## 5 Experimental Analysis
### Algorithm Performance
#### 5.2.4 Pareto Front Analysis  
This study employs a multi-objective optimization approach to address the joint distribution problem involving drones and trucks. The convergence performance of the algorithm throughout the iterative process is illustrated through Pareto front analysis. Figures 12-15 depict the evolution of the non-dominated solution set corresponding to the following three critical optimization objectives: demand coverage, distribution cost, and distribution time, at various stages of iteration. Figure 11: Chart depicting the analysis of algorithm stability. Figure 12: Primary representation of the Pareto front. Figure 13: A side view representation of the Pareto front illustrating the relationship between delivery time and cost. Figure 12 illustrates the three-dimensional perspective of the Pareto front, effectively demonstrating the progression of the non-dominated solution set as it approaches the ideal point throughout the iterations. The blue region in the left subgraph delineates the set of Pareto optimal solutions, commonly referred to as the Pareto front. This front is characterized as a three-dimensional hypersurface comprising non-dominated solutions that are not outperformed by any other solutions within the context of the multi-objective optimization process. This region effectively illustrates the trade-off relationships among the three objectives: delivery time, delivery cost, and demand coverage. As the iterations  
Figure 14: Aerial representation of the Pareto front, illustrating the relationship between demand coverage and delivery cost. Figure 15: Analytical diagram illustrating the Pareto front and representative solutions. advance (transitioning from red to blue), the solutions progressively converge towards this region, signifying that the algorithm is successfully approaching the global Pareto front. During the initial iteration phase (represented by red dots), the solution set appears relatively dispersed and distant from the ideal point. As the iterations advance to 25% (indicated by green squares) and 50% (depicted by blue diamonds), the solution set progressively converges towards the Pareto front. In the final iteration (represented by yellow triangles), a distinct non-dominated solution set emerges, signifying that the algorithm has successfully converged to the Pareto optimal solution set. The convex hull surface of the final Pareto front further delineates the boundary of the non-dominated solutions, thereby assisting decision makers in comprehending the extent of the feasible solution space. Figures 13 and 14 illustrate the Pareto front from both a lateral and a superior perspective, respectively, emphasizing the trade-off relationships among various objective dimensions. The lateral view presented in Figure 12 specifically highlights the restrictive relationship between distribution cost and distribution time. In practical applications, achieving the simultaneous minimization of these two objectives poses significant challenges. The top view presented in Figure 14 illustrates the relationship between demand coverage and distribution costs. An increase in service coverage typically results in a corresponding rise in costs. Figure 14 depicts the top view of the Pareto front. In Figure 15, the Pareto front corresponding to the final iteration is illustrated, with the following three representative solutions highlighted: the maximum coverage solution (indicated by a red five-pointed star), the minimum cost solution (represented by a green diamond), and the minimum time solution (denoted by a blue square). These three extreme solution points are situated in distinct regions of the Pareto front, reflecting the boundary conditions within the decision-making space. The maximum coverage solution is capable of serving a greater number of customers; however, it necessitates higher costs and time investments. Conversely, the minimum cost solution is economically advantageous but offers a reduced coverage.