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Particle swarm optimization (PSO) is a population-based, stochastic search algorithm inspired by the flocking behaviour of birds. The PSO algorithm has been shown to be rather sensitive to its control parameters and thus performance may be greatly improved by employing appropriately tuned parameters. However, parameter tuning is typically a time-intensive empirical process. Furthermore, a priori parameter tuning makes the implicit assumption that the optimal parameters of the PSO algorithm are not timedependent. To address these issues, self-adaptive particle swarm optimization (SAPSO) algorithms adapt their control parameters throughout execution. While there is a wide variety of such SAPSO algorithms in the literature, their behaviours are not well understood. Specifically, it is unknown whether these SAPSO algorithms will even exhibit convergent behaviour. This paper addresses this lack of understanding by investigating the convergence behaviours of 18 SAPSO algorithms both analytically and empirically. This paper also empirically examines whether the adapted parameters reach a stable point and whether the final parameter values adhere to a well-known convergence criterion. The results depict a grim state for SAPSO algorithms; over half of the SAPSO algorithms exhibit divergent behaviour while many others prematurely converge.

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The particle swarm optimization (PSO) algorithm is a stochastic search technique based on the social dynamics of a flock of birds. It has been established that the performance of the PSO algorithm is sensitive to the values assigned to its control parameters. Many studies have examined the long-term behaviours of various PSO parameter configurations, but have failed to provide a quantitative analysis across a variety of benchmark problems. Furthermore, two important questions have remained unanswered. Specifically, the effects of the balance between the values of the acceleration coefficients on the optimal parameter regions, and whether the optimal parameters to employ are timedependent, warrant further investigation. This study addresses both questions

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