2.1 Introduction 2.1.1 Overview of PSO2.2 Mathematical Modeling 2.3 Advances in PSO 2.3.1 Comprehensive Learning Particle Swarm Optimization (CLPSO)2.3.2 Heterogeneous Comprehensive Learning Particle Swarm Optimization 2.3.3 Extraordinary Particle Swarm Optimization 2.3.4 Improved Random Drift PSO (IRDPSO)2.3.5 Autonomous Particle Groups for Particle Swarm Optimization (AGPSO)2.3.6 Improved Particle Swarm Optimization Using Dynamic Parameter Configuration2.3.6.1 An Enhanced PSO with Time Varying Accelerator Coefficients2.3.6.2 A Modified PSO with Adaptive Acceleration Coefficients2.3.6.3 PSO with Asymmetric Time Varying Acceleration Coefficients2.3.7 Fractional-Order Darwinian PSO2.3.8 Guaranteed Convergence PSO (GCPSO)2.3.9 Vector-Evaluated PSO (VEPSO)2.4 Hybrid PSO2.4.1 Hybridization of PSO with Genetic Algorithm2.4.2 Hybridization of PSO with Differential Evolution (DE)2.4.3 Hybridization of PSO with Simulated Annealing (SA)2.4.4 Hybridization of PSO with Cuckoo Search (CS)2.4.5 Hybridization of PSO using Artificial Bee Colony (ABC)2.5 Conclusion References