Using vector operations to identify niches for particle swarm optimization

In some problems described by objective functions, it is important to find all optimal solutions in the problem space. The particle swarm optimizer has originally been designed to locate a single optimum and avoid premature convergence on suboptimal solutions. To locate all optimal solutions, niches have to be identified containing good candidate solutions. In this paper a technique is introduced using vector operations to demarcate the boundaries of those niches and maintain subswarms in order to find optimal solutions.