Palabras clave
Interacting particle systems
asymptotical convergence
Feynman-Kac formula
measure valued processes
Algoritmos genéticos
sistemas de partículas interactuantes
convergencia asintótica
fórmula de Feynman-Kac
procesos valuados en medida
Cómo citar
Resumen
En este trabajo presentamos un enfoque natural de Sistemas de Partículas Interactuantes (IPS) para modelar y estudiar el comportamiento asintótico de Algoritmos Genéticos (GAs). En este modelo, una población es vista como una distribución (o medida) en el espacio de búsqueda, y el Algoritmo Genético como un sistema dinámico valuado en medida. Este modelo permite aplicar resultados recientes sobre convergencia de la literatura sobre IPS para estudiar la convergencia de GAs cuando el tamaño de la población tiende al infinito.
Primero revisamos algunos enfoques para modelar GAs y resultados relacionados con la convergencia. Enseguida describimos un modelo general y de tiempo discreto abstracto para GAs, basado en un IPS, y proponemos una breve revisión de algunos resultados asintóticos recientes acerca de la convergencia de N-IPS modelos de aproximación (de GAs de población finita de tamaño N), que conducen al modelo IPS (de GAs de población infinita), incluyendo teoremas de leyes de los grandes números, LLp-media y cota exponencial, así como principios de grandes desviaciones.
Finalmente, se detalla el impacto de modelar Algoritmos Genéticos con nuestro enfoque de IPS sobre diferentes clases de algoritmos genéticos genéricos que incluyen mutación, cruzamiento y selección proporcional. Exploramos las conexiones entre los flujos de distribución de Feynman-Kac y el algoritmo geético simple. Esta representación de Feynman-Kac del modelo de población infinita es usada luego para desarrollar resultados de estabilidad asintótica y convergencia con respecto al parámetro de tiempo.
Citas
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