Understanding Particle Swarm Optimization: A Component-Decomposition Perspective

Particle Swarm Optimization is an effective algorithm because of the combination of the stochastic behavior of particles and the swarm structure. Unfortunately these features also make it difficult to understand the dynamics of PSO. Common methods of analyzing PSO rely on simplifying the algorithm, e.g., assuming stagnation (a state where the swarm ceases finding better solutions) or treating the stochastic factors as constants. In this paper, we expand on earlier work to understand the dynamics of PSO which used input-to-state stability analysis. In particular, we decompose PSO more completely and use the properties of combinations of input-to-state stable components to model convergence at all levels up to and including the entire swarm. This approach allows us to conceptualize the swam as a leader-follower structure and analyze the swarm under a variety of conditions including various fitness functions.