Towards Swarm Diversity: Random Sampling in Variable Neighborhoods Procedure Using a Lévy Distribution

Hacia la diversidad de la bandada: procedimiento RSVN usando una distribución de Lévy

Gonzalo Nápoles¹, Isel Grau², Marilyn Bello¹, and Rafael Bello¹

¹ Artificial Intelligence Laboratory, Universidad Central "Marta Abreu" de Las Villas, Cuba. gnapoles@uclv.edu.cu, mbello@uclv.edu.cu, rbellop@uclv.edu.cu

Abstract

Particle Swarm Optimization (PSO) is a non-direct search method for numerical optimization. The key advantages of this metaheuristic are principally associated to its simplicity, few parameters and high convergence rate. In the canonical PSO using a fully connected topology, a particle adjusts its position by using two attractors: the best record stored for the current agent, and the best point discovered for the entire swarm. It leads to a high convergence rate, but also progressively deteriorates the swarm diversity. As a result, the particle swarm frequently gets attracted by sub-optimal points. Once the particles have been attracted to a local optimum, they continue the search process within a small region of the solution space, thus reducing the algorithm exploration. To deal with this issue, this paper presents a variant of the Random Sampling in Variable Neighborhoods (RSVN) procedure using a Lévy distribution, which is able to notably improve the PSO search ability in multimodal problems.

Keywords: Swarm diversity, local optima, premature convergence, RSVN procedure, Lévy distribution.

Resumen:

Particle Swarm Optimization (PSO) es un método de búsqueda no directo para la optimización numérica. Las principales ventajas de esta meta-heurística están relacionadas principalmente con su simplicidad, pocos parámetros y alta tasa de convergencia. En el PSO canónico usando una topología totalmente conectada, una partícula ajusta su posición usando dos atractores: el mejor registro almacenado por el individuo y el mejor punto descubierto por la bandada completa. Este esquema conduce a un alto factor de convergencia, pero también deteriora la diversidad de la población progresivamente. Como resultado la bandada de partículas frecuentemente es atraída por puntos sub-óptimos. Una vez que las partículas han sido atraídas hacia un óptimo local, ellas continúan el proceso de búsqueda dentro de una región muy pequeña del espacio de soluciones, reduciendo las capacidades de exploración del algoritmo. Para tratar esta situación este artículo presenta una variante del procedimiento Random Sampling in Variable Neighborhoods (RSVN) usando una distribución de Lévy. Este algoritmo es capaz de mejorar notablemente la capacidad de búsqueda de los algoritmos PSO en problemas multimodales de optimización.

Palabras clave: Diversidad de la bandada, óptimos locales, convergencia prematura, procedimiento RSVN, distribución de Lévy.

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