Analysis of the particle swarm algorithm in the optimization of a three-phase slurry catalytic reactor
► PSO was employed to optimize the productivity of a three-phase catalytic slurry reactor. ► The reactor was represented by a multivariable non-linear rigorous mathematical model. ► Four sets of PSO parameters values suggested by the literature were evaluated. ► PSO was efficient and robust to solve...
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Published in | Computers & chemical engineering Vol. 35; no. 12; pp. 2741 - 2749 |
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Main Authors | , , , , |
Format | Journal Article |
Language | English |
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Elsevier Ltd
14.12.2011
Elsevier |
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Online Access | Get full text |
ISSN | 0098-1354 1873-4375 |
DOI | 10.1016/j.compchemeng.2011.06.001 |
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Abstract | ► PSO was employed to optimize the productivity of a three-phase catalytic slurry reactor. ► The reactor was represented by a multivariable non-linear rigorous mathematical model. ► Four sets of PSO parameters values suggested by the literature were evaluated. ► PSO was efficient and robust to solve the constrained optimization problem. ► Optimization effectiveness was independent of the values of the PSO parameters.
The Particle Swarm Optimization (PSO) method was employed to optimize an industrial chemical process characterized by being difficult to be optimized by conventional deterministic methods. The chemical process is a three phase catalytic slurry reactor (tubular geometry) in which the reaction of the hydrogenation of o-cresol producing 2-methyl-cyclohexanol is carried out. The optimization problem was formulated considering as input variables the operating conditions of the reactor and as objective function the maximization of productivity, subject to the environmental constraint of conversion. The process was represented by a multivariable non-linear rigorous mathematical model and in order to solve the optimization problem, the performance of the PSO algorithm was evaluated considering four sets of parameters values suggested by the literature. PSO demonstrated to be efficient and robust to solve the constrained optimization problem, independently of the values of the PSO parameters. The solution of the rigorous mathematical model of the reactor was associated with a high computational burden, and although the PSO algorithm presented high rate of convergence, the attempt to make possible the optimization in a timeframe suitable to real time applications failed because the algorithm lost robustness (fraction of the number of runs the algorithm reached the optimization goal) when run with a reduced number of function evaluations. Therefore, if this type of application is desired, simplified mathematical models with fast and simple numerical methods must be preferred. |
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AbstractList | The Particle Swarm Optimization (PSO) method was employed to optimize an industrial chemical process characterized by being difficult to be optimized by conventional deterministic methods. The chemical process is a three phase catalytic slurry reactor (tubular geometry) in which the reaction of the hydrogenation of o-cresol producing 2-methyl-cyclohexanol is carried out. The optimization problem was formulated considering as input variables the operating conditions of the reactor and as objective function the maximization of productivity, subject to the environmental constraint of conversion. The process was represented by a multivariable non-linear rigorous mathematical model and in order to solve the optimization problem, the performance of the PSO algorithm was evaluated considering four sets of parameters values suggested by the literature. PSO demonstrated to be efficient and robust to solve the constrained optimization problem, independently of the values of the PSO parameters. The solution of the rigorous mathematical model of the reactor was associated with a high computational burden, and although the PSO algorithm presented high rate of convergence, the attempt to make possible the optimization in a timeframe suitable to real time applications failed because the algorithm lost robustness (fraction of the number of runs the algorithm reached the optimization goal) when run with a reduced number of function evaluations. Therefore, if this type of application is desired, simplified mathematical models with fast and simple numerical methods must be preferred. ► PSO was employed to optimize the productivity of a three-phase catalytic slurry reactor. ► The reactor was represented by a multivariable non-linear rigorous mathematical model. ► Four sets of PSO parameters values suggested by the literature were