The paper "Analysis of Particle Swarm Optimization Algorithm" by Qinghai Bai from the College of Computer Science and Technology at Inner Mongolia University for Nationalities provides an in-depth analysis of the Particle Swarm Optimization (PSO) algorithm. PSO is a heuristic global optimization method inspired by the social behavior of bird and fish flocks. The algorithm is widely used due to its simplicity, ease of implementation, and the few parameters required for tuning. The paper begins with an introduction to PSO, highlighting its origins and key principles. It explains how the algorithm works, comparing the movement of particles in a swarm to the behavior of birds and fish in search of food. The basic PSO algorithm is then detailed, including the three main principles: maintaining inertia, adjusting based on the most optimistic position of the individual particle, and adjusting based on the most optimistic position of the swarm. The advantages and disadvantages of the basic PSO algorithm are discussed. Its strengths include its applicability in various fields, simplicity, and fast convergence. However, it also suffers from partial optimism, which can lead to less accurate solutions and limitations in handling complex optimization problems. The current research situation of PSO is reviewed, noting that while the algorithm has shown promise, it lacks a solid mathematical foundation and systematic calculation methods. Most research focuses on its application in evolutionary neural networks, with limited studies on its mathematical properties and convergence. The paper also explores several improvements to the PSO algorithm, including the use of inertia weights, increasing the convergence factor, incorporating selection mechanisms, and blending PSO with other intelligent algorithms such as simulated annealing and ant colony optimization. These enhancements aim to improve the algorithm's performance and applicability. Finally, the paper concludes with a discussion on future research directions, emphasizing the need for further development in the mathematical theory, topology of the particle swarm, integration with other optimization algorithms, and expanding the application areas of PSO.The paper "Analysis of Particle Swarm Optimization Algorithm" by Qinghai Bai from the College of Computer Science and Technology at Inner Mongolia University for Nationalities provides an in-depth analysis of the Particle Swarm Optimization (PSO) algorithm. PSO is a heuristic global optimization method inspired by the social behavior of bird and fish flocks. The algorithm is widely used due to its simplicity, ease of implementation, and the few parameters required for tuning. The paper begins with an introduction to PSO, highlighting its origins and key principles. It explains how the algorithm works, comparing the movement of particles in a swarm to the behavior of birds and fish in search of food. The basic PSO algorithm is then detailed, including the three main principles: maintaining inertia, adjusting based on the most optimistic position of the individual particle, and adjusting based on the most optimistic position of the swarm. The advantages and disadvantages of the basic PSO algorithm are discussed. Its strengths include its applicability in various fields, simplicity, and fast convergence. However, it also suffers from partial optimism, which can lead to less accurate solutions and limitations in handling complex optimization problems. The current research situation of PSO is reviewed, noting that while the algorithm has shown promise, it lacks a solid mathematical foundation and systematic calculation methods. Most research focuses on its application in evolutionary neural networks, with limited studies on its mathematical properties and convergence. The paper also explores several improvements to the PSO algorithm, including the use of inertia weights, increasing the convergence factor, incorporating selection mechanisms, and blending PSO with other intelligent algorithms such as simulated annealing and ant colony optimization. These enhancements aim to improve the algorithm's performance and applicability. Finally, the paper concludes with a discussion on future research directions, emphasizing the need for further development in the mathematical theory, topology of the particle swarm, integration with other optimization algorithms, and expanding the application areas of PSO.