Multi-objective optimization in combinatorial chemistry applied to the selective catalytic reduction of NO with C3H6

Article abstract of DOI:10.1016/j.jcat.2007.09.025

A high-throughput approach, aided by multi-objective experimental design of experiments based on a genetic algorithm, was used to optimize the combinations and concentrations of a noble metal-free solid catalyst system active in the selective catalytic reduction of NO with C₃H₆. The optimization framework is based on PISA [S. Bleuler, M. Laumanns, L. Thiele, E. Zitzler, Proc. of EMO'03 (2003) 494], and two state-of-the-art evolutionary multi-objective algorithms-SPEA2 [E. Zitzler, M. Laumanns, L. Thiele, in: K.C. Giannakoglou, et al. (Eds.), Evolutionary Methods for Design, Optimisation and Control with Application to Industrial Problems (EUROGEN 2001), International Center for Numerical Methods in Engineering (CIMNE), 2002, p. 95] and IBEA [E. Zitzler, S. Kuenzli, Conference on Parallel Problem Solving from Nature (PPSN VIII), 2004, p. 832]-were used for optimization. Constraints were satisfied by using so-called repair algorithms. The results show that evolutionary algorithms are valuable tools for screening and optimization of huge search spaces and can be easily adapted to direct the search towards multiple objectives. The best noble metal free catalysts found by this method are combinations of Cu, Ni, and Al. Other catalysts active at low temperature include Co and Fe.

Full text of DOI:10.1016/j.jcat.2007.09.025

Journal of Catalysis 252 (2007) 205–214
www.elsevier.com/locate/jcat
Multi-objective optimization in combinatorial chemistry applied
to the selective catalytic reduction of NO with C3H6
Oliver Christian Gobin, Alberto Martinez Joaristi, Ferdi Schüth ∗
Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, Mülheim an der Ruhr, Germany
Received 21 May 2007; revised 14 September 2007; accepted 27 September 2007
Abstract
A high-throughput approach, aided by multi-objective experimental design of experiments based on a genetic algorithm, was used to optimize
the combinations and concentrations of a noble metal–free solid catalyst system active in the selective catalytic reduction of NO with C H . The
3
6
optimization framework is based on PISA [S. Bleuler, M. Laumanns, L. Thiele, E. Zitzler, Proc. of EMO’03 (2003) 494], and two state-of-the-art
evolutionary multi-objective algorithms—SPEA2 [E. Zitzler, M. Laumanns, L. Thiele, in: K.C. Giannakoglou, et al. (Eds.), Evolutionary Methods
for Design, Optimisation and Control with Application to Industrial Problems (EUROGEN 2001), International Center for Numerical Methods
in Engineering (CIMNE), 2002, p. 95] and IBEA [E. Zitzler, S. Künzli, Conference on Parallel Problem Solving from Nature (PPSN VIII),
2004, p. 832]—were used for optimization. Constraints were satisfied by using so-called “repair algorithms.” The results show that evolutionary
algorithms are valuable tools for screening and optimization of huge search spaces and can be easily adapted to direct the search towards multiple
objectives. The best noble metal free catalysts found by this method are combinations of Cu, Ni, and Al. Other catalysts active at low temperature
include Co and Fe.
© 2007 Elsevier Inc. All rights reserved.
Keywords: Multi-objective evolutionary optimization; Genetic algorithm; High-throughput experimentation; Selective catalytic reduction; Mixed metal oxides;
DeNOx; SPEA2; IBEA
1. Introduction
of biocatalysts [8–10]. The design of combinatorial libraries in
the drug industry has one application of this method [11–13].
In the field of heterogeneous catalysis, Wolf et al. [14] were
the first to use an evolutionary approach to optimize the com-
binations of elements of multicomponent solid catalysts. Since
then, several groups have optimized solid catalysts with the aid
of genetic algorithms [15–19]. However, up to now, the search
has been conducted toward one sole objective. In real world
problems and especially in catalysis, several, often conflicting
objectives generally must be taken into account. Thus, methods
that are able to find optimal solutions with respect to several
goals are needed.
In general, a multi-objective optimization problem can
be defined as finding a vector of decision variables, x =
(x1, x1, ... , xm) ∈ X, in the decision space X that optimizes
a vector function f : X → Y by assigning the quality of a
specific solution x to a vector of objective variables y =
(y1, y1, ... , yn) ∈ Y in the multidimensional objective space Y.
In the case of a solid catalyst, the decision variables can be any
High-throughput experimentation (HTE) and combinatorial
methods for the development of new catalysts are attracting in-
creasing attention in both industry and academia [1–6]. One
important element in HTE, common to both homogeneous and
heterogeneous catalysis, is the design of experiments and of li-
braries to find new and improved catalysts. The need is for intel-
ligent methods that are able to direct the screening to the desired
direction and minimize the number of experiments needed to
achieve a significant improvement. Evolutionary methods, such
as genetic algorithms, have been found to be efficient and highly
flexible in solving various combinatorial and global optimiza-
tion problems in complex and multidimensional spaces [7]. Di-
rected evolution has proven a versatile and powerful method
for the generation of combinatorial libraries and development
*
Corresponding author.
