## 1 Introduction  
With the rapid development of modern logistics, where clients increasingly demand time-sensitive and reliable transportation services, the logistics industry faces critical challenges in reducing operational costs, enhancing transportation efficiency, and mitigating carbon emissions [1]. Traditional unimodal transportation systems have become inadequate to meet multifaceted market requirements, while uncertainties in transit time, freight pricing, and transportation demand increasingly compromise service reliability [2, 3, 4]. Multimodal transportation emerges as an efficient, flexible, and environmentally sustainable collaborative solution that systematically enhances operational efficiency, strengthensservice reliability, and significantly reduces carbon emissions through the integrated optimization of multiple transport modes [5]. Addressing uncertainty-induced impacts and formulating adaptive multimodal solutions under diverse scenarios thus represents a pivotal approach to advancing organizational competence and competitive advantage in multimodal operations [6].  
Containerized multimodal transport constitutes a complex dynamic system facing numerous challenges characterized by uncertainty, where fluctuations in transportation costs present a persistent difficulty in cargo transactions, primarily stemming from market dynamics--such as fluctuating supply and demand during peak logistics seasons leading to capacity constraints and route congestion, coupled with volatile fuel prices driven by international crude oil markets and geopolitical factors directly impacting unit rates--and disruptive emergencies, including natural disasters or policy adjustments necessitating additional cross-regional transport segments and resulting in multifaceted cost increases that amplify price uncertainty [7]. Beyond cost uncertainty, transport time uncertainty is equally critical, as operations are frequently disrupted by emergencies and unforeseen events like extreme weather, seasonal bottlenecks, equipment failures, and urgent order insertions, impeding adherence to planned schedules [8]. While existing research predominantly addresses either transport time uncertainty or demand uncertainty in isolation, a notable gap persists concerning multimodal transport path optimization under the combined uncertainty of both transportation costs and time, thereby establishing the theoretical significance and practical implications of this paper's focus.  
This paper develops a methodological framework incorporating carbon taxation, carbon trading, mandatory emission limits, and carbon offset mechanisms to regulate emissions while simultaneously addressing uncertainties in cargo arrival times and unit freight pricing. By analyzing the time-value attributes of heterogeneous cargo types. A cost-minimization optimization model for low-carbon multimodal routing is formulated, solved through an improved whale optimization algorithm (IWOA). Parametric sensitivity analysis is conducted to examine cargo-specific routing patterns across scenarios. Government transportation departments or multimodal transport operators may be interested in this study.  
The remainder of this study is organized as follows: Section 2 reviews literature on multimodal transportation, low-carbon logistics, and optimization algorithms. Section 3 formalizes the problem statement and mathematical model. Section 4 details the enhanced WOA and its implementation. Section 5 presents case studies comparing algorithm performance. Finally, Section 6 concludes with theoretical contributions and policy implications while outlining future research directions.