Two-stage sea-railway combined transportation network toughness optimization method under uncertainty cascade failure

Abstract

The invention relates to a two-stage sea-railway combined transportation network toughness optimization method under uncertain cascade failure, which comprises the following steps of: S1, acquiring a failure hub node, and generating a container operation load redistribution scheme based on a sea-railway combined transportation network dynamic load redistribution stochastic programming model under the uncertain cascade failure, the sea-railway combined transportation network dynamic load redistribution stochastic programming model under the uncertainty cascade failure aims at minimizing the total loss expectation of all alternative nodes and the container freight volume which cannot be redistributed, and the original container operation demand of the original failure hub node is distributed to the surrounding uninterrupted alternative nodes; s2, taking the generated container operation load redistribution scheme as the input of the sea-railway combined transportation network transportation organization optimization model under the interruption of the key interval, generating a new train operation demand, reconstructing a path through the sea-railway combined transportation network transportation organization optimization model when the new train operation demand is subjected to the interruption of the key interval, and performing the operation of the sea-railway combined transportation network transportation organization optimization model. And a new feasible restorative transportation scheme is generated. Compared with the prior art, the method has the advantages.

Description

Technical Field

[0001] This invention relates to the field of transportation, and in particular to a two-stage sea-rail intermodal network resilience optimization method under uncertain cascading failure. Background Technology

[0002] Global supply chain networks are facing increasingly complex disruption risks, ranging from regional port disruptions to damage to cross-regional railway infrastructure. These unforeseen events exhibit significant uncertainty in their impact on logistics systems. As a core link in international multimodal transport, the resilience of sea-rail intermodal transport networks in responding to disruptions depends not only on the redundancy design of physical facilities but also on the accurate assessment of failure propagation mechanisms and the dynamic optimization of recovery strategies. However, currently widely used deterministic cascading failure models, which rely solely on whether the load reaches design capacity as the criterion for determining the interruption status of nodes, fail to capture the actual operational scenarios where interruptions may occur even when the load does not reach design capacity, or where short-term operation is possible even when the load exceeds design capacity. This leads to a systematic bias in the assessment of failure uncertainty in cascading failures.

[0003] Existing technologies face a dual constraint in enhancing the resilience of logistics networks: On the one hand, traditional failure assessment methods oversimplify the uncertainty transmission process in real-world scenarios, neglecting the nonlinear correlation between the actual load, design capacity, and failure probability of nodes; on the other hand, optimization research for network outages is often limited to single fault types or single recovery phases, failing to effectively coordinate the differentiated impacts of hub node outages and transportation interval outages, and also failing to achieve temporal synergy between demand reallocation and transportation organization optimization. Specifically, in terms of transportation network resilience optimization scenarios, existing transportation networks exhibit four typical disturbance scenarios: local outage scenarios, cascading failure dynamic propagation scenarios, specific disaster scenarios, and operational disturbance scenarios. Taking local outage scenarios as an example, these refer to scenarios where nodes or links fail independently, such as link capacity reduction caused by natural disasters, port closures due to pandemics, or failures of critical facilities (such as substations). These technologies improve local resilience through resource reallocation, route optimization, or emergency facility location selection. However, these technologies generally assume that disturbance events occur in isolation, failing to consider the dynamic propagation effects of failures.

[0004] In optimizing transportation network resilience, incorporating cascading failure mechanisms provides a more realistic reflection of the dynamic nature of global functional degradation caused by localized outages in actual operations. However, current technologies tend to characterize outage scenarios using deterministic states. While this simplification reduces model complexity, it has significant limitations: it essentially ignores the inherent randomness of outage events in the real world and fails to effectively study the probability of different outage scales, frequencies, and combinations. Ultimately, the designed resilience strategies may only be effective for specific pre-defined scenarios, and their adaptability is often insufficient to support resilience optimization decisions in real-world scenarios due to real-world uncertainties. Although some research attempts to introduce outage probabilities to characterize this uncertainty, these studies choose to directly assign fixed failure probabilities to local networks or use linear assumptions to describe the relationship between load and risk. These methods fail to meet the complex characteristics of the nonlinear increase in failure probability when hub loads approach critical values ​​in actual sea-rail intermodal transport networks. This simplification also further leads to quantitative biases in the synergistic influence of multiple random factors. When dealing with related events such as port congestion triggering railway delays, calculating the joint failure probability of heterogeneous random variables (some following a normal distribution while others exhibit heavy-tailed characteristics) presents significant challenges. This forces analyses to employ strong assumptions such as variable independence or specific distribution forms, weakening the accuracy of interruption probability assessment in cascading propagation. More concerning is the resulting computational efficiency bottleneck: while computationally intensive methods like Monte Carlo simulations can handle such complex probabilistic problems, the massive computational demands of repeatedly generating cascading failure paths in large-scale network scenarios severely restrict the solution efficiency and engineering applicability of optimization models.

