# A Hybrid Adaptive Particle Swarm Optimization Algorithm for Enhanced Performance
## 1 Introduction  
As technology advances and societal needs evolve, optimization techniques have become essential across various industries. Traditional optimization methods frequently encounter difficulties when addressing complex, multidimensional challenges, which complicates the pursuit of optimal solutions. This has spurred increased interest in the development of more efficient and intelligent optimization algorithms. One notable example is particle swarm optimization (PSO) [1], which is distinguished by its capacity to address both mixed-space and continuous optimization problems, thus serving as a valuable tool. PSO has been effectively applied in numerous domains, including parameter optimization [2], neural network training [3], clustering analysis [4], combinatorial optimization [5], pattern recognition [6], and image processing [7]. Furthermore, the intelligent optimization capabilities of PSO present significant potential for advancement in artificial intelligence [8] and machine learning [9]. By conducting comprehensive research on the PSO algorithm, we can gain deeper insights into its underlying mechanisms and performance, thereby facilitating its enhancement and wider application. Numerous researchers have made great efforts to enhance PSO algorithms in terms of running performance, convergence, and parameter settings. To address high-dimensional complex problems, [PERSON] et al. introduced a novel method for adjusting the inertia weightfactor, which they modified to decrease linearly from 0.9 to 0.4 [10]. Subsequently, they adjusted the inertia weights to random values between 0.5 and 1 and designed a new algorithm, PSO-RIW, which demonstrated improved robustness in experimental tests [11]. [PERSON] et al. proposed a variable acceleration factor mechanism that proved more effective than time-varying inertia weights for optimizing single-peak functions in simulations [12]. [PERSON] et al. introduced the GLBEST-PSO algorithm, which modifies inertia weights by averaging the global and individual optima during iterations [13]. [PERSON] et al. developed the PSOSCALF algorithm by integrating the hybrid PSO algorithm, the positive cosine algorithm, and [PERSON]'s flight method, thereby enhancing the exploration capabilities of PSO and influencing local optimal positions with a degree of temptation [14]. A recent study [15] introduced a self-learning strategy alongside a nonlinear weight factor strategy aimed at enhancing the local search capabilities of the algorithm. This was achieved by employing [PERSON]'s flights to perturb the positions of the population, thereby assisting in escaping local optima. The authors of [16] presented a normal cloud model designed to adjust both the range of the wolf population's positions and the optimal individual, as well as the dispersion of the wolf population. This approach effectively improved the algorithm's local exploitation ability and convergence accuracy. Furthermore, several novel metaheuristic algorithms have been developed, including the dung beetle optimization algorithm [17], the vulture search algorithm [18], the sand cat swarm optimization algorithm [19], and the adaptive hybrid variational differential evolution (a-HMDE) [20]. [PERSON] et al. [21] proposed a new differential evolutionary algorithm based on particle swarm optimization, which utilizes differential evolution variants in the initial stages to broaden the search space, identify more promising solutions, and mitigate the risk of premature convergence. [PERSON] et al. [22] introduced the comprehensive learning particle swarm optimizer (CLPSO) for addressing complex multimodal problems. This method leverages the historical optimal experiences of other particles to enhance population diversity and global search capabilities. Concurrently, some researchers have integrated concepts from various optimization algorithms to improve convergence speed and search accuracy.