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In this paper we theoretically investigate underlying assumptions that have been used for designing adaptive particle swarm optimization algorithms in the past years. We relate these assumptions to the movement patterns of particles controlled by coefficient values (inertia weight and acceleration coefficient) and introduce three factors, namely the autocorrelation of the particle positions, the average movement distance of the particle in each iteration, and the focus of the search, that describe these movement patterns. We show how these factors represent movement patterns of a particle within a swarm and how they are affected by particle coefficients (i.e., inertia weight and acceleration coefficients). We derive equations that provide exact coefficient values to guarantee achieving a desired movement pattern defined by these three factors within a swarm. We then relate these movements to the searching capability of particles and provide guideline for designing potentially successful adaptive methods to control coefficients in particle swarm. Finally, we propose a new simple time adaptive particle swarm and compare its results with previous adaptive particle swarm approaches. Our experiments show that the theoretical findings indeed provide a beneficial guideline for successful adaptation of the coefficients in the particle swarm optimization algorithm. |
