## 5 Conclusions  
In the context of the increasing informatization and digitization of transportation infrastructure, there is a growing demand for the use of digital, informational, and intelligent software in transportation engineering projects. The construction of transportation infrastructure involves a multidisciplinary and interdisciplinary process, which implies that the digital software used in this process must possess the capability of integrating information from various domains. This paper proposes a method for calculating the ontology-based semantic similarity of transportation infrastructure concepts, which enables the computation of semantic correlations between different concepts within the transportation infrastructure domain. It can facilitate the alignment of information from diverse data sources during the process of information integration, enabling the integrated management and utilization of data. As a typical form of transportation infrastructure, bridges were chosen as the subject of our experiments. We conducted similarity calculation experiments using concepts related to bridges. The outcomes of these experiments demonstrate that results derived from the SHO-BP algorithm yield the smallest maximal, average, and standard deviation among the various algorithms assessed. Furthermore, the correlation coefficients between these results and evaluation values surpass those of other algorithms, thus affirming the superiority of the SHO-BP algorithm.  
However, the experiments also show that there is a significant relative error when comparing the similarity of two concepts with low ontology similarity. This phenomenon might be due to the fact that the majority of concepts in the bridge ontology exhibit relatively high similarity, and concepts with low similarity are underrepresented in the dataset. The aforementioned issue could potentially impact the future integration of information in transportation infrastructure engineering projects related to BIM systems. Therefore, further research is still required to investigate the ontology structure and the computation methods for semantic similarity of transportation infrastructure. Moreover, the calculation model constructed in this study demonstrates adaptability to complex ontology structures, enabling comprehensive utilization of information within ontology models in the field of transportation infrastructure. This implies the potential applicability of this approach to other domains characterized by intricate ontology structures, such as transportation, urban planning, and hydraulic engineering, among others. These domains' ontology models share similarities with the structure of transportation infrastructure and exhibit certain levels of relevance to it. Future research can verify the reliability of this method in other domains, thereby expanding the applicability of this computational approach.  
Figure 11: Convergence curve under test function \(f_{10}(x)\).  
**Author Contributions:** Conceptualization, T.B. and J.Y.; methodology, T.B., Z.Z. and H.Z.; software, T.B. and Z.Z.; validation, T.B., H.Z. and J.Y.; formal analysis, T.B. and J.Y.; investigation, T.B. and H.Z.; resources, T.B., H.Z. and Z.Z.; data curation, T.B. and H.Z.; writing--original draft preparation, T.B. and J.Y.; writing--review and editing, T.B., H.Z. and J.Y.; visualization, T.B. and Z.Z.; supervision, K.C. and J.Y.; project administration, Q.A.; funding acquisition, Q.A. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Key Research and Development Project of China (2021 YFB2600302).  
Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest. The sponsors had no role in the design, execution, interpretation, or writing of the study.