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

[1]  Kalyanmoy Deb,et al.  A genetic algorithm based augmented Lagrangian method for constrained optimization , 2012, Comput. Optim. Appl..

[2]  Mahmoud M. El-Halwagi,et al.  Targeting Techniques for Enhancing Process Yield , 2006 .

[3]  Robin Smith,et al.  Chemical Process: Design and Integration , 2005 .

[4]  David M. Himmelblau,et al.  Constrained Nonlinear Optimization by Heuristic Programming , 1969, Oper. Res..

[5]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[6]  Shengdun Zhao,et al.  A flexible tolerance genetic algorithm for optimal problems with nonlinear equality constraints , 2009, Adv. Eng. Informatics.

[7]  Lixing Han,et al.  Implementing the Nelder-Mead simplex algorithm with adaptive parameters , 2010, Computational Optimization and Applications.

[8]  Antonio José Gonçalves Cruz,et al.  Nonlinear constrained optimization using the flexible tolerance method hybridized with different unconstrained methods , 2017 .

[9]  E. Croft,et al.  Smooth and time-optimal trajectory planning for industrial manipulators along specified paths , 2000 .

[10]  Alfred A. Susu,et al.  Application of Tikhonov Regularization Technique to the Kinetic Data of an Autocatalytic Reaction: Pyrolysis of N-Eicosane , 2011 .

[11]  David Mautner Himmelblau,et al.  Applied Nonlinear Programming , 1972 .

[12]  FLEXIBLE TOLERANCE SIMPLEX-METHOD AND ITS APPLICATION TO MULTICOMPONENT SPECTROPHOTOMETRIC DETERMINATIONS , 1989 .

[13]  Michael D. Naish,et al.  Sensing-System Planning for the Surveillance of Moving Objects , 2004 .

[14]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization , 1999, Evolutionary Computation.

[15]  Jing J. Liang,et al.  Problem Deflnitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization , 2006 .

[16]  Ana Carolina Hortua.  Chemical process optimization and pollution prevention via mass and property integration , 2009 .

[17]  M. El‐Halwagi.  Pollution prevention through process integration : systematic design tools , 1997 .