[0005] Therefore, there is an urgent need to develop a systematic probabilistic framework that can accurately characterize complex nonlinear failure boundaries, efficiently handle multi-source correlated random variables, and provide analytical or semi-analytical failure probability assessment and key failure point identification capabilities, so as to more scientifically and efficiently support the resilience optimization design of sea-rail intermodal transport networks under uncertain cascading failures. Summary of the Invention

[0006] The purpose of this invention is to provide a two-stage sea-rail intermodal transport network resilience optimization method under uncertain cascading failure.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] A two-stage sea-rail intermodal transport network resilience optimization method under uncertain cascading failures includes:

[0009] Step S1: Obtain the failed hub node, and generate a container operation load redistribution scheme based on the dynamic load redistribution stochastic programming model of the sea-rail intermodal network under uncertain cascading failure. The dynamic load redistribution stochastic programming model of the sea-rail intermodal network under uncertain cascading failure aims to minimize the total expected loss of all alternative nodes and the container freight volume that cannot be redistributed, and allocates the original container operation demand of the original failed hub node to the surrounding uninterrupted alternative nodes.

[0010] Step S2: Use the generated container operation load redistribution scheme as input to the sea-rail intermodal transport network transport organization optimization model under critical section interruption to generate new train operation demand. When the new train operation demand occurs in the critical area, the path is reconstructed through the sea-rail intermodal transport network transport organization optimization model to generate a new feasible recovery transport scheme.

[0011] The objective function of the stochastic programming model for dynamic load redistribution in the sea-rail intermodal transport network under uncertain cascading failure is:

[0012]

[0013] Where: Φ(·) is the cumulative distribution function of the standard normal distribution, Let be the total demand for container operations at the replacement node a after load redistribution within period t. This indicates whether train k cannot be assigned during period t. The value is 1 if it cannot be assigned, and 0 if it can be assigned. Let O be the container freight volume of train k in period t, and let O be the set of interruption nodes. o μ is the set of alternative nodes that can be used to distribute load for interrupt node o. a To replace the rated container handling capacity of node a for one cycle, σ a To replace the standard deviation of the freight handling capacity of node a over one cycle, To replace the standard deviation of the total load of node a during period t, The set of trains with interruption node o as the starting or ending point within period t.

[0014] The constraints of the stochastic programming model for dynamic load redistribution in the sea-rail intermodal transport network under the uncertainty cascade failure condition include:

[0015] Load redistribution status constraints for container sea-rail intermodal freight trains: When only one of the origin and destination of a train is interrupted, the train is either assigned to a feasible alternative node or marked as unassigned. When both the origin and destination are interrupted, the train must be assigned to the alternative nodes of its original origin and destination at the same time, otherwise it will be marked as unassigned at the same time.

[0016] Replacement node failure threshold constraint:

[0017]

[0018] in: The maximum allowable failure probability for replacement node a;

[0019] Alternative node load dynamic update constraints:

[0020]

[0021] in: To replace the initial load of node a in period t, This indicates whether the starting point of train k is assigned to a substitute node a during cycle t. If yes, the value is 1; otherwise, the value is 0. Whether the destination of train k is assigned to a substitute node a in cycle t. If yes, the value is 1; otherwise, the value is 0.

[0022] Spatiotemporal reachability constraint: When a train is assigned from the interruption node to the replacement node, the time it takes to travel from the interruption node to the replacement node by road shall not exceed the duration of one cycle.

