# Selection Criterion of Reanalysis Methods for Plane Truss Optimization
## 6 Conclusions  
This paper presents a selection criterion for reanalysis methods that can improve the efficiency of structural analysis in the optimization of plane trusses. The proposed criterion selects automatically the most suitable reanalysis method according to the structural modification type. The effects of different structural modifications, such as size, shape, and topology, are first analyzed qualitatively to establish the correspondence between different modification types and candidate reanalysis methods. Then, the number of floating point operations (flops) and the storage space of input/output and intermediate variables (MS values) are statistically calculated for all the candidate methods. The flop ratio (_Fr_) and Ms ratio (_Mr_) are defined to investigate the most suitable reanalysis method under different structural modifications in a quantitative manner.  
Based on the analysis, this study establishes a selection criterion for reanalysis methods. Specifically, when a structure undergoes size modifications and topology modifications with unchanged degrees of freedom (DOFs), the Epsilon and PCG methods are recommended for computation, respectively. The UMFT method is recommended for shape modification when the row of the first non-zero element that appears in the incremental stiffness matrix is greater than 30% of the structural DOFs. The Guyan + PCG method and the MPCG method are recommended for topology modifications with increased DOFs and decreased DOFs, respectively. It should be noted that the overall error \(\varepsilon\) of the computation results should not exceed 0.01. Otherwise, an accurate solution method should be applied.  
Finally, two types of numerical examples are conducted to confirm the effectiveness of the proposed criterion, in which the selection criterion is combined with the Structural Topology and Shape Annealing (STSA) algorithm.  
In future work, the extended study will focus on the exploration of more comprehensive indicators for assessing computational efficiency beyond flops and MS values. The objective is to provide a more accurate reflection of algorithmic performance. Furthermore, the development of space structure generation algorithms will be undertaken to validate the effectiveness of the proposed criterion in the computation of three-dimensional structures.  
Conceptualization, T.Z. and X.Z.; methodology, T.Z. and W.X.; software, T.Z.; validation, T.Z., X.Z. and W.X.; formal analysis, T.Z.; investigation, T.Z.; resources, X.Z.; data curation, T.Z.; writing--original draft preparation, T.Z.; writing--review and editing, W.X. and X.Z.; visualization, T.Z. and W.X.; supervision, W.X. and X.Z.; project administration, X.Z.; funding acquisition, X.Z. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Indicator** & **Case 1** & **Case 2** \\ \hline Total optimization time & 291.032 s & 1394.512 s \\ Cholesky time & 116.104 s & 733.956 s \\ Selection criterion time & 100.195 s & 510.468 s \\ Time proportion of Cholesky & 39.89\% & 52.63\% \\ Efficiency improvement ratio & 13.70\% & 30.45\% \\ \hline \hline \end{tabular}
\end{table}
Table 9: Computational efficiency information based on STSA.  
**Funding:** This research was funded by Shanghai Qi Zhi Institute, grant number SYXF0120020110. The corresponding author was supported by the Fundamental Research Funds for the Central Universities, grant number 22120230230.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding author upon request.  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.