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June 13-17, 2011 MCDM2011, Jyväskylä, Finland
On Metamodel-based Multiobjective
Optimization of Simulated Moving Bed Processes
Jussi HakanenDept. of Mathematical Information Technology
University of Jyväskylä, [email protected]
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Outline
Motivation
Simulated Moving Bed (SMB) process
Multiobjective optimization of SMBs
Metamodelling
Metamodelling-based global optimization of SMBs
Conclusions and future research
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Motivation
SMB processes are applied to many important separations in sugar, petrochemical, and pharmaceutical industriesDynamic process operating on periodic cycles, non-convex (bilinear) functions → challenging optimization problemOptimization of SMBs involves several conflicting objectives → need for multiobjective optimizationEfficient (gradient-based) local optimizers exist but using global optimizers is time consuming (one simulation of an SMB takes seconds)
Is there a need for global optimization of SMBs?Can metamodelling techniques enable fast global optimization of multiobjective SMBs?
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Based on liquid chromatographic separation
Utilizes the difference in the migration speeds of different chemical components in liquid
Simulated Moving Bed processes (SMB)
Periodic adsorption processes for separation of chemical products
* http://www.pharmaceutical-technology.com
*
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5. Recover 2nd product4. Recover 1st product2. Feed
Desorbent Feed (Mixture of two components)
1. Initial state Column is filled with desorbent
3. Elution
Chromatography (single column)
Chromatographic Column(Vessel packed with adsorbent particles)
Pump
Adapted from Y. Kawajiri, Carnegie Mellon University
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Simulated Moving Bed
CycleStep
Liquid Flow
FeedDesorbent
Extract Raffinate
1
Liquid Flow
FeedDesorbent
Extract Raffinate
2
Liquid Flow
FeedDesorbent
Extract Raffinate
3
Liquid Flow
FeedDesorbent
Extract Raffinate
4
Liquid Flow
FeedDesorbent
Extract Raffinate
5
Liquid Flow
FeedDesorbent
Extract Raffinate
6
Liquid Flow
FeedDesorbent
ExtractRaffinate
7
Liquid Flow
FeedDesorbent
ExtractRaffinate
8
Liquid Flow
FeedDesorbent
ExtractRaffinate
9
Liquid Flow
FeedDesorbent
ExtractRaffinate
10
Liquid Flow
Feed Desorbent
ExtractRaffinate
11
Liquid Flow
Feed Desorbent
ExtractRaffinate
12
Liquid Flow
Feed Desorbent
ExtractRaffinate
13
Liquid Flow
Feed Desorbent
ExtractRaffinate
14
Liquid Flow
Feed Desorbent
Extract Raffinate
15
Liquid Flow
Feed Desorbent
Extract Raffinate
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Liquid Flow
FeedDesorbent
Extract Raffinate
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Adapted from Y. Kawajiri, Carnegie Mellon University
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Cyclic Operation
Switching interval (Step Time)
Liquid Velocities
Operating Parameters:
Adapted from Y. Kawajiri, Carnegie Mellon University
• Two inlet and two outlet streams are switched in the direction of the liquid flow at a regular interval (steptime)• Feed mixture and desorbent are supplied between columns continuously• Raffinate and extract, are withdrawn from the loop also continuously
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Multiobjective SMB problem
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Hakanen et al., Control & Cybernetics, 2007
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Multiobjective SMB problemCase study: separation of glucose/fructose (fructose used in most soft drinks and candies, price varies depending on purity)4 objective functions
maximize T = Throughput [m/h]minimize D = Desorbent consumption [m/h]maximize P = Purity of the product [%]maximize R = Recovery of the product [%]
Full discretization of the SMB model (both spatial and temporal discretization) → huge system of algebraic equations33 997 decision variables and 33 992 equality constraints5 degrees of freedom: 4 zone velocities and steptime
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Previous results (local optimizer)4 objective SMB problem was solved by using an interactive IND-NIMBUS software (Hakanen et al., Control & Cybernetics, 2007)
IND-NIMBUS – an implementation of the NIMBUS method for solving complex (industrial) problems (Miettinen, Multiple Criteria Decision Making '05, 2006)
Scalarized single objective problems produced by IND-NIMBUS were solved with IPOPT local optimizer (Wächter & Biegler, Math. Prog., 2006)
13 PO solutions generated, single PO solution took 16.4 IPOPT iterations (27.6 objective function evaluations) and 65.8 CPU s on average
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Remarks of the results
Multiobjective SMB problem is non-convex (includes bilinear functions)
Can we obtain better results by using global optimizers for scalarized problems?
