A hybrid swarm intelligence with improved ring topology for nonlinear equations

Abstract

Solving nonlinear equations (NEs) is one of the most important yet challenging tasks in numerical computation, especially for the simultaneous location of multiple roots in a single run. In this paper, a hybrid swarm intelligence approach with improved ring topology is proposed to tackle this problem. It has three main features: (i) the improved ring topology is developed to effectively use the neighborhood knowledge; (ii) the hybrid swarm intelligence enhances the search efficiency; and (iii) an individual reinitialization mechanism is proposed to enrich the population diversity. The performance of this approach is tested on eight NE problems with multiple roots, experimentally confirming that it can simultaneously locate multiple roots in a single run. In addition, it can provide better results than conventional methods in terms of both root and success rates.