## 6 Conclusions  
This study presents a multi-objective optimization model for low-carbon multimodal transport scheduling, considering transportation cost, transit time, and carbon emissions under carbon tax constraints. The model incorporates flexible time window control, enhancing its adaptability to real-world scheduling scenarios. To solve this complex optimization problem efficiently, we propose the IGWOHHO algorithm, which combines the global exploration capability of the GWO algorithm with the local exploitation strength of the HHO algorithm. Additionally, the algorithm uses Tent chaotic mapping to improve initial population diversity, adaptive dynamic weight switching to balance exploration and exploitation, and an elite retention-perturbation strategy to enhance solution quality and avoid local optima.  
Extensive benchmark tests on six classical test functions show that IGWOHHO outperforms GWO, HHO, SSA, WOA, and DBO in terms of convergence accuracy, robustness, and solution stability. In a case study based on a 35-node multimodal transport network, the algorithm achieves the best objective value, reducing total transport cost and carbon emissions by approximately 11.8% and 18.7%, respectively. Sensitivity analysis of weight parameters reveals that decision-makers with different strategic preferences can derive optimal transport solutions, supporting diverse policy or enterprise objectives. Furthermore, carbon tax simulations show that a moderate increase in carbon pricing can encourage shifts toward rail and water transport, effectively reducing emissions while keeping costs within a manageable range.  
Future research could explore dynamic elements such as uncertain demand, traffic congestion, equipment failures, and supply chain disruptions to improve model adaptability and robustness. Incorporating such elements would enable the scheduling framework to better respond to complex and time-varying logistics environments. Additionally, alternative multi-objective optimization methods, such as Pareto front solutions, fuzzy preference models, or goal programming, could better address flexible decision-making preferences in scenarios with multiple stakeholders. Future studies may also focus on inland port scheduling with operational constraints, such as berth availability, yard capacity, and container handling time. With the increasing use of clean energy vehicles, integrating electric or hydrogen-powered transport into multimodal routing could further reduce emissions. Furthermore, applying the IGWOHHO algorithm in real-world systems, supported by artificial intelligence, deep learning, and large-scale data platforms, could enable intelligent and adaptive logistics scheduling under dynamic conditions.  
Conceptualization, S.L. and M.J.; methodology, S.L.; software, S.L.; validation, S.L. and F.W.; formal analysis, S.L.; investigation, S.L.; resources, Y.Z.; data curation, S.L.; writing--original draft preparation, S.L.; writing--review and editing, M.J.; visualization, G.W.; supervision, M.J. and Z.P.; project administration, M.J.; funding acquisition, M.J. and Z.P. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Natural Science Foundation of China (Grant No. 72271222), the National Natural Science Foundation of China (Grant No. 51605442), and Zhejiang Provincial Natural Science Foundation of China (Grant No. LGN18G010002).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available, because they relate to the data privacy of the project.  
**Conflicts of Interest:** The authors declare no conflicts of interest.