## 4 Optimization Method
### Improved Scheduling Strategy
#### 4.1.5 Improved Artificial Bee Colony Algorithm  
In the typical ABC algorithm, there are three types of individuals: hired bees, observer bees and detection bees [38]. Each hired bee corresponds to a defined honey source (solution vector), and the area of the honey source is searched during the iteration. According to the abundance of the nectar source (the size of the adaptive value), a roulette wheel is used to select observer bees to collect honey (search for new nectar source). If the honey sourcesare not improved after several updates, the honey  
Figure 3: Flowchart of four strategies. source are abandoned and the hired beesare turned into detection bees to search for the new honey source randomly [39]. (a) Population Initialization  
Random numbers matching the predefined range are randomly generated on each element of the honey source position matrix to fill the honey source position matrix. The expression of the population initialization is expressed as follows. \[x_{i,d}=l_{d}+\textit{llsdesign}(0,1)\cdot(u_{d}-l_{d}) \tag{23}\]  
where \(ld\) and \(ud\) are the lower and upper bounds of the d-dimensional search space, respectively; _llsdesign_(0,1) represents a random number of (0,1) generated by Latin hypercube sampling. Compared with the traditional _rand_ distribution, _llsdesign_ can make every individual in each dimension of the initial population within the interval of uniform distribution, ensuring that the initial population can contain locally optimal individuals and ensuring the convergence of the algorithm. (b) Hired Bee Stage of the Hybrid Whale Search Strategy  
The hired bees are responsible for finding suitable honey sources within the designated search area. Then, the information of the source is saved. The formula for searching the honey source is shown as follows. \[u_{i,d}=x_{i,d}+r\big{(}x_{i,d}-x_{k,d}\big{)} \tag{24}\]  
where \(u_{i,d}\) represents the location of the new nectar source. \(x_{i,d}\) is the \(d\)-dimension values of the \(i\)th nectar source. \(x_{k,d}\) is the \(d\)-dimensional value of a randomly selected nectar source among \(N\) nectar sources, and \(k\
eq i\). \(r\) represents the random number within the interval [-1,1]. In the typical ABC, both hirer and observer bees use Equation (24) to conduct one-dimensional operations, which has a strong global search ability but low search efficiency. Thewhale optimization algorithm (WOA) is a new algorithm to simulate the hunting behavior of humpback whales in the ocean [40]. The contraction enveloping mechanism is simulated by Equation (25). A spiral equation is established between the position of whale and prey to simulate the spiral motion of humpback whales as shown in Equation (26). In order to simulate the simultaneous occurrence of both movements in the humpback whale, it is assumed that there is a 50% probability that a choice can be made between the narrowing of the enveloping mechanism and the spiral model, as shown in Equation (27). This paper combines the WOA to improve the search mode of hired bees. The behavior of bees searching for honey is modeled based on that of humpback whales searching for prey. \[\left\{ \begin{array}{c}A=2a\cdot r-a\\ C=2\cdot r\\ D=\big{|}C\cdot x_{d}^{*}-x_{i,d}\big{|}\\ u_{i,d}=\ x_{i,d}-A\cdot D\end{array} \right. \tag{25}\]  
\[u_{i,d}=D\cdot e^{bl}\cdot\cos(2\pi l)+x_{i,d} \tag{26}\]  
\[u_{i,d}=\left\{ \begin{array}{cc}x_{i,d}-A\cdot D&p<0.5\\ D\cdot e^{bl}\cdot\cos(2\pi l)+x_{i,d}&\textit{otherwise}\end{array} \right. \tag{27}\]  
where \(a\) is the iteration number that decreases linearly from 2 to 0; \(r\) is a random number within the range [0,1]; \(x_{d}^{*}\) is the \(d\)-dimension value of the current optimal nectar source; \(b\) is a constant; \(l\) is the random number within the range of [-1,1]; \(p\) is a random number within the range [0,1]. When the new honey source is obtained, the fitness values of new and old honey sources are calculated by Equation (28). \[fit_{i}=\left\{