## 5 Simulation Results
### Simulation Results
#### 5.2.2 Performance Comparisons of Different Algorithms  
For the same network topology, we evaluate the performance of the proposed algorithm with the same multi-objective based genetic algorithm and single-objective based random placement algorithm in terms of delay, security, load rate, and link overhead. To this end, we choose Bellcanada topology to conduct simulation experiments and obtain the performance of MODECP compared with other algorithms. Additionally, we set two delay states to describe the impact on the placement results by varying the delay calculation parameters. State 1 indicates that all delays are considered, namely the switch-controller propagation delay, the inter-controller propagation delay, transmission delay, and processing delay. State 2 indicates that only the switch-controller propagation delay and the inter-controller propagation delay are considered, without considering the transmissiondelay and processing delay. At the same time, we evaluate the time consumption for different algorithms and different topologies. Figure 4 shows the performance comparison of the MODECP with genetic algorithm and random placement algorithm under the same topology. For Bellcanada topology, the three algorithms have different performances in the evaluation parameters of end-to-end delay, security, load rate, and link overhead. No matter the point of view, MODECP in delay state 1 generally outperforms the same multi-objective based genetic algorithm in delay state 1 and the single-objective based random placement algorithm. Due to the uncertainty of the random placement algorithm, its performance exhibits a trend of unstable fluctuations. The performance trend of the MODECP and the genetic algorithm is basically similar, but the accuracy of the MODECP is better. In addition, by varying the delay model calculation parameters, it can be demonstrated that MODECP in state 2 performs slightly better than state 1 in terms of delay evaluation. The reason for this performance is that state 2 does not take processing delay and transmission delay into account as much as state 1. It can also be seen from the comparison that the difference in performance between state 1 and state 2 is minimal, which indicates that processing delay and transmission delay have less impact on the network performance. In terms of security, load, and link overhead, there is no significant trend of changing the delay model parameters in the deployment results. Figure 2: Cumulative distribution functions for different target states. (**a**) Performance of different states regarding end-to-end latency. (**b**) The performance of different states regarding node security. (**c**) The performance of different states regarding the control node load rate. (**d**) The performance of different states regarding the link overhead. Figure 5 shows the running time of the three algorithms under the Bellcanada topology and the running time of the proposed algorithm under different topologies, including Xspedius, Bellcanada, and Uninett2010. As can be seen from the description, the running time of the MODECP increases with the number of controllers for the same topology. For different topologies, the greater the number of switches in the network, the greater the range of switches that can be selected to place control nodes, so the longer the running time. Comparing the MODECP with the genetic algorithm and random placement algorithm, the running time of the random placement algorithm is consistently the shortest. This is because the random placement algorithm is based on the principle of minimum delay, and it does not have an iterative process to select the optimal result. Under the same conditions, the proposed algorithm has shorter running time and better convergence performance than the multi-objective based genetic algorithm. Since the mutated individuals in MODECP are obtained by differentiating the parent individuals and crossover with the parent individuals to generate new individuals, they are finally selected directly with the parent individuals.