E-mail address: schueth@mpi-muelheim.mpg.de (F. Schüth).
0021-9517/$ – see front matter © 2007 Elsevier Inc. All rights reserved.
doi:10.1016/j.jcat.2007.09.025

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O.C. Gobin et al. / Journal of Catalysis 252 (2007) 205–214
set of appropriate descriptors to be optimized. A functional re-
lation should exist between the m decision variables and the
n objective functions. A quantitative structure activity relation-
ship (QSAR) model, which can assign the quality of a solution x
to the objective vector y, can be used for modeling such a prob-
lem [20–22]. However, up to now QSAR, modeling of complex
systems, such as solid catalysts, carries a high error in predic-
tion. Thus, a model must first be developed. For this reason,
when screening for new solutions in unknown decision spaces,
evaluation of the objective functions can be done only exper-
imentally or using a hybridization of an experimental and a
QSAR approach. In the present work, we focus on the purely
experimental approach.
In the last few years, in the light of the energy problem
and global warming, additional efforts have been made to pre-
vent the release of substances that amplify these environmen-
tal problems. Therefore, diesel and lean-burn gasoline engines
are becoming more and more attractive compared with regu-
lar gasoline engines due to the higher efficiency with respect to
fuel consumption. Also, increasingly stringent emission regu-
lations of harmful substances for vehicles urgently require new
catalysts that are highly active for the selective reduction of ni-
trogen oxides in oxygen-rich conditions. One group of possible
catalysts are noble metal–free metal oxides. The number of pos-
sible combinations is vast, and some have been investigated on
various supports in recent years [23–25].
vated carbon (R1424, Carbotec/Rütgers) from the same activa-
tion batch was used as an exotemplate because of its exceptional
properties: high purity (ash content <0.5 wt%) and very high
BET surface area (1800 m2/g) and pore volume (0.9 cm3/g).
The pore system consists of a very high fraction of micropores
with diameter <1 nm, with particles almost uniform spheres
200–400 µm in diameter. The impregnation was carried out by
an automated liquid-handling robot (ABIMED) using 2 M pre-
cursor solutions of the corresponding metal nitrates: Ni(NO3)2
from Fluka, purum p.a.; Cu(NO3)2, Co(NO3)2, La(NO3)3
from Fluka puriss p.a.; Al(NO3)3, K(NO3), Sr(NO3)2,
Mn(NO3)2, Fe(NO3)3 from Merck, GR for analysis; Ce(NO3)3
and Sm(NO3)3 from Acros Organics (99.9% pure). After the
precursor solutions were mixed by the robot, the mixed so-
lutions were used to impregnate the activated carbon using a
slight excess of solution (for 1 g of activated carbon, 0.99 mL
of solution). Calcination was performed without additional dry-
ing at 973 K for 3 h in air to combust the carbon, resulting in
the formation of the mixed metal oxides. The resulting mixed
oxide particles were also uniform and spherical in most cases,
and of similar diameter as the carbon exotemplate, as can be
seen in Fig. S1 for a representative Cu/Ni/Al particle.
2.2. Characterization
Powder X-ray diffraction (XRD) patterns were obtained us-
ing a Bragg–Brentano diffractometer (PANalytical, X’Pert Pro).
The data were collected using CuKα radiation (1.54056 Å),
a secondary Ni-filter, and an X’Celerator detector. Patterns
were recorded in the range of 15–70◦ 2Θ and a step width
of 0.0167◦. Nitrogen physisorption isotherms were measured
using a Quantachrome NOVA 3000e sorptometer at liquid ni-
trogen temperature (77 K), after outgassing under vacuum at
523 K for at least 2 h. Particle shape and size were estimated by
scanning electron microscopy (SEM) using a Hitachi S-3500N
scanning electron microscope operating at 10 kV. The samples
were coated with a thin layer of gold before analysis.
In this work, we present a method for experimental optimiza-
tion with respect to multiple objectives. We focus on the opti-
mization of metal oxides consisting of combinations of 11 ele-
ments, selected from the transition metal (Cu, Ni, Co, Fe, Mn),
lanthanide (La, Ce, Sm), and alkali metal (K, Sr) groups. Alu-
mina was used as the support, because of its ability to develop
high surface area and its high hydrothermal stability. A combi-
natorial, evolutionary directed, high-throughput multi-objective
optimization approach was applied to this system. Due to its
importance in industry, the selective catalytic reduction of ni-
trogen oxide with C3H6 is used as a test case for this approach.
Two important factors that determine the quality of a cata-
lyst include the maximum conversion that can be achieved and
the temperature at which high conversion is possible. Due to
the fact that most of the restricted compounds are emitted in the
early phase of the driving cycle, when the catalyst is still cold,
a low temperature for high conversion is preferable. Thus, the
catalysts will be optimized with respect to two objectives: the
conversion to nitrogen and the temperature at which the yield is
maximal (the so-called “peak” or “light-off” temperature). We
applied two different multi-objective algorithms—SPEA2 [26]
and IBEA [27]—to this problem. We compare and discuss the
results of the two algorithms, emphasizing some implementa-
tion and encoding issues common to heterogeneous catalysis.
