The example of an ammonia synthesis plant has been
used to demonstrate that metamodel ing can be an effective
approach for solving chemical process design optimizat ion
problems. A total of six input variables, three control
variables and three noise variables, were investigated for
their impact on the operating cost of the plant. The method
produced a solution equivalent to the previously reported
best result while using a total of only 32 simulation runs to
collect data for three stages of metamodel generation. At
each stage, the best solution was produced by a model that
combined predictions from separate kriging metamodels of
basic output variables.
The metamodeling approach resembles traditional
Response Surface Methodology (RSM). The data collection
and modeling stages proceed sequentially. The size and
location of the input variable space is adjusted from stage to
stage. The results from one stage inform the selection of a
re ned space fo r the next stage. The metamodeling
approach differs from RSM in the tools that are used to
explore the deterministic simulation’s input–output relation-
ships. Derivatives of strati ed sampling, such as the Mini-
mum Bias Latin Hypercube Design (MBLHD), are used as
the data collection plans. Simple interpolating functions,
such as the kriging model, are used for the surface model-
ing. Randomized search techniques, such as the simulated
annealing algorithm, are used to optimize the surface model.
There are opportunities to investigate re nements of the
tools. Improvements in metamo del approximation error
could be obtained by use of interpo lating functions with
greater exibility. Data collection plans could be optimized
for use with speci c metamodel forms. The trade-off
between approximation error and th e number of simulation
runs in the data collection plan could be detailed. Improve-
ments in the ef ciency of the optimization algorithm could
be found by considering alternative global optimization
techniques. There is a need to demonstrate the application
of the tools to problems with a larger number of input
variables and problems involving integer input variables.
Also, automation of the process would make it less cumber-
some to implement.
However, the appeal of the metamodeling approach
should be obvious. This technique provides a means to
optimize process designs while requiring only a small
number of simulation runs. The use of computer simulation
in process design can only be expected to increase in the
future. The complexity of processes that we wish to simulate
and optimize will l ikewise increase. As engineers, we
should be receptive to the usefulness of a simplifying
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We wish to thank Russell Barton (Pennsylvania State University) for
providing us with a copy of his FORTRAN code for estimating kriging
Correspondence concerning this paper should be addressed to Professo r
K. Palmer, Department of Industrial and Systems Engineering, University
of Southern California, Los Angeles, California 90089-0193, USA.
The manuscript was received 15 October 2001 and accepted for
publication after revision 5 September 2002.
Trans IChemE, Vol 80, Pa rt A, October 2002
782 PALMER and REALFF