of optimal control problemusing a new global optimization technique, Proceedings of the 8th International Symposium on Process Systems Engineering, 2003, pp. 416-421.
[24] R. Luus, Piecewise linear continuous optimal control by iterative dynamic programming, Ind. Eng. Chem. Res. 32 (5) (1993) 859-865.
[25] L. Grűne, An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation, Numer. Math. 75 (3) (1997) 319-337.
[26] L. Grűne,W. Semmler, Using dynamic programming with adaptive grid scheme for optimal control problems in economics, J. Econ. Dyn. Control. 28 (12) (2004) 2427-2456.
[27] S. Patra, S.K. Goswami, B. Goswami, Fuzzy and simulated annealing based dynamic programming for the unit commitment problem, Expert Syst. Appl. 36 (3) (2009) 5081-5086.
[28] H.P. Christos, S. Kenneth, Combinatorial Optimization: Algorithms and Complexity, Princeton Press, New Jersey, 1982.

A Three-section Algorithm of Dynamic Programming Based on Three-stage Decomposition System Model for Grade Transition Trajectory Optimization Problems

A Three-section Algorithm of Dynamic Programming Based on Three-stage Decomposition System Model for Grade Transition Trajectory Optimization Problems

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 0

编辑推荐

Metrics

本文评价