2.3. Catalytic testing
A stage II high-throughput screening concept using a 49
parallel stainless steel gas-phase reactor from hte Aktienge-
sellschaft, built according to the principles described in Kiener
et al. [30], was used for testing the catalytic activity of the
mixed oxide catalysts in the selective catalytic reduction of
NO with C3H6 under lean-burn conditions. Fig. 1 shows sev-
eral images of the reactor setup. The catalysts were activated
at 573 K under a nitrogen flow for at least 2 h before cat-
alytic testing. The measurements were performed under a mix-
ture of 2000 ppm C3H6, 1500 ppm NO, and 5% O2 at GSHV
∼20,000 h−1 and a reactor pressure of 1.2 bar at up to 10 differ-
ent temperatures for each catalyst. To reduce the time needed
for the catalytic testing of all 49 catalysts, the temperature of
the reactor was increased steadily from 473 to 773 K at a rate
of 12 K/h. Thus, the complete testing of all 49 catalysts at up
to 10 different temperatures took about 25 h.
2. Experimental
2.1. Catalyst synthesis
The mixed oxide catalysts were prepared by the activated
carbon route [28,29], using metal nitrates as precursors. Acti-

O.C. Gobin et al. / Journal of Catalysis 252 (2007) 205–214
207
new and improved solutions in an intelligent way. Interactions
among design variables or components are intrinsically consid-
ered. These techniques are inspired by evolutionary biology;
they maintain several potential solutions in parallel (a pop-
ulation), and the solutions undergo recombination, mutation,
and selection steps during each iteration. One iteration loop is
called a generation. After a certain number of generations, the
algorithm converges, and, ideally, it finds the globally optimal
solution.
Genetic algorithms are also suited for experimental design
with respect to several goals or objective functions. In single-
objective optimisation, the optimal solution is clearly defined,
and only one possible solution exists. In the case of multi-
objective optimization, where we attempt to optimize all of the
objectives at the same time, the situation is completely differ-
ent, because two optimal solutions may differ. Thus, the optimal
solution is a composite of all optimal solutions with respect to
multiple objectives and usually forms a set of optimal trade-off
surfaces that also includes the single objective optimum. This
set of optimal solutions is designated the Pareto-optimal set. In
multi-objective optimization, generally the goal is to approxi-
mate this set and keep the population as diverse as possible.
The platform and programming language independent inter-
face for search algorithms (PISA) [31] was chosen to build up
the optimization framework. PISA was recently developed by
Bleuler et al. [31] to reduce the programming and implemen-
tation overhead for application engineers and to facilitate the
use of different optimization methods on different test prob-
lems. The idea behind PISA is to divide the implementation of
an optimization method into an application-specific part (e.g.,
screening for new catalysts) and in an algorithm-specific part.
The application-specific part is written in Matlab and is desig-
nated the variator, because it includes all of the variation op-
erators. The algorithm-specific part is designated the selector,
because it performs the ranking and selection of solutions. Ran-
dom numbers were obtained from RANDOM.ORG [32], which
offers true random numbers generated from atmospheric noise.
SPEA2 [26] and IBEA [27] were used as selector algorithms.
For IBEA, an ε-indicator was used. The IBEA parameters κ
and ρ were set to 0.05 and 1.1, respectively. Elitism is im-
plemented in both algorithms using an additional population,
the so-called “external” or “archive” population. In SPEA2,
diversity along the Pareto-optimal front is preserved through
a density estimation technique that uses a k-nearest-neighbor
clustering algorithm. The fitness assignment of IBEA is already
diversity-preserving, and thus no additional density estimation
technique is needed.
Fig. 1. Images of the 49 parallel channel reactor set-up: (A) side view on the
complete setup, (B) closed reactor and (C) top view on the open reactor.
The exhaust gas compounds were analyzed by Fourier trans-
form infrared (FTIR) spectroscopy, using a Thermo Electron
Nicolet Avatar 370 with a 17-mL gas cell heated to 303 K. The
resolution of the system was set to 1.0 cm−1, the aperture to
100, and the gain to 8. The pressure at the outlet of the gas cell
was set to 1.2 bar. Eight scans were obtained for each spectrum,
and a total of four spectra were recorded for each analysis.
2.4. Calculations
From the IR spectra, the gas concentrations of NO, NO2,
N2O, C3H6, CO, CO2, and H2O were evaluated at two charac-
teristic wavelengths. The N2 concentration was calculated from
the NO, NO2, and N2O concentrations using the nitrogen mass
balance; it was assumed that no additional nitrogen compounds
were formed. Both objective functions are to be minimized and
are obtained by normalization of the maximum conversion of
NO to N2 and of the temperature at which the conversion is
maximal:
out
out
out
[NO] − [NO2] − 2[N2O]
1 − yield to N2 = 1 −
,
in
[NO]
Tmax,yield − 800 K
normalized temperature = 1 −
.
150 K − 800 K
In this work, to ensure robustness to noise, new solutions
were preferred to old solutions during the selection process, to
reduce the impact of fortuitously good solutions. In addition,
population size is a critical factor [33,34], and the selection in-
tensity [35] should be correctly chosen to reduce the effects of a
noisy environment. A low selection intensity was obtained us-
ing a binary tournament selection algorithm. A detailed study
of the behavior of different algorithms in the presence of noise
was conducted by Hancock [36].
