An improved flexible tolerance method for solving nonlinear constrained optimization problems: Application in mass integration

doi:10.1016/j.cjche.2016.07.019

›› 2017, Vol. 25 ›› Issue (5): 617-631.DOI: 10.1016/j.cjche.2016.07.019

• Process Systems Engineering and Process Safety • 上一篇下一篇

An improved flexible tolerance method for solving nonlinear constrained optimization problems: Application in mass integration

Alice Medeiros Lima^1,2, Wu Hong Kwong^2,3, Antonio José Gonçalves Cruz^2,3

1 Chemical Engineering Graduate Program, Federal University of São Carlos, São Carlos, Brazil;
2 Department of Chemical Engineering, Rod. Washington Luiz, Km 235-SP 310, São Carlos/SP, 13565-905, Brazil;
3 Department of Chemical Engineering, Federal University of São Carlos, São Carlos, Brazil

收稿日期:2016-04-28 修回日期:2016-07-31 出版日期:2017-05-28 发布日期:2017-07-06
通讯作者: Alice Medeiros Lima,E-mail address:alice.medeirosdelima@gmail.com

An improved flexible tolerance method for solving nonlinear constrained optimization problems: Application in mass integration

Alice Medeiros Lima^1,2, Wu Hong Kwong^2,3, Antonio José Gonçalves Cruz^2,3

1 Chemical Engineering Graduate Program, Federal University of São Carlos, São Carlos, Brazil;
2 Department of Chemical Engineering, Rod. Washington Luiz, Km 235-SP 310, São Carlos/SP, 13565-905, Brazil;
3 Department of Chemical Engineering, Federal University of São Carlos, São Carlos, Brazil

Received:2016-04-28 Revised:2016-07-31 Online:2017-05-28 Published:2017-07-06

摘要/Abstract

摘要： This paper proposes the use of the flexible tolerance method (FTM) modified with adaptive Nelder-Mead parameters and barrier to solve constrained optimization problems. The problems used to analyze the performance of the methods were taken from G-Suite functions, and the methods with the best performance were applied in mass integration problems. Four methods were proposed:(1) flexible tolerance method (FTM) using adaptive parameters (FTMA), (2) flexible tolerance method with scaling (FTMS) and with adaptive parameters (FTMAS), (3) FTMS including the barrier modification (MFTMS) and (4) MFTMS hybridized with PSO (MFTMS-PSO). The success rates of these methods were 100% (MFTMS), 85% (MFTMS-PSO), 40% (FTMAS) and 30% (FTMA). Numerical experiments indicated that the MFTMS could efficiently and reliably improve the accuracy of global optima. In mass integration, the method was able, from current process situation, to reach the optimum process configuration that includes integration issues, which was not possible using FTM in its standard formulation. The hybridization of FTMS with PSO (without barrier), FTMS-PSO, was also able to solve mass integration problems efficiently.

关键词: Flexible tolerance method, Adaptive parameters, Scaling, Constrained optimization, Barrier, PSO, Mass integration

Abstract: This paper proposes the use of the flexible tolerance method (FTM) modified with adaptive Nelder-Mead parameters and barrier to solve constrained optimization problems. The problems used to analyze the performance of the methods were taken from G-Suite functions, and the methods with the best performance were applied in mass integration problems. Four methods were proposed:(1) flexible tolerance method (FTM) using adaptive parameters (FTMA), (2) flexible tolerance method with scaling (FTMS) and with adaptive parameters (FTMAS), (3) FTMS including the barrier modification (MFTMS) and (4) MFTMS hybridized with PSO (MFTMS-PSO). The success rates of these methods were 100% (MFTMS), 85% (MFTMS-PSO), 40% (FTMAS) and 30% (FTMA). Numerical experiments indicated that the MFTMS could efficiently and reliably improve the accuracy of global optima. In mass integration, the method was able, from current process situation, to reach the optimum process configuration that includes integration issues, which was not possible using FTM in its standard formulation. The hybridization of FTMS with PSO (without barrier), FTMS-PSO, was also able to solve mass integration problems efficiently.