[0023] Node capacity constraints:

[0024]

[0025] Dynamic Evolution Constraints of Train Reassignment Demand: Train Sets It consists of all trains that departed from interruption node o in cycle t but were not assigned, and all trains originally scheduled to depart from interruption node o in cycle t.

[0026] The mathematical expression for the load redistribution state constraint of the container sea-rail intermodal freight train is:

[0027]

[0028] Where: N is the set of hub nodes that need to be redistributed after the interruption. In non-interrupted operation, whether train k starts from node m is the determining factor. If yes, the value is 1; otherwise, the value is 0. k,m ∈{0,1} indicates whether train k ends at node m in the non-interrupted state. If yes, the value is 1, otherwise the value is 0.

[0029] The mathematical expression for the spatiotemporal reachability constraint is:

[0030]

[0031] Where: d o,a v represents the road transport distance from the interrupted node o to the replacement node a. roadLet Δt be the average speed of road transport, and Δt be the length of one period.

[0032] The objective function of the sea-rail intermodal transport network transportation organization optimization model under the interruption of the critical section is:

[0033]

[0034] Where: c transport The transportation cost per unit path length. Path in uninterrupted state Whether it passes through the interval r, if yes, the value is 1, otherwise the value is 0, γ r,p This indicates whether path p passes through interval r. If it does, the value is 1; otherwise, the value is 0. r Let r be the length of the interval. This parameter determines whether the sea-rail intermodal freight train k selects route p to operate during cycle t. If yes, the value is 1; otherwise, it is 0. r Let c be the length of the interval r. loss The unit value loss for unshipped containers. To determine whether the sea-rail intermodal freight train k is interrupted during cycle t, P k Let R be the set of feasible routes for train k under interrupted conditions, and let R be the set of links in the container sea-rail intermodal transport network.

[0035] The constraints of the sea-rail intermodal transport network transportation organization optimization model under the condition of interruption in the key section are as follows:

[0036] Train transport status constraint: If the sea-rail intermodal train k does not resume operation through route reconstruction in cycle t, it is marked as interrupted transport;

[0037] Path connectivity constraints:

[0038]

[0039] in: This parameter determines whether the sea-rail intermodal freight train k selects route p to operate during cycle t. If yes, the value is 1; otherwise, the value is 0. This indicates whether the interval r is interrupted during the period t. If it is, the value is 1; otherwise, the value is 0.

[0040] Inter-section capacity limit constraint: The total number of sea-rail intermodal freight trains passing through each link within a cycle cannot exceed the capacity limit of that section;

[0041] Station capacity constraints: The total number of sea-rail intermodal freight trains passing through each node within a cycle cannot exceed the capacity limit of that node.

[0042] The method further includes:

[0043] A resilience evaluation was conducted on the generated feasible recovery transportation schemes, calculating the resilience improvement effect on the container sea-rail intermodal transport network under different critical section disruptions. The resilience evaluation index χ² is:

[0044]

[0045] in: The total cost of the recovery transportation plan after the disruption of critical sections. This represents the total cost of the original transportation plan before the critical section was disrupted.

[0046] A two-stage sea-rail intermodal transport network resilience optimization device under uncertain cascading failure includes a memory, a processor, and a program stored in the memory, wherein the processor executes the program to implement the method described above.

[0047] A storage medium having a program stored thereon, which, when executed, implements the method described above.

