## 4 DHD-MEPO Algorithm
### Optimizing the Emperor Penguin Algorithm to Repair Holes
#### 4.4.2 Multi-Objective Fitness Function Design  
A multi-objective fitness function is designed by combining the important occupancy of the hole region, the energy balance coefficient of the candidate repair node, and the distance of the repair node from the blind zones. The three sub-goal factors collectively characterize the amount of coverage that a repair node can achieve by moving. 1. Significant percentage of hole regions Based on environmental learning to sense the importance level of the target monitoring region, the environmental monitoring region is learned iteratively, and the importance level of each cell area is continuously changed based on the data information value of the target point and the surrounding environment's customization factors. By setting the importance value of each cell area, the repair nodes will prioritize covering the hole regions with a high importance value, and the repair nodes can cooperate with each other to prioritize learning and concentrate on the hole regions with a high cell importance value index, which can save the nodes unnecessary energy consumption and collecting data information of unimportant blind zones. Therefore, the importance value of the cell hole region is an important factor to be considered when coverage blind zones occur. Based on the custom environmental information perception factors, the quantity of important levels is determined based on the quantity of cells divided into each layer of the area. For example, as shown in Figure 8a for a part of the target region, the red area is the hole region, as each layer is divided into four cells. As shown in Figure 8b, the area cells will be divided into four levels, the importance level \(G_{(x,y,z)}\) from one to four increasing, in the figure with the color from increasing from light to dark importance level in turn. The quantity of each important area rank and the location of the same rank distribution are uneven, reflecting the dynamic and random nature of environmental perception areas. From Figure 8, it can be seen that cell hole \(D_{(4,2,1)}\) and cell hole \(D_{(2,2,3)}\) have rank 4, so they are the hole regions that the repair nodes prioritize for coverage. 2. Energy balance factor of candidate repair nodes The energy balance coefficient \(\theta\) for a candidate repair node is calculated as:  
\[\theta=\frac{Max\Big{(}E_{resp}\Big{)}-Min\Big{(}E_{resp}\Big{)}}{\frac{\ln} {\ln}\sum_{p=1}^{m}E_{resp}} \tag{20}\]  
Figure 8: Hole classification chart: (**a**) Map of hole regions; (**b**) Unit grade distribution map. where \(E_{resp}\) is the residual energy of candidate repair node \(s_{p}\); \(m\) is the quantity of candidate repair nodes; and \(\theta\) denotes the energy consumption equalization factor of the repair nodes. The larger the value of \(\theta\), the more nodes unbalanced the energy consumption, and conversely, the more balanced the energy consumption. 3. Distance of the repair node from the blind zone  
The ratio between the distance of the repair node from the blind zone and the maximum distance the repair node can move is judged, and only the case when the ratio is less than 1 is considered. The smaller the ratio, the closer the node is to the hole. If the ratio is not less than 1, the repair node is directly excluded from repairing this hole repair. The maximum distance, \(d_{max_{p}}\), that the repair node can move is calculated by Equation (6). The multi-objective fitness function can be expressed as:  
\[Fitness=\omega_{1}\bigg{(}\frac{1}{k/c}\times G_{(x,y,z)}\bigg{)}+\omega_{2} (1-\theta)+\omega_{3}\Bigg{(}1-\frac{d\Big{(}s_{p},D_{hole(x,y,z)}\Big{)}}{d_ {max_{p}}}\Bigg{)} \tag{21}\]  
where \(G_{(x,y,z)}\) denotes the importance rank ratio occupied by this coverage hole region and \(d\Big{(}s_{p},D_{hole(x,y,z)}\Big{)}\) denotes the distance of this repair node from this coverage hole. \(\omega_{1}\), \(\omega_{2}\), and \(\omega_{3}\) are weighting coefficients, \(\omega_{1}+\omega_{2}+\omega_{3}=1\). The determination of the weighting parameters is given in Section 5.1.