The normalization parameters were chosen to have the same
scale for both objectives.
3. Experimental design by evolutionary multi-objective
optimization
Evolutionary techniques such as genetic algorithms are
global search techniques, which can be used for experimen-
tal design. They include heuristic strategies for searching for

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O.C. Gobin et al. / Journal of Catalysis 252 (2007) 205–214
The initial population size (α), parent population size (μ),
Table 1
Discrete encodings of the element concentrations
and offspring population size (λ) were all set to 24 individuals.
Also, the archive size was set to 24. In a preliminary test, 48
randomly chosen catalysts were tested, and 19 catalysts cov-
ering the whole decision space were selected to build up the
initial population. Along with these 19 randomly created cata-
lysts, five selected single-oxide catalysts (10 and 33 mol% Cu,
10 mol% Mn, 10 and 33 mol% Ni, and Al as remainder) were
included in the initial population. It was the same for both algo-
rithms, to ensure the same starting point for the optimization
process. The catalysts were encoded using binary vectors of
27 bits. We discuss this decision in more detail and provide an
exact definition of the space explored in the next section. An
extended version of this section with a more detailed explana-
tion of the algorithm and additional implementation guidelines
is available in the supplementary material.
Genotype
Phenotype (mol%)
with support
Phenotype (mol%)
without support
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
0.5
1.0
2.0
4.0
6.0
8.0
10
12
16
20
24
28
32
33.3
34
35
2.0
4.0
8.0
12
16
20
25
30
33.3
35
40
50
63
75
88
100
4. Representation of solid catalysts and definition of the
space to be explored
4.1. Encoding of the element combinations and concentrations
A total of 11 elements in different combinations and vary-
ing concentrations compose the search space of the so-called
“deNOx problem”—finding the best combination and compo-
sition of elements in a catalyst active at low temperature in
HC-SCR. The elements can be classified into three groups:
(1) elements acting as support with a high molar fraction in
the catalyst, (2) the main elements with likely a major contribu-
tion to the catalytic reactivity of the catalyst, and (3) elements
acting as promoter, with only a small molar fraction in the cat-
alyst. As stated before, Al was chosen as the element for the
support; Cu, Ni, Co, Fe, Mn, La, Ce, and Sm were chosen as
the main elements; and K and Sr were chosen as the promot-
ers. Some boundary conditions (denoted as constraint C.i) were
introduced to reduce the search space and incorporate chem-
ical knowledge into the encoding. Systems with and without
support were treated separately; the maximum number of main
elements in a catalyst was four or fewer (constraint C.1). For
systems with support, the Al concentration had to be >33.3 and
<95.0 mol%. The concentration of each main element was lim-
ited to 35 mol% (C.2). For systems without support, the maxi-
mum allowed Al concentration in a catalyst was 33.3 mol%, and
the concentration for each main element was unrestricted (C.3).
Only a maximum of two elements from the lanthanides se-
ries could be present simultaneously in a catalyst (C.4). The
sum of the concentrations of the promoter elements was lim-
ited to 5.0 mol%; a catalyst could contain both promoter ele-
ments (C.5). Superimposed on these self-introduced boundary
conditions was the trivial requirement that the sum of all con-
centrations equal 100 mol%. For both systems, Al constituted
the remainder (C.6).
Various encodings can be considered for encoding the com-
binations of the elements. For such combinatorial problems,
a binary representation is generally chosen [37]. Vectors of in-
teger numbers also could be used, but special genetic operators
would be required. We chose to encode the combinatorial part
of the problem by a binary vector. The most direct way to do
this is to use 1 bit for each element [14].
In contrast to encoding the combinations, encoding of the
element concentrations is a continuous problem. For such prob-
lems, using an evolution strategy with floating point vectors as
data type seems to be the natural way to represent the search
space properly. But using binary vectors has some important
advantages, especially when dealing with experimental opti-
mization problems. Using continuous data structures in experi-
mental optimization makes sense only if the experimental error
of the design variables tends toward zero. Typically, the exper-
imental procedures are not as accurate, and an unintentional
discretization of the search space occurs; therefore, binary en-
coding seems more reasonable. The step size should be signif-
icantly larger than the expected experimental error. Thus, an
advantage of the discretization of a continuous problem is re-
duced accuracy and dimension of the search space to promote
faster convergence [38]. Moreover, if both the combinatorial
and the continuous part of the problem are represented by a
single binary vector, then no special variation operators are re-
quired, and adaptation by building blocks as described by the
schema theorem is valid [39].
We chose to discretize the concentrations into 16 steps by
using a binary representation of 4 bits for each main element.
Due to the maximal number of four main elements in a catalyst
(constraint C.1), 16 bits are required for encoding the concen-
trations. Using the ABIMED robot for synthesis of the catalyst,
the minimal volume that can be handled is about 1–3 µL; thus,
a minimal step size of 5 µL (roughly 0.5 mol%) is reasonable.
