## 5 Simulation and Analysis
### Performance Analysis  
In this work, we mainly compare the CPD performance of different heuristics in the inter-layer link. Two classic heuristics, viz. Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), are selected as the baseline algorithms. The parameter settings of the baseline algorithms are the same as that of MPSO in this paper, and the iteration times and group size are 500 and 100, respectively. The crossover rate and mutation rate of GA are set to 0.6 and 0.05, and the GA adopts the elitism strategy of the survival of the fittest when picking offspring [42]. The inertia weight in the PSO algorithm is set to 0.6, and the local learning factor and global learning factor of the algorithm are the same as those of MPSO in this paper, which are 2 and 2, respectively. Additionally, to compare all algorithms as fairly as possible, the evaluation function of all algorithms is the same as MPSO.  
Since the three algorithms reserve the optimal individual during the iteration process, their fitness gradually increases with the number of iterations in Figure 7. Specifically, the crossover in GA can reorganize the binary strings in a large scale, and increase the diversity of individuals in the group. Therefore, the fitness of GA is lower than PSO in the early stage, while the gap between GA and PSO in fitness gradually narrow with iteration times. Different from the traditional PSO, MPSO relies on the historical optimal and worst positions for adjusting the search direction of particles. This method can fully expand the diversities of individuals and improve the search ability of the algorithm. In addition, the dynamic inertia weight in MPSO enables the algorithm to balance the guidance between the particle historical experience and the self-exploration during the iteration process, and to improve the search ability.  
In Figure 8, since the PSO does not adopt a targeted optimization strategy for the MLSCN, its link consumption falls into a local optimization trap at the early stage of iteration. On the contrary, in order to expand the diversity among the particles in the initial group, MPSO designs a grid-based initialization and develops a quaternary optimization scheme to guide the optimization efficiently. As a result, the downward trend of link consumption of MPSO is more distinct than that of PSO.  
In Figure 9, the delivery time refers to the time that it takes to transfer all packets in the network. The delivery time of MPSO shows a trend of fluctuating downward. This can be accounted that the fitness is not only determined by the delivery time, but also closely related to the arrival rate of data. Similarly, it can be seen from the figure that the differences in the delivery time is not as apparent as the difference on fitness. Again, this is because the fitness is not only based on the delivery time, but also the arrival time of each data flow and the arrival rate of data.  
Figure 6: Network architectures in STK. (**a**) 2D network model; (**b**) 3D network model.  
Figures 10 and 11 show the arrival rate and the average delivery time with the iteration times. And the performance trend in Figures 7 and 10 are almost the same, which can be accounted the fact that the arrival rate will greatly affect the fitness when the data cannot be delivered within the lifetime.  
Figure 8: Comparison of link consumption with the iteration times.  
Figure 7: Comparison of fitness with the iteration times.  
Figure 9: Comparison of delivery time with the iteration times.  
In terms of average arrival time of packets, the advantage of arrival rate in MPSO makes most of the packets arrive to the destination node earlier, compared with the baseline algorithms.