## 5 Reliability Optimization Design Method Oriented to the Stability of Configuration Transformation
### Reliability Optimization Design Based on Improved Genetic Algorithm  
With the development of optimization theory and computer technology, many new optimization algorithms have been produced and widely used. The different results of reliability optimization are often due to the different optimization algorithms. In the paper, an improved genetic algorithm combining genetic algorithm with nonlinear programming algorithm (fmincon function) is adopted. Compared with other optimization algorithms, the improved genetic algorithm has obvious advantages in many aspects. Compared with the ant colony algorithm (ACO), the improved genetic algorithm emphasizes more effective global optimization ability and adaptability in solution space search. Compared with particle swarm optimization (PSO), the improved genetic algorithm pays more attention to the local optimization ability of genetic operation while maintaining population diversity. Compared with the Markov Chain Monte Carlo method (MCMC), it avoids the long-term dependence of Markov Chain through population evolution mechanism and is more suitable for efficient large-scale optimization problem solving. Genetic algorithm simulates the process of biological evolution in nature. First, an initial population is generated, in which each individual represents a possible solution. Then, the population is gradually optimized through operations such as selection, crossover and mutation to achieve the final stop condition. Due to the limitation of population number and iteration times, genetic algorithm has strong global search ability but weak local search ability. In addition, the algorithm also has some defects, such as \"premature\", which leads it to attain the sub-optimal solution of the problem sometimes but not the optimal solution. The nonlinear programming algorithm is also a mathematical optimization method, which aims to find the best solution to complex problems by solving the maximum or minimum value of the objective function. Nonlinear programming algorithm relies on the gradient information of objective function to guide the adjustment of decision variables in order to achieve the best solution. Nonlinear programming algorithm has strong local search ability but weak global search ability. Therefore, the two algorithms can be combined to form an improved genetic algorithm. The tuning process of the improved genetic algorithm is shown in Figure 10.  
The tuning process of the improved genetic algorithm is interpreted in detail as follows:  
(1) Population initialization. The paper adopts the real number coding method, and each chromosome is a real number vector. (2) Individual fitness. The fitness function is the standard to evaluate the quality of individuals in a population. It is generally obtained by transforming the objective function. In the paper, the objective function of the optimization model is taken as the fitness function. (3) Selection. Selection is based on the sorting results of individuals according to fitness values to eliminate poor individuals and retain excellent individuals to pass on to the next generation. The paper uses the roulette wheel selection, the probability of individual selection \(p_{i}\) is as follows:  
\[p_{i}=\frac{f_{i}}{\sum\limits_{j=1}^{N}f_{j}} \tag{46}\]  
\(f_{i}\) is the individual fitness value; \(N\) is the total number of individuals in the population. (4) Crossover. Crossover is to simulate the sexual reproduction process of natural organisms. It exchanges some genes between two jointed chromosomes according to the crossover probability to form two new individuals. Since individuals are encoded by real numbers, the real number crossover method is used in the paper to simulate the uniform crossover of binary representation. The crossover operation method of the \(k\)th chromosome \(a_{k}\) and the \(l\)th chromosome \(a_{l}\) at position \(j\) is as follows:  
\[\left\{ \begin{array}{l}a_{kj}=a_{kj}(1-b)+a_{lj}b\\ a_{lj}=a_{lj}(1-b)+a_{kj}b\end{array} \right. \tag{47}\]  
\(b\) is a random number in the interval [0,1].