## 3 Optimization Model and Evaluation Indexes
### DEWGO Algorithm
#### 3.2.2. Grey Wolf Optimization  
[PERSON] et al. [40] first proposed a novel meta-heuristic named Grey Wolf Optimizer (GWO) in 2014, which was inspired by the hunting behaviour of grey wolves. The algorithm imitates the leadership structure and hunting strategy of grey wolves in nature. \(\alpha\), \(\beta\), \(\delta\), and  
Figure 3: BPNN topology structure. \(\omega\) are the four varieties of grey wolves that are applied to simulate the leadership structure. Furthermore, the primary steps of hunting, searching for prey, surrounding prey, and attacking prey are implemented to search for the best solution. In the GWO algorithm, \(\alpha\) is considered the best agent, while the candidate agent of \(\omega\) is less superior to the other three. Grey wolves surround prey during the hunting process, and the surrounding behaviour is expressed by the mathematical model:  
\[\left\{ \begin{array}{l}D=\left|\stackrel{{\rightharpoonup}}{{ \mathcal{C}}}\times\stackrel{{\rightharpoonup}}{{X}}_{p}(t)- \stackrel{{\rightharpoonup}}{{X}}(t)\right|\\ \stackrel{{\rightharpoonup}}{{X}}(t+1)=\stackrel{{ \rightharpoonup}}{{X}}_{p}(t)-\stackrel{{\rightharpoonup}}{{A}} \times\stackrel{{\rightharpoonup}}{{D}}\\ \stackrel{{\rightharpoonup}}{{A}}=2\stackrel{{ \rightharpoonup}}{{a}}\times\stackrel{{\rightharpoonup}}{{r}}_{1}- \stackrel{{\rightharpoonup}}{{a}}\\ \stackrel{{\rightharpoonup}}{{C}}=2\cdot\stackrel{{ \rightharpoonup}}{{r}}_{2}\\ a=2\Big{(}1-\frac{t}{t_{\max}}\Big{)}\end{array} \right. \tag{5}\]  
where \(t\) indicates the current iteration; \(\stackrel{{\rightharpoonup}}{{A}}\) and \(\stackrel{{\rightharpoonup}}{{C}}\) are coefficient vectors; \(\stackrel{{\rightharpoonup}}{{X}}_{p}(t)\) is the position vector of the prey; \(\stackrel{{\rightharpoonup}}{{X}}(t)\) indicates the position vector of a grey wolf; component \(D\) of \(\stackrel{{\rightharpoonup}}{{D}}\) is the distance between the grey wolf and the prey; \(\stackrel{{\rightharpoonup}}{{X}}(t+1)\) is the updated position of a grey wolf; \(\stackrel{{\rightharpoonup}}{{a}}\) is the vector representing the attack range of a grey wolf; component \(a\) of \(\stackrel{{\rightharpoonup}}{{\alpha}}\) is the convergence factor affecting the change of \(\stackrel{{\rightharpoonup}}{{A}}\), ranging from 0 to 2.0; \(r_{1}\), \(r_{2}\) are random vectors in (0, 1.0). During hunting, the position of the prey is estimated using the updating positions of \(\alpha\), \(\beta\), and \(\delta\) wolves:  
\[\left\{ \begin{array}{l}D_{\alpha}=\left|\stackrel{{\rightharpoonup}}{{ C}}_{1}\times\stackrel{{\rightharpoonup}}{{X}}_{\alpha}- \stackrel{{\rightharpoonup}}{{X}}\right|\!,\;D_{\beta}=\left| \stackrel{{\rightharpoonup}}{{C}}_{2}\times\stackrel{{ \rightharpoonup}}{{X}}_{\beta}-\stackrel{{\rightharpoonup}}{{X}} \right|\!,\;D_{\delta}=\left|\stackrel{{\rightharpoonup}}{{C}}_{2} \times\stackrel{{\rightharpoonup}}{{X}}_{\delta}-\stackrel{{ \rightharpoonup}}{{X}}\right|\!\\ \stackrel{{\rightharpoonup}}{{X}}_{1}=\stackrel{{ \rightharpoonup}}{{X}}_{\alpha}-\stackrel{{ \rightharpoonup}}{{A}}_{1}\times\stackrel{{ \rightharpoonup}}{{D}}_{\alpha},\stackrel{{ \rightharpoonup}}{{X}}_{2}=\stackrel{{\rightharpoonup}}{{X}}_{ \beta}-\stackrel{{\rightharpoonup}}{{A}}_{2}\times\stackrel{{ \rightharpoonup}}{{D}}_{\beta},\stackrel{{\rightharpoonup}}{{X}}_{3} =\stackrel{{\rightharpoonup}}{{X}}_{\delta}-\stackrel{{ \rightharpoonup}}{{A}}_{3}\times\stackrel{{ \rightharpoonup}}{{D}}_{\delta}\\ \stackrel{{\rightharpoonup}}{{X}}(t+1)=(\stackrel{{ \rightharpoonup}}{{X}}_{1}+\stackrel{{ \rightharpoonup}}{{X}}_{2}+\stackrel{{\rightharpoonup}}{{X}}_{3} )/3\end{array} \right.