Velocity-free particle swarm optimiser with centroid

A velocity-free particle swarm optimiser with centroid is proposed. Similar to bare bones PSO, particles in the proposed algorithm only have position without velocity. Besides, not only the 'social' and 'cognitive' components of the particle swarm but also the 'centroid' component of the particle swarm is considered to update the particle position. In the 'centroid' component, the swarm's centroid is incorporated. The proposed algorithm determined by three real parameters is analysed theoretically and the convergent condition is derived. The theoretical analysis implies that the particle of the swarm tends to converge to a point among the triangle consisting of the personal best position, the global best position and the swarm's centroid. Because of discarding the particle velocity and using the 'centroid' information of swarm, the algorithm is simpler and more effective. The proposed algorithm is applied to some well-known benchmarks. The relative experimental results show that the algorithm achieves better solutions and faster convergence.