## 3 Optimization Algorithm
### Verification of Improved Optimization Algorithms  
In order to verify the effect of the advanced algorithm, four standard functions are used to test the global optimization capacity of the GA algorithm and MAGA algorithm. \(f_{1}(x)\) is the Rosenbrock function, as shown in Equation (S1). It is a single-peak function, but it is pathological. \(f_{2}(x),f_{3}(x)\), and \(f_{4}(x)\) are the Griewank function, the Rastrigrin function, and the Shaffer function, respectively, as shown in Equation (S2), Equation (S3), and Equation (S4). They are multi-peak and typical nonlinear multi-modal functions with a wide search space. All functions have many local minimum points but only one global minimum point.  
Figure 7: Flow chart of the Mind-evolved Advanced Genetic Algorithm (MAGA).  
The setting parameters of different algorithms are shown in Table 6. These setting parameters are also applied in the optimization of neural network. The number of individuals in the population is set to 40. All the optimization processes are done on a 64-bit computer with a 3.80 GHz, AMD Ryzen 9 3900X 12-Core Processor CPU and 16 GB RAM.  
Table S1 lists the optimal solutions of different optimization algorithms for different test functions under dimensions D = 2 and D = 20, respectively. Each value is the best solution obtained in the 100 independent runs of each algorithm. The theoretical minimum value of each test function is zero, which represents the global optimal solution. It can be seen from the comparison of the results that the optimal solution of the MAGA algorithm is obviously better than GA algorithm and closer to the theoretical minimum value in the definition domain. When D = 2, for \(f_{1}(x),f_{2}(x),f_{3}(x)\), and \(f_{4}(x)\), the values of the MAGA algorithm are very close to the minimum value of zero, where the value of \(f_{1}(x)\) is slightly larger. In contrast, the values of GA algorithm are greater than those of the MAGA algorithm, and it is prematurely trapped in the local solution. As shown in Figures S1-S4, the position of the best individual can be directly observed, where the yellow dot with red circle \(\bigcirc\) marks the global minimum value, and the red dot with green circle \(\bigcirc\) marks the optimal solution of the algorithm. It can be seen that the best individuals of the GA algorithm are all trapped in the local position, and its distance to the global minimum point is much larger than that of the MAGA algorithm. This shows that MAGA has a stronger ability to jump out of the local area and find the global optimal solution. When D = 20, the optimal values of GA and MAGA algorithms on all test functions are larger than those at D = 2. However, comparing the two algorithms at D = 20, the optimal solutions of the MAGA algorithm are still much smaller than the GA algorithm, where \(f_{2}(x)\) has the best effect. Figures S5 and S6 show the iterative history of the two algorithms in different test functions, where MAGA convergence performance is better than the GA algorithm. It can be seen that the MAGA algorithm is suitable for functions of different dimensions with single or multi peaks, and its optimal performance is superior to the GA algorithm. Therefore, the improved optimization algorithm MAGA is reliable and can be applied to the optimization of the prediction model with the same setting parameters in Section 4. By optimizing the initial thresholds and weights of the neural network, the best initial values can be obtained. The fitness value is the test error of the neural network to obtain the smallest prediction error and improve the model accuracy.