Summary

Optimization problems arising from the biotechnological and food industries are usually of
non-convex nature and they often exhibit several local minima. Even though advances in
global optimization research have been outstanding in recent years, the current state-of-the-
art is not completely satisfactory, specially when one considers the global optimization of
complex process models (typical of biotechnological and food industries). These models are
complex due to their dynamic behavior and large number of states. Besides, one of the most
important drawbacks for optimizing these complex models is the computation time required
to perform every simulation. Due to the large number of differential and algebraic equa-
tions (DAE's) defining the mathematical models which describe complex processes and/or
full industrial plants, the time needed to perform a single simulation may vary between some
minutes and hours on a standard personal computer. This can lead to unaffordable computa-
tion times from the practical point of view when the optimization of such processes is carried
out.

The reasons exposed above advise to treat complex models as black boxes in many situa-
tions, that is, as a simple relationship between inputs and outputs without further informa-
tion about relationships among the decision variables. For this kind of problems, stochastic
global optimization methods (and metaheuristics in particular) have proved to be efficient
and robust. Indeed, even though these methods can not ensure the convergence to the global
optimum, they provide very good solutions in practice (the global optimum in some cases)
in reasonable computation times. Besides, stochastic methods permit to treat mathemati-
cal models as black-boxes and are easy to implement, making them robust for any kind of
problem.

The use of the so-called metamodels allows to build surrogate models which interpolate or
approximate the original models, and predict their function values with a certain probability,
being less difficult to evaluate from the computational point of view. Taking advantage of
their statistical properties, these surrogate models allow us to formulate hypotheses about
the location of the global optimum and to find it (or high quality solutions) in a number
of simulations much lower than these employed by traditional optimization methods, thus
considerably reducing the final optimization time.

In the first part of this work we present an introduction to global optimization in the
biotechnological area, including the main type of existing problems and the available opti-
mization methods to solve them. An introduction to a special class of stochastic methods
(metaheuristics) is provided, pointing out the most popular and successful among them. Con-
sidering that our proposed method is based on the scatter search methodology, we describe
it in Chapter 3.

In the second part the methodology proposed for the optimization of complex bioprocesses
is explained. We present a scatter search-based algorithm for the global optimization of non-
linear dynamic systems. A set of new heuristics and improved features have been developed to
handle the main drawbacks inherent to this kind of problems. We have also developed another
optimization algorithm (based on scatter search too) which makes use of surrogate models for
the optimization of computationally expensive problems. In particular, the algorithm uses a
kriging interpolation algorithm which provides predictions and statistics associated to those
predictions, in order to minimize the number of simulations to locate the global optimum.
The scatter search framework makes the algorithm autonomous to select the set of points in
which the predictions must be done. The associated software tools for both algorithms have
been developed, and we present their documentation in Appendix A. Their effectiveness is
demonstrated by the resolution of a set of benchmark problems.

The final part of this work is dedicated to the application of the proposed methodologies to
different problems arising in the biotechnological and food industries. The three main types
of problems described in the first part are considered, and the performances of our algorithms
are compared with those of other state-of-the-art optimization algorithms, showing that our
approach is efficient and robust for the global optimization of this kind of problems.