## 4 GWO Algorithm Based on the Dynamic Adjustment of the Proportional Weight and Convergence Factor
### Improved GWO Algorithm  
The GWO algorithm is a new intelligent optimization algorithm proposed by [PERSON] in 2014. The GWO algorithm simulates the social hierarchy and predatory behavior of the grey wolf. The grey wolf is considered the predator at the top of the food chain. The GWO algorithm has the advantages of reduced parameter adjustment, simple principles, and ease of understanding. In the context of function optimization, the GWO algorithm surpasses the basic particle swarm algorithm in terms of accuracy and stability [30]. The search for the optimal solution is performed according to the three important steps in the hunting strategy of wolves: approaching, surrounding, and attacking prey. This process and the associated results were used to establish the model. Every grey wolf represented a potential solution in the population. The wolves were divided into four levels in the GWO algorithm: \(\alpha\), \(\beta\), \(\delta\), and \(\omega\). The current best individual was \(\alpha\), which represented the optimal solution. The second- and third-best individuals were \(\beta\) and \(\delta\), respectively, which represented the suboptimal solution and third-best solution. The other individuals were recorded as \(\omega\), which represented an ordinary solution. The corresponding hierarchical relationship was \(\alpha>\beta>\delta>\omega\). A detailed description of the algorithm was provided in Reference [30]. However, the GWO algorithm also exhibits the problem of easily reaching a local optimal solution, as with any other swarm intelligence algorithm [35; 36; 37; 38]. To address this problem, the GWO algorithm was improved in this study as follows:  
(1) According to Reference [30], the value of \(\overset{\rightarrow}{A}\) had a strong relationship with the local and global searches in the GWO algorithm. In Formula (19), \(\overset{\rightarrow}{A}\) changes with the transformation of the convergence factor \(\overset{\rightarrow}{a}\). The convergence factor \(\overset{\rightarrow}{a}\) linearly decreases from 2 to 0 with continued iterations, easily resulting in a local optimal solution. In order to improve the global search abilities of the wolves, the improved nonlinear formula about the convergence factor \(\overset{\rightarrow}{a}\) proposed in this study is shown in Formula (18). The original formulas of convergence factor \(\overset{\rightarrow}{A}\), \(\overset{\rightarrow}{a}\) are shown in Formula (19). \[\overset{\rightarrow}{a}=\overset{\rightarrow}{a_{\text{ini}}}-(\overset{ \rightarrow}{a_{\text{ini}}}-\overset{\rightarrow}{a_{\text{fin}}}+1)( \frac{t}{t_{\text{max}}})^{2}. \tag{18}\]  
\[\left\{ \begin{array}{l}\overset{\rightarrow}{A}=2\overset{\rightarrow}{a }\overset{\rightarrow}{r_{2}}-\overset{\rightarrow}{a}\\ \overset{\rightarrow}{a}=2-2(t/t_{\text{max}})\end{array} \right., \tag{19}\]where \(a_{\text{ini}}^{\rightarrow}\) and \(a_{\text{fin}}^{\rightarrow}\) are the initial and final values, respectively, of convergence factor \(\overrightarrow{a}\), with values of 2 and 0, respectively. (2) In the later portion of the iterative process, loss of group diversity occurred because all grey wolves were close to the best individual region. If the current best individual grey wolf was the local optimal solution, then the GWO algorithm suffered from local optimization, resulting in premature convergence. Based on the PSO algorithm, a new proportional weight factor was introduced in this study. By adjusting the weight, the global search and local search abilities of the algorithm were balanced, and the convergence rate of the algorithm was improved. The proportional weight formulas were as follows:  
\[\left\{