## 3 Particle Swarm Optimization
### Recent Advancements in PSO for a Better Convergence Rate
#### 3.6.1 Ring Topology in Particle Swarm Optimization  
The ring topology in PSO is a variation of the algorithm where the particles are arranged in a circular ring structure instead of a fully connected network [99]. Figure 4 shows the settings of the ring topology in PSO. In this topology, each particle is only connected to its immediate neighbors, creating a cyclic structure [100]. In the ring topology, the communication and information sharing among particles are limited to the adjacent neighbors. This arrangement allows for a more-localized interaction, as each particle only  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Year** & **Advancement** \\ \hline
1995 & Introduction of PSO algorithm by [PERSON] and [PERSON] [1; 82] \\ \hline
1997 & Inclusion of inertia weight to balance exploration and exploitation [83] \\ \hline
1998 & Exploration of PSO variants such as constriction factor approach [84] \\ \hline
1999 & Incorporation of adaptive parameter settings for improved performance [85] \\ \hline
2001 & Multi-objective PSO developed for handling optimization problems with multiple conflicting objectives [86] \\ \hline
2003 & Hybridization of PSO with other metaheuristic or local search algorithms [87] \\ \hline
2004 & Introduction of dynamic PSO variants to adapt to changing environments [88] \\ \hline
2006 & Application of PSO in solving complex real-world problems, such as the optimization of neural networks and data clustering [89] \\ \hline
2008 & Development of parallel and distributed PSO algorithms for enhanced computational efficiency [90] \\ \hline
2010 & Integration of PSO with machine learning techniques for improved optimization and prediction tasks [91] \\ \hline
2012 & Self-adaptive PSO algorithms introduced to dynamically adjust algorithm parameters during optimization [92] \\ \hline
2014 & Improved PSO variants focusing on handling dynamic and uncertain environments [93] \\ \hline
2016 & Application of PSO in feature selection, image processing, and bioinformatics problems [94] \\ \hline
2018 & Exploration of hybrid PSO algorithms with deep learning models for enhanced optimization and decision-making [95; 96] \\ \hline
2020 & Advancements in multi-objective PSO algorithms for solving complex optimization problems with conflicting objectives [97] \\ \hline
2022 & Development of PSO variants incorporating social-network-inspired behaviors for collective decision-making and coordination [98] \\ \hline \hline \end{tabular}
\end{table}
Table 2: Advancements in the PSO algorithm.  
exchanges information with its neighbors, rather than the entire swarm [101]. The neighbor particles influence the velocity and position updates of a given particle. During each iteration, the particle evaluates its fitness based on the objective function and updates its personal best position. It then exchanges information with its neighbors, considering both its own best position and the best position found by its neighbors. The particle's velocity and position are updated using the information obtained from these local interactions [102]. In the ring topology, the updating equation for velocity and position remains the same as in the standard PSO algorithm. However, the difference lies in the information-sharing process, where particles only consider the personal best position and the best position of their adjacent neighbors when updating their velocity and position [103].