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In this paper we theoretically investigate underlying assumptions that havebeen used for designing adaptive particle swarm optimization algorithms in thepast years. We relate these assumptions to the movement patterns of particlescontrolled by coefficient values (inertia weight and acceleration coefficient)and introduce three factors, namely the autocorrelation of the particlepositions, the average movement distance of the particle in each iteration, andthe focus of the search, that describe these movement patterns. We show howthese factors represent movement patterns of a particle within a swarm and howthey are affected by particle coefficients (i.e., inertia weight andacceleration coefficients). We derive equations that provide exact coefficientvalues to guarantee achieving a desired movement pattern defined by these threefactors within a swarm. We then relate these movements to the searchingcapability of particles and provide guideline for designing potentiallysuccessful adaptive methods to control coefficients in particle swarm. Finally,we propose a new simple time adaptive particle swarm and compare its resultswith previous adaptive particle swarm approaches. Our experiments show that thetheoretical findings indeed provide a beneficial guideline for successfuladaptation of the coefficients in the particle swarm optimization algorithm.

A theoretical guideline for designing an effective adaptive particle swarm