# A Hybrid Adaptive Particle Swarm Optimization Algorithm for Enhanced Performance
## 1 Introduction
These advancements have facilitated the widespread application of PSO in power network optimization [23], mechanical design innovation [24], and logistics and distribution scheduling [25]. Although a lot of research has been conducted on the PSO algorithm, the main problems of the algorithm have not been fully solved. First, the algorithm itself has the problem of premature convergence. For example, when the algorithm uses complex multi-peak functions, it is easy to fall into local optimization. Meanwhile, the algorithm is highly sensitive to parameter settings such as inertia weights and acceleration coefficients, but there is no generalized parameter setting mechanism. Second, it often faces an imbalance between global and local search. Too much focus on the global search capability leads to inefficiency and slow convergence, while too much emphasis on the local search capability increases the risk of falling into a local optimum. Third, when facing a high-dimensional optimization problem, the search space exponentially expands, leading to a significant increase in computational complexity, and the algorithm is more likely to converge to a local optimum. In addition, the interaction mechanism between particles is complex, making it difficult to effectively guide the search direction. In practice, engineering optimization problems often contain both equal and unequal constraints. In such scenarios, methods need to be developed that can handle these constraints while maintaining the performance of the algorithm. Therefore, improvements to the algorithms still require significant work. This paper proposes an adaptive selection particle swarm optimization algorithm and investigates its applications. Central to the algorithm is the integration of enhancement strategies into the standard particle swarm approach, which allows the particles to perform a more nuanced search within the solution space, thereby enhancing population diversity. The enhancement strategies examined in this paper include the following:  
* Initializing the particle swarm using hybrid chaotic mapping to achieve a more uniform distribution of the population within the solution space, thereby enhancing population diversity. * Focusing on dynamically adjusting the inertia weights through adaptive weights, allowing particles to conduct precise searches at each stage. * Dividing the population into three subsets and updating the velocity and position of the particles by applying cross-learning and social learning mechanisms to the elite particles, which aims to improve the exploration performance of the particles. * Employing the evolutionary strategies DE/best/1 and DE/rand/1 on ordinary particles to enhance their utilization, while also introducing a mutation mechanism to prevent the improved algorithm from converging on local optimal solutions during the search process. A variety of strategies, including composite chaotic mapping for population initialization, adaptive inertia weights, an elite particle learning mechanism, and a differential evolution strategy for ordinary particles, are integrated to develop a novel particle swarm optimization algorithm referred to as APSO. This integration seeks to enhance the algorithm's search efficiency, mitigate convergence to local optima, and bolster its robustness. To assess the effectiveness of the improved APSO algorithm, we conduct tests and comparisons with other algorithms, evaluating the optimal value, standard deviation, and average value for each. Ultimately, the algorithm is applied to real-world engineering problems to derive practical solutions.