Transcript Dia 1 - MCDM Society

Jussi Hakanen
Dept. of Mathematical Information Technology
University of Jyväskylä, Finland
[email protected]
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
On Metamodel-based
Multiobjective
Optimization of Simulated
Moving Bed Processes
Motivation
Simulated Moving Bed (SMB) process
Multiobjective optimization of SMBs
Metamodelling
Metamodelling-based global optimization of
SMBs
Conclusions and future research
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
Outline
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, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
Motivation
Simulated Moving Bed processes (SMB)
Based on liquid chromatographic separation
Utilizes the difference in the migration speeds of different
chemical components in liquid
* http://www.pharmaceutical-technology.com
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
*
Dept. of Mathematical Information Technology
Periodic adsorption
processes for
separation of
chemical products
Adapted from Y. Kawajiri, Carnegie Mellon University
Chromatography (single column)
Feed (Mixture of
two components)
st product
2.
4. Elution
Feed
Recover
1nd
3.
1.
Initial state
5.
2
product
Column is filled with desorbent
Pump
Chromatographic Column
(Vessel packed with adsorbent particles)
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
Desorbent
Adapted from Y. Kawajiri, Carnegie Mellon University
Step
Cycle
9617
13
14
15
16
8712
11
54321
Desorbent
Feed Desorbent
Feed
Feed Desorbent
Feed Desorbent
Feed Desorbent
Feed 10
Feed Desorbent
Feed Desorbent
Feed Desorbent
Liquid
Flow
Liquid
LiquidFlow
Flow
Extract
Raffinate
Raffinate
Raffinate
Raffinate
ExtractExtract
Raffinate
Extract
Raffinate
Extract
RaffinateExtract
Raffinate
Raffinate
Extract
Extract
Extract
Raffinate
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
Simulated Moving Bed
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
Operating Parameters:
Switching interval
(Step Time)
Liquid Velocities
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
Cyclic Operation
Hakanen et al., Control & Cybernetics, 2007
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
Multiobjective SMB problem
Multiobjective SMB problem
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
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
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
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
Previous results (local optimizer)
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, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
Remarks of the results
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
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
Metamodelling
Radial Basis Function (RBF)
2
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
Training data consists of pairs ( xi , yi ), i  1,, k
Basis functions e.g.
r

(
r
)

e
, 0
– Gaussian:
– polyharmonic spline:  (r )  r j , j  1, 3, 5,
Dept. of Mathematical Information Technology
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
–  (r )  r 3 for throughput and desorbent consumption
–  (r )  e8 r 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)
2
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
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
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
Results
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
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
Remarks
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
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
Conclusions and future research
References
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
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 LargeScale Nonlinear Programming, Mathematical
Programming, 106, 2006
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)
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
Acknowledgements
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/
June 13-17, 2011
MCDM2011, Jyväskylä, Finland
Dept. of Mathematical Information Technology
Thank You!