## 5 Build an Optimal Security Strategy
### Framework of RODE
This is because after the introduction of opposition-based learning, there is a high probability of jumping out of the local optimal solution in subsequent iterations, which is not available in other algorithms. Therefore, the experimental results can prove that the RODE algorithm in this paper can largely resist the influence of the initial population, has strong robustness, and can quickly and accurately find the optimal strategy set. The disadvantage of this method is that it can only passively prevent attacks [39, 40] in advance. If faced with frequent and changeable attack methods, the effect will be greatly discounted. For this reason, the main direction in the future is to study how to apply RODE to dynamic protection [41]. \begin{table}
\begin{tabular}{c c c} \hline \hline Algorithm & 200 & 10 \\ \hline PSO & 91 & 100 \\ \hline RLPSO & 76 & 99 \\ \hline DE & 0 & 75 \\ \hline RIDE & 4 & 99 \\ \hline RODE & 0 & 16 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The number of times each algorithm falls into the local optimal solution. Figure 11: Algorithm convergence test when the initial population size is 10. (**a**) DE algorithm runs 100 times. (**b**) PSO algorithm runs 100 times. (**c**) RLDE algorithm runs 100 times. (**d**) RLPSO algorithm runs 100 times. (**e**) RODE algorithm runs 100 times. ### Discussion

As we all know, in view of the characteristics of industrial control security defense, the accuracy and speed of the selection strategy are particularly critical, which requires that the selected evolutionary algorithm not only solve the problem of convergence accuracy but also solve the problem of convergence speed, and consider the impact of population size. However, the previous evolutionary algorithms seem to focus on solving one of the problems, and they do not consider the effect of population size, because their tests are all carried out under the premise that the population size remains unchanged [7], while RODE considers the effect of population size. At the same time, reinforcement learning and opposition-based learning are also used to solve the problems of convergence speed and convergence accuracy, respectively. Furthermore, we verify the effectiveness of RODE at different population sizes through the above two sets of experiments. Last but not least, in the second experiment, comparing RLDE and RODE in Figure 10, that is, when the population is 200, the performance of RODE and RLDE is almost the same, indicating that RODE has played a role in reinforcement learning. Comparing RLDE and RODE in Figure 11, that is, when the population is 10, the effect of RODE is much higher than that of RODE, because RODE has the effect of opposition-based learning at this time. So, we have reason to believe that RODE greatly improves the performance of the DE algorithm, and our method also provides a good idea for improving other evolutionary algorithms. ## 7 Conclusions

The scientific deployment of security strategies is the key to reducing the risk of ICS being attacked. In this paper, a differential evolution algorithm based on reinforcement learning and opposition-based learning is proposed to obtain the optimal security strategy by combining fitness functions. First, a Bayesian attack graph is used to model the potential attack paths of the industrial control system. Then, we calculate the attack benefit of each node and the cost of implementing the security strategy, and we build a fitness function based on the attack benefit and security cost. The fitness function can effectively evaluate the value of the selected solution. Finally, the RODE algorithm is used to select the security strategy scheme. The RODE algorithm is suitable for populations of various sizes.