## 4 Optimization of Tunable Parameters with HWOA
### Coyotes Optimization Algorithm  
The conventional COA contains four main steps: initialization parameters and the wolf pack, growth within the group, birth and death, and the expulsion and acceptance by the group. Different from the GWOA, the COA focuses on social structure and cultural  
Figure 4: Schematic diagram of speed controller.  
exchange instead of social hierarchy and ruling rules. The improved COA is designed to further enhance the convergence speed and global searching performance. The general steps are grouped into three main steps.  
The first step is to set the parameters, including coyote group number \(N_{p}\), number of coyotes in the group \(N_{c}\), parameter ranges and iterations, and total coyote population \(N\), where \(N=N_{p}\times N_{c}\) and \(N_{c}>3\). The social condition of each coyote is randomly initialized, and \(N_{p}\) and \(N_{c}\) are dynamically tuned for easier operation. Then, group randomly and calculate the social condition of each coyote.  
The second step is the growth of coyotes. Concretely, the best coyote, \(a\), in all packs instead of the corresponding pack on the conventional COA can be found, which accelerates the approach speed to the current optimum. The cultural trend of \(j\)th pack \(cult_{j}\) can be calculated as follows:  
\[cult_{j}=\begin{cases}O_{(N_{c}+1)/2,j}&,N_{c}\text{ is odd}\\ (O_{N_{c}/2,j}+O_{N_{c}/2+1,j})/2,otherwise\end{cases} \tag{24}\]  
where \(O_{j}\) is the sequence of social factors after ranking.  
The growth pattern of coyotes can be expressed as follows:  
\[new\_soc_{c}{}^{n,j}=soc_{c}{}^{n,j}+h_{1}\cdot\delta_{1}+h_{2}\cdot\delta_{2} \tag{25}\]  
\[\delta_{1}=a-soc_{r1}^{j} \tag{26}\]  
\[\delta_{2}=cult_{j}-soc_{r2}^{j} \tag{27}\]  
where \(h_{1}\) and \(h_{2}\) are the Gaussian numbers, respectively. Compared with the random numbers in conventional COA, the introduction of Gaussian numbers has better global searching performance. \(soc_{r1}^{j}\) and \(soc_{r2}^{j}\) are social conditions of two random coyotes in the \(j\)th pack.  
The third step is the birth and death of coyotes, and the newborn coyotes are influenced by the inheritance of randomly selected parents and environmental factors, which can be expressed as (28).  
\[newborn_{i}=\begin{cases}soc_{r1,i},\ r_{i}<P_{s}\text{ or }i=i_{1}\\ soc_{r2,i},\ r_{i}\geq P_{s}+P_{u}\text{ or }i=i_{2}\\ R_{i},\ \ \ \ otherwise\end{cases} \tag{28}\]  
\[\begin{cases}P_{s}=1/D\\ P_{u}=(1-P_{s})/2\end{cases} \tag{29}\]  
where \(soc_{r1,i}\) and \(soc_{r2,i}\) are the \(i\)th dimension of the random coyote \(r_{1}\) and \(r_{2}\), respectively. \(r_{i}\) is the random number uniformly distributed in [0, 1], \(i_{1}\) and \(i_{2}\) are two randomly selected dimension labels, \(R_{i}\) is the variation value randomly generated in the \(i\)th dimension decision variable range, and \(P_{s}\) and \(P_{u}\) are the dispersion probability and the association probability, respectively.  
The COA equipped with a unique search model and structure has excellent optimization ability, especially in dealing with complex optimization situations. Correspondingly, partial defects, including search efficiency, convergence speed, and operability, exist.