dept. of mathematical information technology june 13-17, 2011mcdm2011, jyväskylä, finland on...

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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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June 13-17, 2011

Outline

Motivation

Simulated Moving Bed (SMB) process

Multiobjective optimization of SMBs

Metamodelling

Metamodelling-based global optimization of SMBs

Conclusions and future research

MCDM2011, Jyväskylä, Finland

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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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June 13-17, 2011

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

16

Liquid Flow

FeedDesorbent

Extract Raffinate

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Cyclic Operation

Switching interval (Step Time)

Liquid Velocities

Operating Parameters:


• 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


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:


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)


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!

June 13-17, 2011

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

[email protected]

http://users.jyu.fi/~jhaka/en/


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