## 1 Introduction  
Traditional urban last-mile delivery is conducted by couriers utilizing vehicles within the urban road network. However, this network is susceptible to various unpredictable factors, including natural disasters, traffic accidents, public health events, and large-scale gatherings. Such factors can lead to issues such as localized road congestion, closures, and even regional paralysis. Consequently, these disruptions are likely to result in delays or interruptions in last-mile delivery, thereby incurring significant losses for both delivery companies and end customers. In 1984, [PERSON] and [PERSON] [1] introduced the concept of emergency logistics, integrating the challenge of emergency supply delivery into the logistics management system. In light of the increasing frequency of natural disasters and emergencies in recent years, research pertaining to emergency logistics has seen a significant rise. Consequently, the facility location route optimization problem (LRP) has emerged as a prominent area of research interest. Scholars both domestically and internationally have developed planning models tailored to the unique characteristics of emergency logistics, with the objective of minimizing transportation costs and time, while also taking into account factors such as equity and uncertainty. [PERSON] et al. [2] introduced a multi-objective dynamic planning model for the allocation of emergency supplies, aiming to maximize fairness while minimizing both time and costs. Similarly, [PERSON] et al. [3] proposed an integer linear programming model focused on minimizing costs and maximizing satisfaction, which is informed by the dynamic demand characteristics inherent in emergency logistics. [PERSON] et al. [4] identified various risk factors, thoroughly evaluated rescue efficiency and cost, and developed a two-level programming model. [PERSON] et al. [5] examined factors such as varying time periods following an earthquake, different types of fuzzy demands, and limitations in facility capacity, subsequently constructing an emergency facility location planning model for the initial phase of rescue operations. Research on emergency logistics within the domestic context began during the SARS outbreak. [PERSON] [6] formulated an emergency material distribution model predicated on forecasting demand in emergency logistics. [PERSON] et al. [7; 8] addressed the uncertain failure characteristics of emergency rescue facilities and proposed a multi-objective optimization model aimed at maximizing the expected coverage of demand points while minimizing distribution time. [PERSON] et al. [9] took into account the urgency of emergency material demands and established a multi-objective optimization model focused on minimizing both time and costs while maximizing the demand urgency index. [PERSON] [10] integrated road interruption scenarios into the emergency logistics location-routing optimization model, creating an optimization model that minimizes time, cost, and system loss, and proposed a location distribution optimization scheme. To address this type of location-routing problem (LRP), intelligent optimization algorithms are frequently employed. [PERSON] et al. [11] developed a shuffled frog-leaping algorithm to tackle the robust mixed-integer linear programming model. [PERSON] et al. [12] introduced an adaptive artificial fish swarm algorithm, noted for its strong local optimization capabilities, to resolve the path optimization issue. [PERSON] et al. [13] utilized an evolutionary algorithm to address the emergency logistics facility location problem. The aforementioned research establishes a robust theoretical framework for emergency logistics transportation. Nevertheless, there exists a notable gap in the literature regarding multi-modal collaborative distribution methods in scenarios where vehicles are unable to execute deliveries due to significant road blockages, such as road interruptions.