evaluated. ► PSO was efficient and robust to solve the constrained optimization problem. ► Optimization effectiveness was independent of the values of the PSO parameters. The Particle Swarm Optimization (PSO) method was employed to optimize an industrial chemical process characterized by being difficult to be optimized by conventional deterministic methods. The chemical process is a three phase catalytic slurry reactor (tubular geometry) in which the reaction of the hydrogenation of o-cresol producing 2-methyl-cyclohexanol is carried out. The optimization problem was formulated considering as input variables the operating conditions of the reactor and as objective function the maximization of productivity, subject to the environmental constraint of conversion. The process was represented by a multivariable non-linear rigorous mathematical model and in order to solve the optimization problem, the performance of the PSO algorithm was evaluated considering four sets of parameters values suggested by the literature. PSO demonstrated to be efficient and robust to solve the constrained optimization problem, independently of the values of the PSO parameters. The solution of the rigorous mathematical model of the reactor was associated with a high computational burden, and although the PSO algorithm presented high rate of convergence, the attempt to make possible the optimization in a timeframe suitable to real time applications failed because the algorithm lost robustness (fraction of the number of runs the algorithm reached the optimization goal) when run with a reduced number of function evaluations. Therefore, if this type of application is desired, simplified mathematical models with fast and simple numerical methods must be preferred. |
Author | Melo, Delba Nisi Cosme de Toledo, Eduardo Coselli Vasco Filho, Rubens Maciel Mariano, Adriano Pinto Costa, Caliane Bastos Borba |
Author_xml | – sequence: 1 givenname: Adriano Pinto surname: Mariano fullname: Mariano, Adriano Pinto email: adrianomariano@yahoo.com.br organization: Laboratory of Optimization, Design and Advanced Control (LOPCA), School of Chemical Engineering – University of Campinas (UNICAMP), Av. Albert Einstein 500, CEP 13083-852, Campinas, SP, Brazil – sequence: 2 givenname: Caliane Bastos Borba surname: Costa fullname: Costa, Caliane Bastos Borba organization: Department of Chemical Engineering, Federal University of São Carlos (UFSCar), Brazil – sequence: 3 givenname: Eduardo Coselli Vasco surname: de Toledo fullname: de Toledo, Eduardo Coselli Vasco organization: Petrobras SA, Paulínia Refinery (REPLAN), Brazil – sequence: 4 givenname: Delba Nisi Cosme surname: Melo fullname: Melo, Delba Nisi Cosme organization: Laboratory of Optimization, Design and Advanced Control (LOPCA), School of Chemical Engineering – University of Campinas (UNICAMP), Av. Albert Einstein 500, CEP 13083-852, Campinas, SP, Brazil – sequence: 5 givenname: Rubens Maciel surname: Filho fullname: Filho, Rubens Maciel organization: Laboratory of Optimization, Design and Advanced Control (LOPCA), School of Chemical Engineering – University of Campinas (UNICAMP), Av. Albert Einstein 500, CEP 13083-852, Campinas, SP, Brazil |
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Keywords | PSO Multiphase reactors Optimization Variable conditions Fourier transformation Evolutionary algorithm Hydrogenation Modeling Goal programming Function evaluation Chemical reactor Function maximization Convergence rate Swarm intelligence Robustness Deterministic approach Productivity Sensitivity analysis Tubular reactor Catalytic reactor Particle suspension Real time Conversion Particle swarm optimization Real time system Operating conditions Constrained optimization Non linear model Objective function Non linear effect Multivariable system Slurries |
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Snippet | ► PSO was employed to optimize the productivity of a three-phase catalytic slurry reactor. ► The reactor was represented by a multivariable non-linear rigorous... The Particle Swarm Optimization (PSO) method was employed to optimize an industrial chemical process characterized by being difficult to be optimized by... |
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SubjectTerms | Algorithms Applied sciences Catalysis Catalysts Chemical engineering Exact sciences and technology Experimental design Inventory control, production control. Distribution Mathematical analysis Mathematical models Mathematical programming Mathematics Multiphase reactors Operational research and scientific management Operational research. Management science Optimization Probability and statistics PSO Reactors Sciences and techniques of general use Statistics |
Title | Analysis of the particle swarm algorithm in the optimization of a three-phase slurry catalytic reactor |
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