## 2 System Model
### UAV Hovering Radius Optimization  
Genetic algorithms have many advantages compared with the traditional optimization algorithm, among which the most significant is the capacity to deal with complex problems and parallelism. The genetic algorithm starts from the randomly generated initial solution, and generates new solutions by selecting, crossover, and mutation. Then, the fitness of the new solution is calculated by the fitness function designed, and the next generation population is obtained by natural selection. After several iterations, the algorithm converges to the optimal population. The genetic algorithm takes the objective function value as the search information directly. It only uses the fitness function value transformed by the objective function value to determine the further search direction and search scope, and does not need some other auxiliary information, such as the derivative value of the objective function. Genetic algorithms simultaneously use search information from multiple search points. The search for the optimal solution by genetic algorithm starts from an initial group composed of many individuals, rather than a single individual. The fitness function is not only the criterion to measure the merits of individuals, but also the only basis for natural selection. Therefore, the design of the fitness function is particularly important. The genetic algorithm basically does not use external information in evolutionary search, only based on fitness function. The objective function is not constrained by continuous differentiability, and its domain can be any set. The only requirement for the fitness function is that the results can be calculated from the input and compared. The algorithm process is shown in Algorithm 2. The goal here is to find the optimal radius \(r\) for a given user scheduling \(A\). The fitness function is designed first. It is assumed that an optimal selection path denoted by \(D\) is obtained through the calculation of the ACA. It should be noted that \(D\) is a sequence of numbers, which represents the time slot that each user accesses and the size of \(D\) is \(1\times N\). The value of the elements in \(D\) are 1 to N and are not repeated. For any given \(r\), the corresponding matrix \(B_{N\times N}\) can be acquired. Therefore, the fitness function can be expressed as follows:  
\[f(r)\ =\ \sum_{i\ =\ 1}^{N}b_{i,d_{(\mathrm{L}i)}}, \tag{17}\]  
where \(b\) is an element of matrix \(B_{N\times N}\), and \(d(1,i)\) is the first row and the \(i\)-th column element of \(D\). The GA is also called the classical genetic algorithm. Its optimization variables are described by binary coding, and the binary codes of several optimization variables are strung together to form chromosomes. The binary string representing the individual is randomly generated with a certain length of subscript when the initial population is created. The selection operation selects individuals from the old population with a certain probability to form a new population in order to reproduce the next generation of individuals. The probability of an individual being selected is related to its fitness value. The fitness with bigger value will be selected with a higher probability. The crossover operation randomly selects the crossover position on the two chromosomes according to the probability, and exchanges the binary values corresponding to these positions to generate two new individuals. The mutation operation randomly selects the mutation position on the randomly selected individual according to the mutation probability, takes the binary value of the bit, and generates a new individual. An initial population is first created where the number of individuals is \(M_{GA}\). Values are assigned to the crossover probability \(P_{cr}\) and the mutation probability \(P_{mn}\). The optimal solution in each generation is denoted by \(OPT\). In addition, let \(gen\) be the maximum number of iterations. The parameters \(V_{m}\) are set to zero at the beginning of the algorithm.