## 3 Methodology
### Multi-Objective Fitness Function  
Our fitness function consists of multiple objectives. Coverage maximization attempts to maximize the area covered by the drone fleet and minimize overlap. Connectivity preservation keeps drones connected in order to facilitate seamless coordination, and energy conservation minimizes excessive travel in order to conserve battery life.  
Each candidate solution's fitness in the GA is determined using a weighted sum approach. The fitness function can be represented as in Equation (1):  
\[\text{F}=\text{w}_{1}\text{C}+\text{w}_{2}\text{N}+\text{w}_{3}\text{E}, \tag{1}\]  
where C denotes the total area covered by UAV communication ranges, calculated using the union of circular coverage areas centered at UAV positions. N represents the network connectivity which can be calculated as Equation (2), measured as the total number of active communication links among UAVs that are within transmission range of each other, normalized by the maximum possible number of connections:  
\[\text{N}=\frac{2\times L}{n\left(n-1\right)} \tag{2}\]  
where \(L\) is the number of established bidirectional communication links and n is the total number of UAVs. This metric ranges from 0 (no connectivity) to 1 (fully connected network), ensuring that the connectivity of the fleet is effectively quantified regardless of fleet size. E denotes energy efficiency, which is calculated as the inverse of the total communication distance among all connected UAVs, promoting energy-aware deployment. The weight coefficients w\({}_{1}\), w\({}_{2}\), and w\({}_{3}\) are used to balance the relative importance of each objective. In our experiments, these were empirically set to w\({}_{1}\) = 0.4, w\({}_{2}\) = 0.4, and w\({}_{3}\) = 0.2 after preliminary tuning. These values provided a good trade-off between maximizing area  
Figure 1: System architecture of the proposed hybrid optimization framework.  
coverage, maintaining reliable connectivity, and minimizing communication-related energy consumption. This trade-off is necessary because maximizing coverage often leads to increased inter-UAV distances, which can reduce connectivity and increase communication-related energy costs. The selected weight values reflect a balanced compromise among these competing objectives, ensuring that no single metric dominates the optimization outcome. Coverage optimization is defined in Equation (3):  
\[\mathrm{C}=(\sum\mathrm{A_{i}})/\mathrm{A_{total}}, \tag{3}\]  
In this context, \(\mathrm{A_{i}}\) is the area covered by drone i, and \(\mathrm{A_{total}}\) is the total mission area. The connectivity maintenance is assessed through a graph-theoretic analysis, where drones are nodes and links depend on signal strength. The model for energy efficiency is expressed in Equation (4). This formulation estimates the energy efficiency based on the normalized total communication distance between UAVs. This approach, though abstracted, is consistent with several studies in the field. In energy-aware UAV mission planning, distance-based metrics are often used to approximate energy consumption due to their proportional relationship with power requirements during flight and communication operations. Similar assumptions are employed in multi-UAV optimization frameworks [22; 32; 36], where path length, turns, and UAV coordination are primary factors influencing energy usage:  
\[\mathrm{E}=1-(\sum\mathrm{d_{i}})/\mathrm{d_{max}}, \tag{4}\]  
where \(\mathrm{d_{i}}\) represents the distance traveled by drone i and \(\mathrm{d_{max}}\) is the maximum allowable distance. Note that the energy efficiency \(\mathrm{E}\) is modeled as a distance-based proxy, which does not account for hardware-level power consumption.