23-11-2012, 10:48 AM
Genetic Algorithms for the Optimization of Catalysts in Chemical Engineering
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Abstract
The paper addresses key problems pertaining
to the commonly used evolutionary approach to
the search for optimal catalysts in chemical engineering.
These are on the one hand the insufficient dealing
in existing implementations of genetic algorithms
with mixed optimization, which plays a crucial role in
catalysis, on the other hand the narrow scope of genetic
algorithms developed specifically for searching
optimal catalyst. The paper proposes an approach to
constrained mixed optimization based on formulating
a separate linearly-constrained continuous optimization
task for each combination of values of the discrete
variables. Then, discrete optimization on the
set of nonempty polyhedra describing the feasible solutions
of those tasks is performed, followed by solving
those tasks for each individual of the resulting population
of polyhedra. To avoid computationally expensive
checking of the non-emptiness of individual
polyhedra, the set of polyhedra is first partitioned
into equivalence classes such that only one representative
from each class needs to be checked.
Introduction
In chemical engineering, much effort is devoted to increasing
the performance of industrially important chemical
processes, i.e., to achieving a higher yield of the desired
reaction products without higher material or energy
costs. Over 90% of the processes use a catalyst to speed
up the reaction or to improve its selectivity to the desired
products. Catalysts are materials that decrease the energy
needed to activate a chemical reaction without being
themselves consumed in it. Catalytic materials typically
consist of several components with different purpose to
increase their functionality. The components typically
can be selected from among many substances. Chemical
properties of those substances usually constrain the
possible ratios of their proportions, but since the proportions
are continuously-valued, they still allow for an
infinite number of catalyst compositions. Moreover, the
catalyst can usually be prepared from the individual components
in a number of ways, and the preparation method
also influences the performance of the chemical process.
Genetic algorithms and their modifications
for constraints
The term ”genetic algorithms” refers to the fact that their
particular way of incorporating random influences into
the optimization process has been inspired by the biological
evolution of a genotype [10, 16, 19]. Basically, that
way consists in:
• randomly exchanging coordinates between two particular
points in the input space of the objective
function (recombination, crossover),
• randomly modifying coordinates of a particular point
in the input space of the objective function (mutation),
• selecting the points for crossover and mutation according
to a probability distribution, either uniform
or skewed towards points at which the objective function
takes high values (the latter being a probabilistic
expression of the survival-of-the-fittest principle).
Implementation by means of a program
generator
To be available for a possibly broad spectrum of optimization
tasks entailed by the search of optimal catalysts
in chemical engineering, the proposed approach has not
been incorporated into a particular GA implementation,
but has been combined with a program generator that
transforms a description of the optimization task to an
executable program. A first prototype of such a generator
has been developed at the Leibniz Institute for Catalysis
(LIKat) in Berlin and is currently in the testing phase.
Differently to a human programmer, a program generator
needs the description to be expressed in a rigorously
formal way, i.e., with some kind of a task description language.
For catalysis, a formal catalyst description language
has been proposed in [6]. It allows expressing a
broad variety of user requirements on the catalytic materials
to be sought by the genetic algorithm, as well as
on the algorithm itself (Figure 3).
Conclusion
The paper has presented solutions to two key problems
encountered when genetic algorithms are used for searching
optimal catalytic materials in chemical engineering.
First, it has proposed an approach to constrained mixed
optimization tasks based on specific properties of the
search for optimal catalysts. Second, it has shown that it
is possible to avoid repeated reimplementations of genetic
algorithms developed specifically for searching optimal
catalysts without having to resort to generic software. To
this end, a program generator has been used that generates
problem-tailored genetic algorithms, based on the
proposed approach to constrained mixed optimization,
from descriptions of optimization tasks. A first prototype
of such a generator has been developed at LIKat
Berlin and is currently in the testing phase.