One simulation of an SMB takes about 4-5 seconds → global optimization takes time
Can we use a faster model for simulation?
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MetamodellingUsed for approximating computationally costly functionsTraining data: a set of points in the decision space and their function values evaluated with the original model (or obtained from measurements)Idea: use training data to fit computationally simple functions to mimic the behaviour of the original modelTechniques e.g. Radial Basis Functions, Kriging, Neural Networks, Support Vector Regression, Polynomial Interpolation
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Radial Basis Function (RBF)
Training data consists of pairsBasis functions e.g.– Gaussian: – polyharmonic spline:
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kiyx ii ,,1),,(
,5,3,1,)( jrr j0,)(
2
rer
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Metamodelling-based optimization of SMBs
Idea: train metamodels for each objective function and use a global optimizer to solve SMB problemRBFs used in metamodelling with– 2500 points in training data (5-dimensional decision
space); training took ≈ 5 s– for throughput and desorbent consumption– for purity and recovery– mean error [%] for objectives in validation (50 points): T: 0.05, D: 0.08, P: 2.6, R: 6.0
Filtered Differential Evolution (FDE) used as a global optimizer (Aittokoski,JYU Technical report, 2008)
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28)( rer
3)( rr
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Aim: study applicability of metamodelling-based optimization in SMB problems Comparison with existing results with IND-NIMBUS; PO solutions produced by solving achievement scalarizing problems (by Prof. Wierzbicki)
Global optimizer FDE gave better results than local IPOPT:– 88% better values (on the average) for the
achievement scalarizing function (from 27% to 121%) → solutions closer to the reference point
→ SMB optimization problem has local optima!
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Results
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RemarksSolving an achievement scalarizing problem with FDE (2000 function evals) took ≈ 15 sPreviously: single PO solution took 16.4 IPOPT iterations (27.6 objective function evaluations) and 65.8 CPU s on averageAccuracy of metamodelling was excellent for the first 2 objectives (error < 1%) and sufficient for the other 2 (2% < error < 6%) → needs more studyingTo summarize: results obtained are promising but more research is needed
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Conclusions and future research
Metamodelling was succesfully applied to SMBs– accuracy varied depending on the objectives
Metamodelling enabled fast global optimization for SMBsSMB problems seem to have local optimaFuture research– study more metamodelling for Purity & Recovery (try
different metamodelling techniques)– adaptive metamodel-based optimization– Evolutionary Multiobjective Optimization (EMO) (or
some hybrid) method with metamodelling
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References
Aittokoski,Efficient Evolutionary Optimization Algorithm: Filtered Differential Evolution, Reports of the Dept. of Mathematical Information Technology, JYU, 2008Hakanen, Kawajiri, Miettinen & Biegler, Interactive Multi-Objective Optimization for Simulated Moving Bed Processes, Control & Cybernetics, 36, 2007Miettinen, IND-NIMBUS for Demanding Interactive Multiobjective Optimization, In Multiple Criteria Decision Making '05, 2006Wächter & Biegler, On the Implementation of an Interior-Point Filter Line-Search Algorithm for Large-Scale Nonlinear Programming, Mathematical Programming, 106, 2006
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Acknowledgements
Timo Aittokoski, Tomi Haanpää, Prof. Kaisa Miettinen & Vesa Ojalehto, JYU
Prof. Lorenz T. Biegler and Yoshiaki Kawajiri, Carnegie Mellon University, USA
Tekes, the Finnish Funding Agency for Technology and Innovation (BioScen project in the Biorefine Technology Program)
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Thank You!
Dr Jussi Hakanen
Industrial Optimization Group
http://www.mit.jyu.fi/optgroup/
Department of Mathematical Information Technology
P.O. Box 35 (Agora)
FI-40014 University of Jyväskylä
http://users.jyu.fi/~jhaka/en/
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