SIMULACIONES COMPUTACIONALES UTILIZANDO SMOOTHED PARTICLE HYDRODYNAMICS PARA LA BÚSQUEDA DE MÍNIMOS DE FUNCIONES
DOI:
https://doi.org/10.47820/recima21.v6i12.7119Palabras clave:
Hidrodinámica de Partículas Suavizadas. Problemas de optimización. Simulación computacional.Resumen
La Hidrodinámica de Partículas Suavizadas, o del inglés Smoothed Particle Hydrodynamics (SPH), es un procedimiento computacional utilizado para simulaciones en medios continuos, como procesos mecánicos y flujos de fluidos, que ha ganado creciente relevancia en la representación de la dinámica de fluidos. Dado un sistema físico compuesto por partículas, el SPH calcula la presión sobre cada partícula considerando las interacciones con sus partículas vecinas, simulando así la dinámica del sistema como un fluido. El objetivo de este trabajo es utilizar la técnica SPH para la búsqueda de mínimos de funciones, simulando la caída gravitacional de un conjunto de partículas sobre una superficie. Esta superficie está representada por una función matemática cuyo mínimo global se desea encontrar.
El uso del SPH, tradicionalmente aplicado en simulaciones físicas e industriales, se explora aquí como una prueba de concepto, demostrando que la técnica también puede adaptarse a problemas de optimización. A través de la dinámica de flujo de las partículas sobre la superficie analizada, es posible identificar la partícula que alcanza el valor mínimo, localizando el punto de mínimo en el dominio de la función. Se realizaron diversos experimentos con funciones que poseen múltiples mínimos locales y un mínimo global, y los resultados mostraron que el SPH es capaz de identificar dicho mínimo con precisión. Para efectos de comparación, también se llevaron a cabo pruebas con la técnica PSO (Particle Swarm Optimization). Los resultados demuestran que el desempeño del SPH es comparable al del PSO.
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