Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm

By Ming Jiang, Yupin Luo, Shiyuan Yang. Information Processing Letters, 2007

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Quantum-Behaved Particle Swarm Optimization: Analysis of Individual Particle Behavior and Parameter Selection (2012, background): “…a lot of theoretical analyses have been done on the algorithm (Kennedy, 1998; Ozcan and Mohan, 1999; Clerc and Kennedy, 2002; van den Bergh, 2002; Shi and Eberhart, 1998b; Trelea, 2003; Emara and Fattah, 2004; Gavi and Passino, 2003; Kadirkamanathan et al., 2006; Jiang et al., 2007; Poli, 2008).”
A New Particle Swarm Algorithm and Its Globally Convergent Modifications (2011, background): “[20] showed that, if 0 ≤ w < 1, c1 + c2 > 0, and f(1) < (c(2)2(1 + w)/6) were all satisfied together, the PSO system converged to Pg .”
Particle Swarm Methods (2018, background): “The first theoretically sound convergence analysis of PSO in [21] was succeeded by a number of theoretical studies [49, 54, 113, 124, 143, 147].”
Cuckoo search: recent advances and applications (2013, background): “Theoretical studies of particle swarm optimization have suggested that PSO can converge quickly to the current best solution, but not necessarily the global best solutions [7, 15, 35].”