## 2 Optimization Method
### Non-Dominated Sorting Genetic Algorithm  
Non-dominated sorting genetic algorithms (NSGA), which were proposed by [PERSON] and [PERSON] [10] in 1995, are genetic algorithms based on the concept of a Pareto optimum and are an improvement on basic genetic algorithms and are performed on the basis of the selection and regeneration method; each individual is classified according to their dominant and non-dominant relations and then the selection operation is conducted, which thus leads to very satisfactory results when conducting multi-objective optimization. With the development of NSGAs, [PERSON] et al. proposed a fast non-dominated sorting genetic algorithm with an elite strategy (NSGA-II) [11; 12] in 2000, which can preserve the solution's diversity. However, it has the disadvantages of slow convergence and falling into a local optimum [13]. With the application of the NSGA-II algorithm to a wider range, these problems have gradually emerged. Many researchers have been devoted to improving the NSGA-II algorithm by introducing advanced strategies, such as the random walk strategy for local searching, the Levy flight strategy for global searching [14] or by combining it with other advanced algorithms [15]. Subsequently, the non-dominated sorting genetic algorithm III (NSGA-III) [16] was developed for cases when there are more than four  
Figure 2: Data interaction diagram. objectives to be optimized and where it is difficult to select the Pareto solutions. The basic process is similar to that of the NSGA-II algorithm, but the method of selecting individuals incorporates a reference-point-based approach, which can effectively reduce the computational costs and maintain a good diversity of the population. It also uses a niching algorithm rather than the crowding distance method used in the NSGA-II algorithm to make the optimal solution be more evenly distributed in space. Therefore, it shows a better diversity and convergence than the NSGA-II algorithm. For actual engineering problems, there are usually two-three objectives that need to be optimized. Thus, the NSGA-II algorithm is the most popular multi-objective optimization algorithm developed so far, and it has a wide range of applications [17; 18; 19; 20]. The core of the NSGA, NSGA-II and NSGA-III algorithms is the non-dominated sorting method. For minimization problems in multi-objective optimization, the objective vector consists of n subobjectives, i.e., \(\vec{f}(\mathbf{X})=(f_{1}(\mathbf{X}),\ f_{2}(\mathbf{X}),\ \cdots,\ f_{n}(\mathbf{X}))\). For any variables \(\mathbf{X}_{p}\) and \(\mathbf{X}_{q}\),  
1. \(\mathbf{X}_{p}\) dominates \(\mathbf{X}_{q}\) if and only if for \(\forall i\in\{1,2,\cdots,n\}\), \(f_{i}(\mathbf{X}_{p})<f_{i}(\mathbf{X}_{q})\);
2. \(\mathbf{X}_{p}\) weakly dominates \(\mathbf{X}_{q}\) if and only if for \(\forall i\in\{1,2,\cdots,n\}\), \(f_{i}(\mathbf{X}_{p})\leq f_{i}(\mathbf{X}_{q})\) and there exists \(j\in\{1,2,\cdots,n\}\) such that \(f_{i}(\mathbf{X}_{p})<f_{i}(\mathbf{X}_{p})\);
3. \(\mathbf{X}_{p}\) and \(\mathbf{X}_{q}\) do not dominate each other if and only if for \(\exists i\in\{1,2,\cdots,n\}\), \(f_{i}(\mathbf{X}_{p})<f_{i}(\mathbf{X}_{q})\) and also \(\exists j\in\{1,2,\cdots,n\}\) such that \(f_{i}(\mathbf{X}_{p})>f_{i}(\mathbf{X}_{q})\). If there is no solution that dominates \(\mathbf{X}_{p}\), then \(\mathbf{X}_{p}\) is known as the Pareto optimal solution. The set of all the Pareto optimal solutions is the Pareto optimal solution set. The mapping of the Pareto optimal solution set in the objective space is called the Pareto front. Due to the advantages of NSGAs in multi-objective optimization problems, there are many examples of their application in opto-mechanical structure optimization problems, especially in the parametric optimization area. [PERSON] [21] et al. applied a genetic algorithm to the main support structure of a space camera in order to achieve a lightweight design.