The discretization of the problem also allows the use of dif-
ferent step sizes and incorporation of some problem-specific
It is important to note due to the premixing of the metal ni-
trates before impregnation, the resulting metal oxides are not re-
ally supported on Al. Al atoms may be part of the active phase.
However, Al is important for obtaining high surface areas, and
by itself has very low activity; therefore, Al is designated a sup-
port if constraint C.2 is fulfilled.

O.C. Gobin et al. / Journal of Catalysis 252 (2007) 205–214
209
Fig. 2. Final encoding using 11 bits for the combinatorial and 16 bits for the
continuous part of the problem.
knowledge. Most of the metal oxides form spinel phases at
33 mol%; thus, these concentrations should be encoded re-
gardless of the step size. Also, it could make sense to use a
smaller step size for the region below 15 mol%. In contrast,
around the spinel concentrations, the step size at high load-
ing can be coarser. Table 1 gives the discrete concentration
encodings (genotypes) with the corresponding decoded values
(phenotypes).
Fig. 2 shows the complete encoding. A binary one-point
crossover operator with a crossover probability of pc = 1 and a
binary bit-flip mutation operator with a mutation probability of
pm = 1/27 = 0.037 were applied on the whole chromosome to
recombine and to mutate the parent solutions.
Fig. 3. Flowchart of a multi-objective optimization algorithm for constrained
problems (see Section 3 and Zitzler et al. [26] for explanation).
4.2. Handling constraints
Michalewicz [37] investigated several techniques for deal-
ing with constrained problems, including (a) the design of two
evaluation functions for the feasible and infeasible domains,
(b) the rejection of infeasible solutions (death penalty), (c) the
penalization of infeasible solutions by penalty functions, (d) the
use of so-called “repair functions” to repair infeasible solutions,
and (e) the adaptation of genetic operators and the use of spe-
cial representations to maintain a feasible population. Although
certainly not complete, this list summarizes some of the most
popular techniques. Only options (d) and (e) (i.e., maintaining
a feasible population by special representations, genetic opera-
tors, or repair functions) seem to be good choices in the case of
experimental optimization, as the evaluation system is used at
maximal capacity. Because repairing infeasible solutions in the
deNOx problem is relatively easy, we chose to use repair func-
tions to repair both invalid combinations of elements and in-
valid concentration ranges. Fig. 3 shows a general flowchart of
a multi-objective optimization algorithm for constrained prob-
lems. Figs. S2 and S3 illustrate the repair algorithms for the
combinatorial and the continuous part of the deNOx problem in
flowcharts.
Fig. 4. NO to N conversion distribution in the reactor. Even positions are filled
2
with with Pt/Al O , and uneven positions with Al O .
2
3
2 3
channels were left empty to determine whether the reactor
channels were influencing each other, which should not be the
case if the flow rate and the dead time are sufficiently high to
guarantee stable conditions. Fig. 4 shows the distribution of the
maximum conversion of NO to N2 at the temperature at which
the conversion is maximal (the peak temperature). The conver-
sion distribution shown in Fig. 4 is very narrow with a standard
deviation of 0.0167, corresponding to an error of about 3.4%.
The maximum deviation from the average value was about 0.03
(6%). This error can be interpreted as the error of the reactor
5. Results and discussion
5.1. Errors of the reactor setup and synthesis
The conversion distribution of the reactor was obtained by
placing the same amount of a reference Pt/Al2O3 catalyst from
the same batch into 24 channels of the reactor. The other 25

210
O.C. Gobin et al. / Journal of Catalysis 252 (2007) 205–214
system and is sufficient for a stage II screening. In the distribu-
tion of the peak temperature of the NO to N2 conversion, the
error was about 2 K (0.4%), as shown in Fig. S4. The flow
rate distribution is shown in Fig. S5. From Figs. 4 and S4,
it can be seen that the channels did not influence each other.
In no case was the maximal conversion of the empty chan-
nels >0.03.
The reproducibility of the synthesis was checked by per-
forming several tests on a series of 10 equal catalysts composed
of a ternary metal oxide supported on Al oxide. The catalysts
were impregnated with a nitrate mixture consisting of 70 mol%
Al, 12 mol% Cu, 6 mol% Fe, and 12 mol% Ce. The results indi-
cate that the reproducibility was sufficiently high for a stage II
screening approach. The maximum NO to N2 conversion was
0.133 0.007, and the peak temperature of the maximal con-
version was 618.6 7.1 K, corresponding to errors of about 5%
(standard deviation) in the peak conversion and of <1.5% in the
peak temperature. The maximum error in the case of the peak
conversion was roughly 9%, corresponding to the maximum
possible error of the catalytic test together with the synthesis
procedure, because the different catalysts were synthesized in
individual batches.
Fig. 5. Evolution of the objective function (1 − yield) for the solutions of the
archive population for SPEA2.
wise manner. The boxes representing 50% of the data increased
in most of the cases, and the lengths of the upper and lower
whiskers tended to decrease during the evolution due to the im-
proved distribution of the solutions along the (1 − yield) axis
and along the peak temperature axis. This is another an indica-
tion of successful convergence toward the Pareto-optimal front
and of the good diversity preservation of both algorithms.
