Mejoramiento del modelo sustituto basado en codificación dispersa denominado SESM: Sparse-encoded surrogate model

Solving real-life problems generally requires a numerical or algorithmic search for parameters that
minimize or maximize a function and this in turn is based on a repeated evaluation of that
function, functions that are mostly complex, with dozens of parameters and high evaluation cost.
In multiobjective optimization processes that rely on objective functions with a high evaluation
cost, defined as so-called "black boxes", the reduction of the required number of costly
evaluations contributes to the efficiency, convergence and speed of the results. This also reduces
the number of resources the algorithm consumes to reach the desired optimum.
In this sense, this proposal is formulated to give continuity to the doctoral thesis of Dr. Cindy
Calderón Arce, entitled "Reduction of evaluations to costly functions in multi-objective optimization
strategies", developed under the advice of Dr. Pablo Alvarado Moya and in which researcher Juan
Pablo Soto Quirós participated in the evaluation committee. As part of the doctoral work, a
surrogate model based on sparse coding was proposed, called "SESM: Sparse-encoded
surrogate model", used to reconstruct and substitute functions of high evaluation cost in
multiobjective optimization problems.
While it is true that there are proposals for multiobjective optimization algorithms that replace
expensive functions by models with low evaluation cost, the construction of such models depends
on a considerable number of evaluations of the original function.
Thus, SESM extends sparse coding techniques, used in applications such as image segmentation
and signal processing, to generate surrogate models from a set of observed data or samples. It
replaces expensive functions with surrogate models in multi-objective optimization processes,
reducing the number of high-cost evaluations and contributing to the reduction in resource
consumption when searching for solutions to optimization problems.
The first results of SESM have been satisfactory and tested in real problems of high evaluation
cost, but its library is currently in a restricted access platform, so it is not accessible or available
for use by the entire scientific community. In addition, as a result of the doctoral research, some
future work was proposed as a complement and improvement to the first version of SESM.
Therefore, the main contribution of this proposal is the improvement of SESM in terms of
efficiency, stability, robustness, adaptability and accessibility. For this, new studies and strategies
related with compressed sensing algorithms, minimization of errors adjusting parameters, objects
reconstruction objects in complex spaces and clustering in spaces partition will be incorporated,
to generalize and adapt them to SESM.

Mejorar la eficiencia, adaptabilidad y estabilidad del
modelo sustituto basado en codificación dispersa denominado SESM:
Sparse-encoded surrogate model.

- Escuela de Matemática:
Matemática aplicada: modelación, simulación, inteligencia artificial, análisis de
datos, visualización de información, optimización y aplicaciones a la ingeniería y
a las ciencias.
- Escuela de Electrónica:
Procesamiento de datos, control y optimización: se enmarcan en esta línea
de investigación las estructuras, algoritmos y los circuitos y sistemas electrónicos
y microelectrónicos diseñados para controlar, optimizar o procesar datos con un
fin específico. Esta área incluye los sistemas de actuación para ejecutar el control
que pueden ser circuitos electrónicos de potencia, sistemas electromecánicos,
hidráulicos y neumáticos. La investigación desarrollada en esta área debe
enfocarse a aplicaciones relacionadas con el agua, el ambiente y los sistemas
agropecuarios sostenibles, la cultura, la energía, el hábitat, el sector productivo y
la salud.