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 • Previous Articles Next Articles

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:2017-07-06 Published:2017-05-28

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

通讯作者: Alice Medeiros Lima,E-mail address:alice.medeirosdelima@gmail.com

Abstract

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

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

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.

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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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