Fig. 6 shows the archive populations of SPEA2 and IBEA
for selected generations in Pareto plots in the objective space.
Because both objective functions are to be minimized, the non-
dominating solutions formed a trade-off front from the upper
left to the lower right part of the plot. Both algorithms ap-
proached the Pareto-optimal front with each generation. The
convergence process can be clearly distinguished, and it also
can be seen that each algorithm approached the Pareto-optimal
front in a different way. SPEA2 was able to find a better solu-
tion for the NO conversion after seven generations than IBEA.
In contrast, IBEA found a better solution with respect to the
peak temperature of NO conversion. IBEA tended to converge
strongly toward Cu-containing catalysts. In Fig. 6, this effect is
illustrated by cluster formation in the region with a high con-
version to N2. For SPEA2, some clustering can be observed,
but it is less pronounced. After the seventh generation for
both algorithms, the solutions were well distributed along the
Pareto-optimal front. However, SPEA2 was able to approach
the Pareto-optimal front better than IBEA, and, in addition, the
distribution was slightly better.
5.2. Experimental optimization of the deNOx problem
In this section, we first present and discuss the experimen-
tal results obtained by two independent single runs for each
algorithm. As already mentioned in Section 3, both initial popu-
lations were identical; however, it is important to note that these
evolutionary processes are stochastic, and a fully valid compar-
ison of the performance of the algorithms is not possible by
only carrying out a single run. Only the results observed here
that can be influenced by random effects can be compared. For a
reliable comparison, many experimental optimization programs
with random initial populations must be compared, which is not
feasible in a reasonable time frame even with high-throughput
methods. But before the experimental optimization was done,
the performance of the algorithms was evaluated using test
functions and encodings with similar properties than the de-
NOx problem by carrying out 100 runs with different random
seeds [40].
In addition, it is very important to point out that in our
case, only a specific system—combinations of 11 elements with
certain restrictions synthesized by the activated carbon route—
was optimized. When using other synthetic protocols, different
combinations of elements or different concentrations may form
the optimal set. However, for the bounded problem given here,
we are fairly confident that the system cannot be improved
much further.
It is noteworthy that the Pareto plots in Fig. 6 provide very
efficient visualization of the objective space, useful for extrap-
olating the solutions and estimating the shape of the Pareto-
optimal front. In addition, the Pareto plots give an estimate how
far one can probably optimize a certain system, since one can
guess by extrapolation of the incremental improvements of the
different populations where the asymptotic Pareto-optimal front
lies. This is a very important information for the screening of
Fig. 5 shows the evolution of the archive population with
boxplots for the objective function (1−yield) for SPEA2. In ad-
dition, Fig. S6 shows the evolution for both objectives and both
algorithms. As can be clearly seen, the average fitness improved
with each generation. The best solution of each generation is
represented by the lower outlier of the boxplot; they demon-
strate that the best solutions did not improve steadily (like the
average fitness of the archive population), but rather in a step-

O.C. Gobin et al. / Journal of Catalysis 252 (2007) 205–214
211
Fig. 7. Evolution of the occurrences of elements in the archive population for
SPEA2 and IBEA.
Fig. 6. Visualization of the evolution of the archive population in the objective
space for SPEA2 and IBEA for selected generations.
and IBEA. In contrast, Sr did not disappear during the evolu-
tion, but neither did it increase. Its occurrence was constantly
in the range of two to three catalysts in the archive. The trends
for Mn, Sm, La, and Ce at higher generation numbers were
negative. The elements did not disappear completely, but clear
decreases in Mn, Sm, and La occurred. The trends for Co- and
Fe-containing catalysts are not clear. The occurrences of both
elements seemed to fluctuate, with only a slightly positive trend
demonstrated.
Table 2 gives the NO-to-N2 yield of selected solutions from
the archive populations of SPEA2 and IBEA. It can be seen that
the Pareto-optimal trade-off front was composed predominantly
of Cu- and Ni-containing catalysts of varying concentrations
and a higher concentration of Al. Interestingly, these binary ox-
ides were more active than the corresponding single-element
oxide catalysts. The incorporation of a third element, such as Co
or Fe, generally resulted in activity loss; however, at tempera-
tures below 600 K, Cu and Ni catalysts in combination with Co,
Fe, and sometimes also Mn were optimal solutions, as shown in
Fig. 8 and Table 2.
new catalytic compositions. In Fig. 6, an extrapolated guess of
the Pareto-optimal front of this system is represented by a gray
line. The shape is linear to spherical, and the front is continu-
ous.
Fig. 7 shows the evolution of the occurrences of the archive
population up to the seventh generation. The maximum num-
ber of occurrences is 24 (the size of the population). As stated
before, the initial population was created randomly, but never-
theless the constraints C.1 to C.6 must be satisfied. This lead
to the elemental distribution of the first generation, as can be
seen in Fig. 7. The evolution demonstrates a clear trend for
most of the elements: Systems with support (constraint C.2)
were preferred over systems without support (C.3); both al-
gorithms converged toward Cu- and Ni-containing catalysts.
