## 5 Build an Optimal Security Strategy  
### Differential Evolution Algorithm  
The differential evolution algorithm, as an efficient global optimization algorithm based on the natural evolution of species, is simple and efficient in practical applications [21]. It evolves a population of Np D-dimensional parameter vectors, mainly through mutation, crossover, and environmental selection operations. That is, first randomly generate initial test solutions; then, generate new test solutions through mutation and crossover operations. Next, determine which test solutions enter the next generation population to become candidate solutions through selection operations, and then repeat the iterative operations of mutation, crossover, and selection until all the experimental solutions are selected. The solution stops when the accuracy of the current solution meets the requirements or when a certain number of iterations is reached. 1. initialization Randomly select Np D-dimensional population individuals in the search space as the initial solution. The random initialization of the \(i\)-th individual \(X_{i}^{t=0}\) is a D-dimensional vector, which is denoted as \(X_{i}^{t=0}=\{X_{i,1}^{0},X_{i,2}^{0},\ldots,X_{i,D}^{0}\}\), and it can be expressed by Equation (12) [22] \[X_{i,j}^{t=0}=X_{\min,j}+rand_{i,j}[0,1](X_{\max,j}-X_{\min,j}),\] (12)where \(X_{\min,j}\) and \(X_{\max,j}\) are the predetermined lower and upper bounds of the search space for the j-th design variable, respectively, and \(rand_{i,j}[0,1]\) is a random number generated in \([0,1]\). 2. Mutations In the individual population \(X_{i}^{t}=\{X_{1}^{t},X_{2}^{t},\ldots,X_{N_{p}}^{t}\}\), three individuals are selected according to the mutation strategy to create a mutation vector \(V_{i}^{t}\), and the three individuals are different from each other. There are several basic evolution strategies [27; 28] in DE. The mutation strategy selected in this paper is \"DE/best/1/bin\", and it can be expressed as Equation (13): \[V_{i}^{t}=X_{best}^{t}+F(X_{r2}^{t}-X_{r3}^{t}),\] (13) where \(i=1,2,\ldots N_{p}\), \(r_{2},r_{3}\) are arbitrary and unequal random integers in the set \(\{1,2,\ldots N_{p}\}\), and \(X_{best}^{t}\) is the best individual. F is the scaling factor, which is a positive control parameter for scaling the difference vector, and it is often selected as 0.8. Then, we check whether the mutation vector violates the boundary constraint, and the violated individual returns the corresponding value according to the condition. The formula can be expressed by Equation (14). \[V\left\{ \begin{array}{ll}2x_{\min,j}-v_{i,j}^{t},\;\;if&v_{i,j}^{t}<x_{\min, j}\\ 2x_{\max,j}-v_{i,j}^{t},\;\;if&v_{i,j}^{t}>x_{\max,j}\\ v_{i,j}^{t},\;\;,\;\;otherwise\end{array} \right.\] (14) where \(v_{i,j}^{t}\) is the \(j\)-th component of \(v_{i}^{t}\); \(x_{\min,j}\) and \(x_{\max,j}\) are the maximum upper limit and the minimum lower limit of the search space of the \(j\)-dimensional variable, respectively. 3. Crossover The crossover operation is very similar to the crossover operation of the classical genetic algorithm, and its purpose is to diversify the individuals of the current population. However, the crossover here is different from the crossover operation of the genetic algorithm. The crossover operation here is for a certain dimension of the entire population, while the crossover in the genetic algorithm is for each individual in the population, and the experimental solution generated after the crossover operation is: \[u_{i,j}^{t}=\left\{ \begin{array}{ll}v_{i,j}^{t},\;\;if&\mathrm{rand}_{i,j}[0,1]\leq Cr\lor randi(1,D)=j\\ x_{i,j}^{t},\mathrm{otherwise}\end{array} \right.\] (15)
4. Selection The experimental solution produced after cross mutation may not be better than the initial solution. Therefore, it is necessary to compare the fitness values of the two objective functions and select individuals with better fitness values as offspring, which can be expressed as: \[x_{t}^{t+1}=\left\{