Solving systems of unconstrained equations using particle swarm optimization

A new particle swarm optimization algorithm (PSO), nbest, is developed in this paper to solve systems of unconstrained equations. For this purpose, the standard gbest PSO is adapted by redefining the fitness function in order to locate multiple solutions in one run of the algorithm. The new algorithm also introduces the concept of shrinking particle neighborhoods. The resulting nbest algorithm is a first attempt to develop a niching PSO algorithm. The paper presents results that show the new PSO algorithm to be successful in locating multiple solutions.