But SPEA2 and IBEA had different convergence rates. The
trends for the promoter elements Sr and K were slightly dif-
ferent; K showed a clear negative trend and disappeared com-
pletely after three or four generations in the case of SPEA2

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O.C. Gobin et al. / Journal of Catalysis 252 (2007) 205–214
Table 2
Peak conversion of NO to N and peak temperature of selected catalysts from
2
the SPEA2 and IBEA archive populations
Catalysts
X
T
max
max
(concentrations in mol%)
(%)
(K)
Al-84–Cu-4–Ni-12
Al-88–Cu-8–Ni-4
Al-84–Cu-12–Ni-4
Al-66–Cu-10–Ni-24
44
39
37
31
21
23
19
14
6
678
645
620
585
589
580
581
555
534
526
Al-64–Cu-20–Ni-16
Al-66–Cu-12–Ni-12–Co-8–Fe-2
Al-54–Cu-12–Ni-28–Co-6
Al-50–Cu-20–Ni-20–Co-8–Fe-2
Al-39–Ni-16–Co-35–Fe-6–Ce-4
Al-40–Cu-2–Ni-33–Co-24–Sm-1
7
Fig. 9. XRD patterns of two selected highly active Al/Cu/Ni catalysts (A)
and (B). In contrast two XRD patterns of Mn and K containing catalysts (C)
and (D) are shown.
at low temperatures generally had a relatively high Ni load-
ing (15 to 30 mol%), whereas those with low metal loading
(5 to 15 mol%) were located in the upper left region (the high-
activity region) of the Pareto front. The XRD pattern of the most
active catalyst (Al-84–Cu-04–Ni-12), with a NO-to-N2 conver-
sion of 44%, is shown in Fig. 9A. As shown, the dominant phase
was composed of large Ni-oxide crystallites. The other reflexes
cannot be unambiguously ascribed to pure Cu-spinel, pure Ni-
spinel, or a simple combination of both. A higher amount of Al
compared with the pure spinel seems to be included in the spinel
phase. The prominent crystalline phase in the case of a similar
catalyst, synthesized with 8 mol% Cu and 6 mol% Ni (Al-84–
Cu-08–Ni-6) was a CuxNix−1Al2O4 mixed spinel with similar
crystallite sizes as can be seen in Fig. 9B. The decrease in the
Ni concentration led to not so large Ni-oxide crystallites as in
Fig. 9A and the increase in Cu allowed the formation of a small
fraction of Cu-oxide. In both samples a significant amount of
amorphous phase also was present. The activity of this sample
was slightly lower (yield ∼38%) than that of Al-84–Cu-04–Ni-
12. In both samples, practically no crystalline Cu-oxide was
present. Therefore, the active phase in the case of Cu seems to
be amorphous Cu-oxide, along with crystalline spinel but not
crystalline Cu-oxide. In contrast, crystalline Ni-oxide and Ni-
spinel are highly active phases. The activity can be increased
by formation of mixed Cu/Ni spinels.
Fig. 10 compares a highly crystalline Al/Cu catalyst and a
corresponding catalyst with La. The catalyst with La had SCR
activity of only about 7%, whereas without La, the activity
increased to 18%. Crystalline Cu-oxide is present in both sam-
ples, but the formation of Cu-spinel on calcination was signifi-
cantly hindered in the presence of La. In this case, it is evident
that the active phase was crystalline Cu-spinel. The negative in-
fluence of La during the formation of a crystalline spinel phase
is likely related to the dimension of the La ions, which makes
fitting them into the framework difficult. This is also valid for
Sm. A significant activity drop was observed in most of the La-
Fig. 8. NO to N conversion curves as a function of the temperature for selected
2
Pareto-optimal solutions.
IBEA was not able to approach the Pareto-optimal front as
well as SPEA2. It is very likely that the fast convergence of
IBEA toward Cu-containing catalysts, as shown in Fig. 7, had
a negative effect on the overall performance of the algorithm.
Nevertheless, in the last two generations, IBEA was able to
find promising Cu and Ni catalysts and showed a strong con-
vergence toward Ni in addition to Cu. In conclusion, it seems
important that a genetic algorithm not strongly favor a single
solution. However, a properly working algorithm still should be
able to find optimal solutions after a few more generations.
In the following a discussion of the underlying physico-
chemical properties of the catalysts and their correlation with
catalytic activity will be given on the basis of the catalytic
screening and on characterisation by adsorption, and XRD in-
vestigations. Cu and Ni were the only elements in this system,
which showed high SCR activity. These two elements predom-
inately formed the Pareto-optimal trade-off front. Cu was espe-
cially active at low metal loadings (around 8–12 mol%); higher
Cu loadings led to a distinct activity drop, although the maxi-
mal conversion happened at lower temperatures. This is some-
what different than for the Ni-containing catalysts, which were
highly active at metal loadings up to 30–35 mol%, depend-
ing on the catalyst composition. Catalysts with a peak activity

O.C. Gobin et al. / Journal of Catalysis 252 (2007) 205–214
213
intermediate species with a higher activity than NO in HC-SCR
[43,44]. In combination with a highly active element for the
SCR such as Cu or Ni, this can lead to catalysts, which are ac-
tive at low temperatures. Fe is known to be highly active in the
SCR of NO by NH3 [45,46]. In this work, adding Fe to a cata-
lyst generated no clear increase in activity.
