Family Particle Swarm Algorithm And Its Parity With The Convergence Analysis

On the study of particle swarm optimization (PSO), it is a noticeable research direction that how many particles are included, what structure is used and what communication ways between the sub-swarms. To the specialty of the population structure in the PSO, this thesis is inspired by the sociology of family and family particle swarm optimization (FPSO) is proposed. The inner structure of the sub-swarm and the communication ways between the sub-swarms are made a thorough study. The study of PSO is widened from the concepts, methods and theories.There are some parts about FPSO in this thesis:1. The family is introduced and the FPSO is proposed. First. A few particles form a family. The family structure and the family relationship are defined for the study of the inner structure and the interaction between particles in a sub-swarm. Second, some families form a family tree. The management of single or multiple family trees is analyzed for the study of the communication ways between the sub-swarms. The experimental results show that the algorithm performance is bad when a family includes too small or too large particles. In the high dimensional space, the algorithm performance is good when a family includes2-5particles.2. From the angle of the family role, different family roles have different works. The direction of the vector and the strategy of piecewise mutation are introduced and the FPSO with family role is proposed for the balance between the global exploitation and the local exploration. The experimental results show that the particles with different directions have different works and it makes the algorithm have faster convergence speed to the global optimal space than the particles with no direction. The swarm can realize to find the adaptive mutation probability to different optimal problems by themselves through the piecewise mutation. The results show that the new algorithm has obvious advantage in the convergence accuracy and the evolution velocity to different test functions.3. FPSO is researched theoretically. The interactive between particles is researched. The odd-even property of FPSO is proposed through the adjustment of the parameters. The convergence condition is obtained by the theoretical analysis of the odd-even property of FPSO. It is deduced that two kinds of different parameters can make the trajectory of family particle alternate regularly. It is verifiable and shown by the figures of particle trajectory.Finally. the thesis is summarized and the future of FPSO is prospected.