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The particle swarm algorithm has just enough moving parts to make it hard to understand. The formula is very simple, it is even easy to describe the working of the algorithm verbally, yet it is very difficult to grasp in one's mind how the particles oscillate around centers that are constantly changing; how they influence one another; how the various parameters affect the trajectory of the particle; how the topology of the swarm affects its performance; and so on. This paper strips away some traditional features of the particle swarm in the search for the properties that make it work. The particle swarm algorithm is modified by eliminating the velocity formula. Variations are compared. In the process some of the mysteries of the algorithm are revealed, we discover its similarity to other stochastic population-based problem solving methods, and new avenues of investigation are suggested or implied.
James Kennedy (Mon,) studied this question.