# Optimization of Multimodal Transport Paths Considering a Low-Carbon Economy Under Uncertain Demand
## 1 Introduction  
As one of the main problems in supply chain management, path optimization has always been a hot research topic [1]. With the rapid development of the modern economy, the demand for transportation is increasing, and carbon emissions are also increasing. In the second United Nations Global Conference on Sustainable Transportation, the United Nations Secretary-General [PERSON] pointed out that \"Transportation carbon emissions account for more than a quarter of global greenhouse gas emissions\" [2]. As an advanced modern logistics technology, multimodal transport can reduce transportation costs and carbon emissions by utilizing the advantages of different modes of transportation. At the same time, because multimodal transportation consists of multiple modes of transportation, compared with a single mode of transportation, it also needs to consider the transfer between different modes of transportation and the influence of railroad andwaterway transportation schedules. This makes it more difficult to choose the transportation path for multimodal transportation than for a single mode of transportation, which has attracted extensive attention from scholars in recent years.  
With the in-depth implementation of the Paris Agreement, low-carbon policies such as mandatory carbon emissions, carbon tax, carbon trading and carbon compensation have emerged and become the main measures to control carbon dioxide emissions. In the context of green low-carbon, British scholars [PERSON] [3] conducted the earliest research on different types of regional carbon emission assessments and predictions; [PERSON] [4] conducted research on the carbon offset mechanism and its governance. And in recent years, more and more scholars have begun to consider the carbon emission problem in intermodal transportation. Low-carbon policies, such as mandatory emissions, carbon tax, carbon trading and carbon offsetting, control carbon emissions or emission costs to achieve the purpose of emission reduction and influence economic decision-making. Different transportation mode selection results will be obtained under different carbon emission control policies; thus, it is necessary to further study the multimodal transportation route selection problem under different policies on the basis of analyzing carbon emissions. In addition to the impact of uncertain demand on multimodal transportation path selection, it will also have an impact on carbon emissions in the transportation process, and different modes of transportation have different unit carbon emissions. Therefore, it is necessary to consider the uncertainty in demand when calculating carbon emissions, based on which transportation modes and routes can be rationally selected.  
In summary, this paper starts from the uncertainty in transportation demand, based on the comprehensive consideration of a soft time window for the limitation of transportation mode shifts, establishes a robust optimization model of multimodal transportation paths with the objective of minimizing the total cost of transportation through the scenario analysis method in robust optimization, analyzes the changes in the costs and the carbon emissions under different carbon emission policies and improves the solution of the ACO algorithm, which adopts the simulated annealing mechanism. The developed algorithm is tested and validated by a solomon arithmetic example, and the traditional ant colony algorithm is compared with the hybrid ant colony algorithm. This paper is organized as follows: Section 2 presents a detailed literature review on multimodal transportation, low-carbon path optimization and heuristic algorithms. Section 3 presents the problem description and optimization model. In Section 4, the improved ACO algorithm and the solution procedure are described. Section 5 provides a case study of the algorithm and compares the improved algorithm with the unimproved algorithm. Finally, Section 6 draws conclusions and suggests possible future improvements.