## 5 Simulation Results
### Simulation Results  
#### 5.2.1 Performance Comparisons of Different Objective Models  
We evaluate the algorithm performance of the improved differential evolution algorithm in single-objective and multi-objective situations and verify its effectiveness in four aspects, which are delay, security, load rate, and link overhead. To this end, we choose Xspedius, Bellcanada, and Uninett2010 topologies to conduct many simulation experiments to obtain the performance of MODECP.  
Figure 2 shows the cumulative distribution functions for multi-objective and different single-objective states. Through a large number of simulation experiments on multiple network topologies, the performance of the MODECP can be obtained under the single-objective conditions and simultaneous fitting of multi-objective conditions. Figure 2a shows that when the end-to-end delay is used as the evaluation parameter, the improved differential evolution algorithm considering only the delay performs the best compared with other objective situations. Since the MODECP considers four objectives at the same time, the end-to-end delay performance is inferior to that of the single-objective algorithm that only considers the delay, but it is better than that of the other three single-objective states. According to the security model in Section 3, security is inversely proportional to the probability of data loss. In other words, when links or nodes fail, the higher the probability of data loss is, the worse the network security performance is. Therefore, we hope for controllers to be deployed on nodes with a low probability of failure and control paths to be distributed on links with a low probability of failure. At this point, the larger the normalized value, the better the security of the network, according to Equation (8). Figure 2b-d shows the performance under five situations when node security, load rate, and link overhead, respectively, are used as evaluation parameters. Similarly, these experimental results show that the performance of the MODECP on three evaluation parameters is inferior to, or similar to, the case where only a single objective is considered.  
To evaluate the impact of link failures on deployment results, we train the SVM model and predict the link state. We randomly generate the link traffic distribution and classify the link state as 0 or 1 to be used in the dataset for training the SVM model. We also simulate link traffic for five time periods in order to highlight the different link failure states due to traffic changes at different periods. The SVM model predicts the links that fail and tests the performance of MODECP in terms of delay, load, and link cost after link failures. Specifically, we vary the percentage of failed links in the network to evaluate performance in the simulation experiments, including 5%, 10%, and 15%.  
Figure 3 presents the performance trends in delay, load, and link overhead at various time periods after MODECP re-deployed the controller when changing the number of links that failed in the network. Based on comparing the number of failed links at 0%, 5%, 10%, and 15% in the Bellcanada topology, there is no significant difference in performance between no links failed and 5% of links failed. Due to the increased number of failed links, the control path length must be increased to deploy controllers with distribution switches to enable communication between the switches and controllers. As a result, the performance of the state with 15% link failures is significantly worse than the other states.