# Artificial Intelligence Algorithm-Based Arrangement Optimization of Structural Isolation Bearings
## 2 Calculation Parameters and Objective Function
### Optimization Objective Function  
In consideration that the cost of the isolation scheme is to a great extent determined by the cost of isolation bearings, which are the primary components in an isolation scheme based on reasonable performance optimization, the more economical isolation design scheme will undoubtedly possess stronger market competitiveness in the bidding-dominated construction market. Therefore, the cost of isolation bearings ought to be taken into account during the process of optimization calculation. The seismic decrease coefficient can still serve the purpose of intuitively testing the damping effect of isolation bearings in a structure, even though isolation design concepts based on an overall analysis approach have been updated by the Chinese design code [38]. Meanwhile, lateral displacement of the base-isolated structure should be more strictly regulated than it is for the non-isolation structure due to the comparatively low lateral resistance of the base-isolated structure. Besides, the optimization arrangement of isolation bearing would be better carried out in conjunction with the market price of bearings, as mentioned above. During the optimization analysis process, because of the significant differences of magnitude between seismic decrease coefficient, story drift ratio, and total cost of bearings, the scale of the latter two factors is lowered by the initial value of the factor to highlight their significance in the optimization objective function. Additionally, the weight coefficient is set respectively to take into account the relative importance of various factors, and the optimization objective function is established as indicated in Formula (1):  
\[f=\min\biggl{(}\alpha\beta+\lambda\frac{\theta_{\max}}{\theta_{0,\max}}+\gamma \frac{p}{p_{0}}\biggr{)} \tag{1}\]  
\[p_{0}=n\times p_{1,\max} \tag{2}\]  
\[\beta=\max(\frac{V_{i}}{V_{0,i}}) \tag{3}\]  
where: \(\alpha\), \(\lambda\), \(\gamma\) are respectively the weight coefficients of seismic decrease coefficient, maximum story drift ratio, and total cost of isolation bearings in the analysis of optimization arrangement. Here, the maximum story drift ratio is equal to the maximum ratio between maximum horizontal displacement and floor height in all the floors except the isolation layer. \(\beta\) is the seismic decrease coefficient for the base-isolated structure, equal to the maximum ratio of inter-story shear force between isolated and non-isolated structures in all floors except the isolation layer. \(V_{i}\), \(V_{0,i}\) are the inter-story shear force of the ith floor for the isolated and non-isolated structure, respectively. Though there is no requirement for this index in Eurocode 8 [39] and AASHTO (American Association of State Highway and Transportation Officials) standards [40], considering that the variation of inter shear force represents the energy dissipation of the isolated structure to some extent, this indicator could still be utilized for optimization when applying Eurocode 8 or AASHTO standards, and could also be replaced with other cared indexes or ignored by taking the weight coefficient as 0. \(\theta_{0,\max}\), \(p_{0}\) are respectively the maximum story drift ratio of the non-isolation structure and the total cost of isolation bearings in the initial scheme of the isolation bearing layout; \(\theta_{\max}\), \(p\) are respectively the maximum story drift ratio of the base-isolated structure and the total cost of isolation bearings during the optimization process. \(p_{1,\max}\) is the price of a single isolation bearing with the largest size used in the initial isolation scheme, and n is the total number of isolation bearings. In the actual design of isolation structures, projects with different construction purposes often have different requirements for factors such as seismic decrease coefficient, structural performance and cost of isolation scheme.