[0048] Compared with existing technologies, this invention has the following advantages: Traditional logistics network resilience optimization faces the challenge of deterministic failure determination methods struggling to quantify the nonlinear risk transmission between node load and capacity, and the inability of single-stage models to collaboratively handle the load redistribution of hub interruptions and the time-series dependence of transportation recovery in inter-station interruptions. Based on this, this invention introduces structural reliability theory and constructs a two-stage resilience optimization stochastic programming model for heterogeneous interruption scenarios in container sea-rail intermodal transport networks under uncertain cascading failures: The first stage proposes a dynamic load redistribution model, which quantifies the failure probability of alternative nodes by establishing a "dynamic load-capacity" interference mechanism, controlling cascading risks and minimizing the expected total loss from hub interruptions; the second stage designs a critical interval interruption recovery model based on dynamically updated transportation demand, minimizing the loss increment of the recovery transportation plan through path reconstruction, and constructing resilience indicators to evaluate performance. Empirical analysis of a certain land-sea new corridor shows that the first-stage model reduces losses by more than 57.78% and strictly controls the failure probability of all alternative nodes to within 70%, which is significantly better than the situation of 26.67% complete node failure under the traditional strategy. The second-stage model achieves a resilience level of more than 85.8% in 864 critical section interruption scenarios, of which 76.62% of the scenarios exceed 98%. This application designs an interdisciplinary integration mechanism of structural reliability theory and cascading failure, breaking through the limitations of traditional deterministic failure judgment. At the same time, it constructs a time-series collaborative resilience optimization scheme of "load redistribution-transportation recovery", providing a resilience optimization strategy with both theoretical significance and engineering applicability for multimodal transport networks to cope with complex interruption scenarios. Attached Figure Description

[0049] Figure 1This is a schematic diagram of the container sea-rail intermodal transport network of the present invention;

[0050] Figure 2 This is a histogram showing the distribution of resilience indicators in 864 key intervals in this embodiment of the invention.

[0051] Figure 3 This is a schematic diagram of the main steps of the method of the present invention. Detailed Implementation

[0052] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0053] 1. Hub node interruption

[0054] like Figure 1 As shown, the resilience recovery process in this scenario involves load redistribution from the interrupted hub node to its corresponding replacement nodes. The load in a container rail-sea intermodal network refers to the volume of containers that a hub node needs to handle within an operating cycle. As shown by arrow A, when a railway freight hub fails, it needs to redistribute its load to nearby replacement stations. The redistributed load will be transferred via short-haul road transport. As shown by arrow B, when a seaport hub fails, it needs to redistribute its load to other nearby seaports with rail-sea intermodal capabilities. However, due to the long distances between seaports, load transfer is achieved through rail transport or by changing the port of call for container ships. During this resilience recovery process, when the sum of the original load of the replacement node or seaport and the partial load of the interrupted hub gradually approaches the node's carrying capacity, a nonlinear and uncertain cascading failure risk may occur. The carrying capacity of a node in a container rail-sea intermodal network refers to the maximum volume of container operations that a node can complete within an operating cycle. In this scenario, the present invention optimizes the load redistribution scheme by introducing structural reliability theory to construct a stochastic programming model for dynamic load redistribution of sea-rail freight trains under uncertain cascading failures. This maximizes the restoration of normal operations of affected containers in the interrupted hub and minimizes the total expected loss of the interrupted hub, its surrounding alternative nodes, and the seaport.

[0055] 2. Interruption of critical interval

[0056] The resilience recovery process in this scenario follows load allocation. Load allocation ultimately generates transportation demand, including the origin, destination, and volume of container sea-rail intermodal transport. Based on transportation demand and constraints such as capacity limitations of each section in the intermodal network, a transportation plan for container sea-rail intermodal transport, including the transportation route, can be obtained. However, a critical section interruption will force the transportation plan containing the interrupted section of the transportation route to be unfeasible. As shown by arrow C in the figure, the resilience recovery process in this scenario is to formulate a restorative transportation plan under critical section interruption by refactoring the route based on the load allocation scheme. In this scenario, this invention minimizes the increase in loss between the restorative transportation plan and the original transportation plan by establishing a sea-rail train transportation organization optimization model under critical section interruption. Finally, based on the basic definition of resilience and relying on the objective function of the resilience optimization model, this invention constructs an evaluation index for the resilience enhancement level of the resilience optimization strategy.

[0057] In this application, the network link is a railway section, and the relevant parameter definitions of this invention are shown in Table 1:

[0058] Table 1

[0059]

[0060] In Table 1, the replacement nodes corresponding to different types of interruption nodes o are also different. If o∈N R Then the set of replacement nodes A o It is the set of other freight stations near the interrupt node o that can perform container operations; these stations are not necessarily N. R The station within. If o∈N P Because seaports differ from railway freight stations, there are no other seaports nearby capable of conducting sea-rail intermodal transport operations; therefore, their alternative node set A is... o That is N P Other hub seaports near the interrupted port.

