Dept. of Mathematical Information Technology
June 13

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

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

17, 2011
Simulated Moving Bed
Cycle
Step
Liquid Flow
Feed
Desorbent
Extract
Raffinate
1
Liquid Flow
Feed
Desorbent
Extract
Raffinate
2
Liquid Flow
Feed
Desorbent
Extract
Raffinate
3
Liquid Flow
Feed
Desorbent
Extract
Raffinate
4
Liquid Flow
Feed
Desorbent
Extract
Raffinate
5
Liquid Flow
Feed
Desorbent
Extract
Raffinate
6
Liquid Flow
Feed
Desorbent
Extract
Raffinate
7
Liquid Flow
Feed
Desorbent
Extract
Raffinate
8
Liquid Flow
Feed
Desorbent
Extract
Raffinate
9
Liquid Flow
Feed
Desorbent
Extract
Raffinate
10
Liquid Flow
Feed
Desorbent
Extract
Raffinate
11
Liquid Flow
Feed
Desorbent
Extract
Raffinate
12
Liquid Flow
Feed
Desorbent
Extract
Raffinate
13
Liquid Flow
Feed
Desorbent
Extract
Raffinate
14
Liquid Flow
Feed
Desorbent
Extract
Raffinate
15
Liquid Flow
Feed
Desorbent
Extract
Raffinate
16
Liquid Flow
Feed
Desorbent
Extract
Raffinate
17
Adapted from Y. Kawajiri, Carnegie Mellon University
MCDM2011, Jyväskylä, Finland
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
Dept. of Mathematical Information Technology
June 13

17, 2011
Multiobjective SMB problem
MCDM2011, Jyväskylä, Finland
Hakanen et al.,
Control & Cybernetics
, 2007
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
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
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, 2011
MCDM2011, Jyväskylä, Finland
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
Dept. of Mathematical Information Technology
Radial Basis Function (RBF)
Training data consists of pairs
Basis functions e.g.
–
Gaussian:
–
polyharmonic spline:
June 13

17, 2011
MCDM2011, Jyväskylä, Finland
k
i
y
x
i
i
,
,
1
),
,
(
,
5
,
3
,
1
,
)
(
j
r
r
j
0
,
)
(
2
r
e
r
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
2
8
)
(
r
e
r
3
)
(
r
r
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
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
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
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
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
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
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