Aproximación numérica mediante algoritmos genéticos optimizados con descenso de gradiente en sistemas heterogéneos

Flores Benavente, Saúl
Muñoz Orbañanos, Adolfo (dir.) ; Suárez Gracia, Darío (dir.)

Universidad de Zaragoza, EINA, 2024
Departamento de Informática e Ingeniería de Sistemas, Área de Lenguajes y Sistemas Informáticos

Máster Universitario en Robótica, Gráficos y Visión por Computador

Resumen: Function approximation models the intricate relationships between input and output variables in many real-world applications, enabling accurate predictions and usage of alternative functions that posses or lack specific properties with respect to the original. This problem is of significant importance and could be applied to fields like computer graphics, where numerical methods are used to compute rendering equations and sampling complex distributions, requiring a significant computation power. This thesis explores the application of Genetic Algorithms (GAs) for function approximation, including integral and inverse approximations. Unlike traditional methods, our approach evolves the mathematical expression’s shape through the algorithm itself. To enhance GA performance, we incorporate gradient descent to optimize constant values within expressions, addressing limitations in mutation and crossover. Recognizing the high computational demands, we employ parallel and heterogeneous computation, leveraging both CPU and GPU resources to reduce evaluation time. This approach exploits data and task parallelism to improve efficiency.

Tipo de Trabajo Académico: Trabajo Fin de Master