Key words: Flexible tolerance method, Adaptive parameters, Scaling, Constrained optimization, Barrier, PSO, Mass integration

Alice Medeiros Lima, Wu Hong Kwong, Antonio José Gonçalves Cruz. An improved flexible tolerance method for solving nonlinear constrained optimization problems: Application in mass integration[J]. , 2017, 25(5): 617-631.

参考文献

[1] D. Paviani, D. Himmelblau, Constrained nonlinear optimization by heuristic programming, Oper. Res. 17(5) (1969) 872-882.
[2] P. Zhang, Y. Ren, Flexible tolerance simplex method and its application to multicomponent spectrophotometric determinations, Anal. Chim. Acta 222(1) (1989) 323-333.
[3] D. Constantinescu, Smooth and time-optimal trajectory planning for industrial manipulators along specified paths, J. Robot. Syst. 17(2000) 223-249.
[4] W. Shang, S. Zhao, Y. Shen, A flexible tolerance genetic algorithm for optimal problems with nonlinear equality constraints, Adv. Eng. Inform. 23(3) (2009) 253-264.
[5] S. Omowunmi, A. Susu, Application of tikhonov regularization technique to the kinetic data of an autocatalytic reaction:Pyrolysis of n-eicosane, Engineering 3(2011) 1161-1170.
[6] M. Naish, Sensing-system planning for the surveillance of moving objects (Ph.D. thesis) Department of Mechanical and Industrial Engineering, University of Toronto, 2004.
[7] A. Lima, W. Kwong, A. Cruz, Comparative study and application of the flexible tolerance method in synthesis and analysis of processes with mass integration, J. Chem. Chem. Eng. 7(3) (2013) 228-238.
[8] A. Lima, W. Kwong, A. Cruz, Nonlinear constrained optimization using the flexible tolerance method hybridized with different unconstrained methods, Chin. J. Chem. Eng. 25(4) (2017) 442-452.
[9] D. Himmelblau, Applied nonlinear programming, McGraw-Hill, 1972.
[10] F. Gao, L. Han, Implementing the Nelder-Mead simplex algorithm with adaptive parameters, Comput. Optim. Appl. 51(1) (2012) 259-277.
[11] J. Liang, T. Runarsson, E. Mezura-Montes, M. Clerc, P. Suganthan, C. Coello, K. Deb, Problem definitions and evaluation criteria for the cec 2006 special session on constrained real-parameter optimization, Tech. Rep, Nangyang Technological University, Singapore, 2006.
[12] S. Deb, K. Srivastava, A genetic algorithm based augmented lagrangian method for constrained optimization, Comput. Optim. Appl. 53(3) (2012) 869-902.
[13] S. Koziel, Z. Michalewicz, Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization, Evol. Comput. 7(1) (1999) 19-44.
[14] J. Liang, P. Suganthan, Comparison of results on the 2006 cec benchmark function set, http://web.mysites.ntu.edu.sg/epnsugan/PublicSite/Shared2006.
[15] R. Smith, Chemical process:Design and integration, Wiley, 2005.
[16] M. El-Halwagi, Process Integration, Process Systems Engineering, Elsevier Science, 2006.
[17] M. El-Halwagi, Pollution Prevention Through Process Integration:Systematic Design Tools, Elsevier Science, 1997.
[18] M. Al-Otaibi, M. El-Halwagi, Targeting techniques for enhancing process yield, Chem. Eng. Res. Des. 84(10) (2006) 943-951.
[19] A. Hortua, Chemical process optimization and pollution prevention via mass and property integration, Master's thesis, Texas A&M University, 2007.

An improved flexible tolerance method for solving nonlinear constrained optimization problems: Application in mass integration

An improved flexible tolerance method for solving nonlinear constrained optimization problems: Application in mass integration

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