Both K and Sr were initially defined as possible promoter el-
ements, and the maximum concentration of these elements was
limited to 5 mol%. For Sr, no clear conclusion can be drawn; the
element did not seem to have any positive or strongly negative
effect on the performance. In contrast, the addition of K resulted
in a very pronounced drop in the activity of the corresponding
catalyst in all cases. It was observed that after calcination, the
resulting catalysts containing K were differently colored and
sometimes very inhomogeneous. Thus, it can be assumed that
the activity drop was due to a negative influence during cata-
lyst synthesis. K is known to strongly promote combustion of
the activated carbon. Thus, a possible explanation for the diffi-
culties encountered during the synthesis of K-containing cata-
lysts could be the formation of hot spots during the calcination
process, which disturb the formation of an active phase and lead
to inhomogeneous particles. This can be confirmed by XRD, as
can be seen in Fig. 9D for a sample consisting of 85 mol% Al,
10 mol% Cu, and 5 mol% K. The SCR activity of this sam-
ple was 8%, more than three times less than the activity of the
corresponding catalyst without K. No evident crystalline phase
could be identified. The sample was predominantly amorphous,
with small amounts of crystalline Cu-oxide and Cu-spinel.
Fig. 10. XRD patterns of a Al/Cu (A) and Al/Cu/La catalyst (B).
or Sm-containing catalysts. During the optimization process,
both algorithms were able to identify the negative influence
of La and Sm, as shown in Fig. 7. In contrast, the Ce in the
archive population was stable during the evolution up to high
generation numbers. For Ce, even for materials with a very low
amount of Al (<10 mol%) but a significant amount of Ce, the
resulting particles exhibited a high BET surface area (at least
80 m2/g). The addition of Ce improved the formation of oxide
particles with a high BET surface area and did not seem to sig-
nificantly affect the properties of the other elements. Also, XRD
investigations of Ce containing catalysts showed the formation
of a crystalline Ce-oxide phase in addition to the other phases.
Thus, if the Ce metal loading is high, then Ce-oxide itself can
be considered a support.
As described previously, the addition of Co and Fe to a cat-
alyst did not result in a clear trend. Sometimes the addition re-
sulted in an improved activity, and other times, no clear change
in activity could be seen. However, in most cases, the catalyst
activity decreased. For Mn, in all cases, an addition resulted in
decreased activity, although Mn by itself showed an SCR ac-
tivity of about 15%. For instance, the addition of 4 mol% Mn
to sample Al-86–Cu-08–Ni-06 resulted in an activity loss of
8–10%. The XRD pattern C in Fig. 9 shows no strong inhi-
bition of the formation of crystalline phases. The addition of
Mn even led to a slightly better crystallization. However, in this
case, the dominant spinel phase was nearly pure Ni-spinel, not a
mixed spinel phase as in the case of Al-86–Cu-08–Ni-06. This
might be one explanation for the activity drop. The formation of
Mn-oxide also could lead to catalysts that are more selective to
the oxidation of C3H6. For instance, as seen during the experi-
ments, most of the Mn-containing catalysts were highly active
at low temperatures for the oxidation of C3H6 by oxygen.
Co and Fe do not significantly decrease the activity of a cat-
alyst. At higher metal loadings, a crystalline Co-oxide emerged
(XRD not shown) that is known to be highly active at low tem-
peratures for the NO oxidation to NO2 [41,42]. NO reduction
over Co-oxide only occurs at higher temperatures when NO ox-
idation is thermodynamically limited. However NO2 can be an
6. Conclusion
Genetic algorithms or evolutionary optimization techniques
have been found to be highly flexible methods for the develop-
ment of catalysts in multi-objective optimization problems. The
stochastic nature and the incorporation of heuristics based on
evolutionary biology better direct the search in the desired di-
rection compared with, for instance, a random search approach,
and makes the technique robust to noise and to the undesired
convergence toward suboptimal solutions. The full strength of
these techniques can be played off, especially for the screen-
ing of unknown, high-dimensional, and constrained spaces. In
addition, they are easily scalable to an arbitrary number of ob-
jectives, which make them suitable for many problems in catal-
ysis.
In this work, we investigated the ability to direct the search
toward two independent objectives using a multi-objective ap-
proach to optimize a noble metal–free solid catalyst system
active in the selective catalytic reduction of NO with C3H6.
Combinations of Cu, Ni, and Al were the best catalysts synthe-
sized through the activated carbon route found by this method.
Other catalysts active at low temperature include Co and Fe.
Visualizing the solutions in the objective space using Pareto
plots allowed us to estimate of the shape and location of the
Pareto-optimal front and determine to what extent this noble
metal–free system is active in the SCR with C3H6.
A hybridization of the developed optimization framework
with neural networks, acting as local search during the evolu-

214
O.C. Gobin et al. / Journal of Catalysis 252 (2007) 205–214
tion, could improve the optimization process. In addition, the
problem of encoding solid catalysts and the impact of such en-
coding on the performance of the experimental evolution should
be investigated in more detail in future studies.
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