A family Particle Swarm Optimization based on the family tree

The concept of the family was previously introduced into Particle Swarm Optimization (PSO). To further study the multi-group structure of the Family PSO (FPSO), this paper introduces the family tree into the FPSO. It made different families form a family tree and a swarm consisted of some family trees. In the experiment, topological distance was used to form a family and three spatial structures of the family trees were simply defined and demonstrated in two-dimensional space. Simulations for seven benchmark functions demonstrated that two family trees in a swarm and each family had 2 particles that performed better than other combinations. Results also showed the multi-group structure of FPSO was a problem deserving of study at high-dimensional space.