## 7 Conclusions  
In order to solve the difficulty of balancing different costs and transport times of multimodal transportation and adapt to the needs of green logistics, this paper proposes a green vehicle comprehensive multimodal transportation model, which considers transportation, transit, quality damage, fuel consumption, carbon emission, and time penalty costs with the introduction of the road congestion index and a hybrid embedded time window, and can well-describe the scenario of green multimodal transport. Then, a new improved sand cat optimization algorithm HSCSO is proposed to solve the model. The following conclusions can be drawn about the algorithm: First, to address the drawbacks of the completely randomly generated initial sand cat population, the Logistic-Tent chaotic map is used to optimize the initial positions of the sand cats, thereby broadening the initial search space. Second, to further enhance the convergence ability of the algorithm, so as to balance the convergence speed and convergence accuracy of the algorithm, the momentum-bellicose strategy and elite crossover pool are introduced to enhance the algorithm's early search ability and mid-to-late convergence ability. Third, for the problem that the SCSO algorithm falls into local extreme values, the adaptive lens opposition-based learning strategy is introduced, so that the algorithm can jump out of the local extreme value multiple times. Next, 10 benchmark functions were tested in 30 dimensions and 100 dimensions, respectively, proving that the HSCSO algorithm has a good optimization effect and convergence accuracy. Finally, the effectiveness of the proposed model and algorithm in planning the path with the lowest cost is verified by practical multimodal vehicle transportation. In  
Figure 8: Path planning result of MVO, SCSO, and HSCSO.  
addition, because of its efficient search performance, the algorithm can be applied to system optimization in some engineering fields, such as aircraft trajectory optimization, urban traffic signal control, and power system scheduling.  
Conceptualization, Z.S. ([PERSON]) and Q.Y.; methodology, Z.S. ([PERSON]); software, Z.S. ([PERSON]); validation, Q.Y., J.L., and X.Z.; formal analysis, Q.Y. and J.L.; investigation, X.Z.; resources, Z.S. ([PERSON]); data curation, X.Z.; writing--original draft preparation, Z.S. ([PERSON]) and Q.Y.; writing--review and editing, J.L. and Z.S. ([PERSON]); visualization, Q.Y.; supervision, Z.S. ([PERSON]) and Z.S. ([PERSON]); project administration, Z.S. ([PERSON]); funding acquisition, Z.S. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
This work was funded by the National Natural Science Foundation of China under Grants (No. 61972208, No. 62272239, No. 62302237, and No. 62303214).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
Author [PERSON] was employed by the company Anhui Yougu Express Intelligent Technology Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.