# Triangular Position Multi-Bolt Layout Structure Optimization
## 3 Results  
### Algorithm Solution  
Based on the MATLAB(2020) software for the multi-bolt connection structure of the spacing a and diameter d of the bolt to find the best calculation, from Figure 6, it can be seen that the objective function and constraints are fully applicable to the gray wolf algorithm program, the iterative effect is good, and finally stable convergence to a fixed value is observed. Its convergence to a stable fitness value is not used as a criterion for judging bolts and nickel steel plates. As can be seen from Figure 7, through different iterations, the particles gradually converge to the best particle, whose best particle is the result sought. The algorithm results in a pitch a = 108.5629 mm and a diameter d = 9.0233 mm. The results optimized by firefly algorithm for the spacing of double-row bolts and triple-row bolts in previous studies [11] are not much different from the optimized bolt spacing in this paper, and are also consistent with the results optimized by [PERSON] et al. [30] for the layout optimization of bolt groups for flameproof boxes used in mines.  
Figure 6: Results of algorithm operation.  
In this paper, the objective function as well as the boundary conditions are applied to the fruit fly optimization algorithm, particle swarm optimization algorithm, gray wolf optimization algorithm, multiverse optimization algorithm and wind driven optimization algorithm, the results of which are shown in Figure 8, with approximately the same algorithmic optimization curves. There is only a slight difference at the initial iteration, which is explained by the fact that the different algorithms contain different principles. As shown in Table 1, the final fitness values were all stable at \(-42.8195\), with the gray wolf algorithm having the highest number of iterations, but none of them exceeded \(500\) iterations.  
Figure 8: Optimization effects of different algorithms.  
Figure 7: Different iteration times of the algorithm.  
Figure 9 shows the optimal result values calculated by various algorithms, and the results calculated by the particle swarm optimization algorithm, multiverse algorithm and gray wolf algorithm are roughly the same. The bolt spacing and bolt diameter calculated by the fruit fly optimization algorithm are both larger, while the bolt spacing and bolt diameter calculated by the wind driven optimization algorithm are larger and smaller. Because the core functions of various algorithms are different, there is a certain deviation, which is also a limitation of artificial intelligence. In this simulation, the maximum deviation of the bolt diameter is 0.59% and maximum deviation rate of bolt spacing is 0.12%, both of which have small deviations and can be ignored. The results show that the optimal solutions of the five algorithms selected in this paper are roughly the same, and the deviation rate is low, which will not cause certain impact on the subsequent simulation analysis. Therefore, this paper can choose the optimal solution calculated by the gray wolf optimization algorithm as the focus of the subsequent analysis and discussion.