1. Dept. of Mathematical Information Technology June 13-17, 2011MCDM2011, Jyväskylä, Finland On Metamodel-based Multiobjective Optimization of Simulated Moving Bed Processes Jussi Hakanen Dept. of Mathematical Information Technology University of Jyväskylä, Finland jussi.hakanen@jyu.fi

2. Dept. of Mathematical Information Technology 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

3. Dept. of Mathematical Information Technology Motivation SMB processes are applied to many important separations in sugar, petrochemical, and pharmaceutical industries Dynamic process operating on periodic cycles, non-convex (bilinear) functions → challenging optimization problem Optimization of SMBs involves several conflicting objectives → need for multiobjective optimization Efficient (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? June 13-17, 2011MCDM2011, Jyväskylä, Finland

4. Dept. of Mathematical Information Technology 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 * MCDM2011, Jyväskylä, Finland

5. Dept. of Mathematical Information Technology June 13-17, 2011 5. Recover 2 nd product 4. Recover 1 st 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 MCDM2011, Jyväskylä, Finland

6. Dept. of Mathematical Information Technology June 13-17, 2011 Simulated Moving Bed Cycle Step Adapted from Y. Kawajiri, Carnegie Mellon University MCDM2011, Jyväskylä, Finland

7. Dept. of Mathematical Information Technology June 13-17, 2011 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 MCDM2011, Jyväskylä, Finland

8. Dept. of Mathematical Information Technology June 13-17, 2011 Multiobjective SMB problem MCDM2011, Jyväskylä, Finland Hakanen et al., Control & Cybernetics, 2007

9. Dept. of Mathematical Information Technology June 13-17, 2011 Multiobjective SMB problem Case 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 equations 33 997 decision variables and 33 992 equality constraints 5 degrees of freedom: 4 zone velocities and steptime MCDM2011, Jyväskylä, Finland

10. Dept. of Mathematical Information Technology June 13-17, 2011 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 MCDM2011, Jyväskylä, Finland

11. Dept. of Mathematical Information Technology 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? June 13-17, 2011MCDM2011, Jyväskylä, Finland

12. Dept. of Mathematical Information Technology June 13-17, 2011 Metamodelling Used for approximating computationally costly functions Training 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 model Techniques e.g. Radial Basis Functions, Kriging, Neural Networks, Support Vector Regression, Polynomial Interpolation MCDM2011, Jyväskylä, Finland

13. Dept. of Mathematical Information Technology Radial Basis Function (RBF) Training data consists of pairs Basis functions e.g. –Gaussian: –polyharmonic spline: June 13-17, 2011MCDM2011, Jyväskylä, Finland

14. Dept. of Mathematical Information Technology June 13-17, 2011 Metamodelling-based optimization of SMBs Idea: train metamodels for each objective function and use a global optimizer to solve SMB problem RBFs 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) MCDM2011, Jyväskylä, Finland

15. Dept. of Mathematical Information Technology 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 MCDM2011, Jyväskylä, Finland

16. Dept. of Mathematical Information Technology June 13-17, 2011 Remarks Solving an achievement scalarizing problem with FDE (2000 function evals) took ≈ 15 s Previously: single PO solution took 16.4 IPOPT iterations (27.6 objective function evaluations) and 65.8 CPU s on average Accuracy of metamodelling was excellent for the first 2 objectives (error < 1%) and sufficient for the other 2 (2% < error < 6%) → needs more studying To summarize: results obtained are promising but more research is needed MCDM2011, Jyväskylä, Finland

17. Dept. of Mathematical Information Technology June 13-17, 2011 Conclusions and future research Metamodelling was succesfully applied to SMBs –accuracy varied depending on the objectives Metamodelling enabled fast global optimization for SMBs SMB problems seem to have local optima Future 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 MCDM2011, Jyväskylä, Finland

18. Dept. of Mathematical Information Technology June 13-17, 2011 References Aittokoski,Efficient Evolutionary Optimization Algorithm: Filtered Differential Evolution, Reports of the Dept. of Mathematical Information Technology, JYU, 2008 Hakanen, Kawajiri, Miettinen & Biegler, Interactive Multi-Objective Optimization for Simulated Moving Bed Processes, Control & Cybernetics, 36, 2007 Miettinen, IND-NIMBUS for Demanding Interactive Multiobjective Optimization, In Multiple Criteria Decision Making '05, 2006 Wächter & Biegler, On the Implementation of an Interior-Point Filter Line-Search Algorithm for Large- Scale Nonlinear Programming, Mathematical Programming, 106, 2006 MCDM2011, Jyväskylä, Finland

19. Dept. of Mathematical Information Technology June 13-17, 2011 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) MCDM2011, Jyväskylä, Finland

20. Dept. of Mathematical Information Technology June 13-17, 2011 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 jussi.hakanen@jyu.fi http://users.jyu.fi/~jhaka/en/ MCDM2011, Jyväskylä, Finland