[0061] The structural reliability theory applied in this application is based on the establishment of a stress-strength interference model to quantify the system failure risk. This theory defines system performance as the competitive relationship between load-bearing capacity (strength) and external load (stress), and its performance function can be expressed as:

[0062] J = SL Formula 21

[0063] In the formula: S represents random load capacity; L represents time-varying load.

[0064] This application provides a two-stage resilience optimization method for sea-rail intermodal transport networks under uncertain cascading failures, such as... Figure 3 As shown, it includes:

[0065] Step S1: Obtain the failed hub node, and generate a container operation load redistribution scheme based on the dynamic load redistribution stochastic programming model of the sea-rail intermodal network under uncertain cascading failure. The dynamic load redistribution stochastic programming model of the sea-rail intermodal network under uncertain cascading failure aims to minimize the total expected loss of all alternative nodes and the container freight volume that cannot be redistributed, and allocates the original container operation demand of the original failed hub node to the surrounding uninterrupted alternative nodes.

[0066] Step S2: Use the generated container operation load redistribution scheme as input to the sea-rail intermodal transport network transport organization optimization model under critical section interruption to generate new train operation demand. When the new train operation demand occurs in the critical area, the path is reconstructed through the sea-rail intermodal transport network transport organization optimization model to generate a new feasible recovery transport scheme.

[0067] Step S1 is the first stage: establish a stochastic programming model for dynamic load redistribution in the sea-rail intermodal transport network under uncertain cascading failure.

[0068] The symbol definition system for the first-stage model is shown in Table 2:

[0069] Table 2

[0070]

[0071]

[0072] The objective function for the one-stage model is set as follows:

[0073] The objective function of the one-stage model is to minimize the expected total loss over period t. The expected total loss consists of two parts: the first part is the expected total loss of all replacement nodes 'a', where the expected loss of a replacement node 'a' is calculated using reliability theory under a load of... The calculated failure risk and total load The product of the two. The second part is the container freight volume that cannot be redistributed, i.e. The corresponding container freight volume. Since this portion of freight volume is confirmed to be untransportable, its failure probability is 100%, and its expected loss is calculated based on this. The total expected loss is the sum of these two parts. It can be expressed by the following formula:

[0074]

[0075] The constraints for the first-stage model are set as follows:

[0076] Load redistribution constraints for container sea-rail intermodal freight trains. When only one of the origin and destination of a train is interrupted, the train is either assigned to a feasible alternative node or marked as unassigned. When both the origin and destination of a train are interrupted, the train must be assigned to the alternative nodes of both its original origin and destination; otherwise, it is marked as unassigned.

[0077]

[0078] Replacement node failure threshold constraint. Dynamic load of all replacement nodes after load redistribution. The failure probability under the following conditions cannot exceed

[0079]

[0080] The load of the replacement node is dynamically updated under constraints. The total container handling demand of the replacement node a after load redistribution within period t is determined by the initial load of node a. This consists of the new load added within period t.

[0081]

[0082] Spatiotemporal reachability constraints. When a train is reassigned from interrupted node o to replacement node a, the time it takes to travel from o to a by road cannot exceed the duration of one cycle, in order to ensure that the reassigned train can depart within that cycle.

[0083]

[0084] Node capacity limit. After load redistribution, the dynamic load of each replacement node cannot exceed its capacity limit of 3σ.

[0085]

[0086] Dynamic evolution constraints on train reassignment demand. The set of trains requiring reassignment at the interruption node o in period t. It consists of all trains that depart from interrupt node o in cycle t-1. And unassigned trains It consists of all trains originally scheduled to depart from interruption node o in cycle t.

[0087]

[0088] Decision variable constraints.

[0089]

[0090] Step S2 serves as the second stage: establishing an optimization model for the sea-rail intermodal transport network under the condition of interruption in key sections.

[0091] The symbol definition system for the two-stage model is shown in Table 3:

[0092] Table 3

[0093]

[0094]

[0095] The two-stage model uses the final result of the one-stage model, namely the load redistribution scheme, as input variables. The new container sea-rail intermodal transport demand is obtained through the load redistribution scheme. Finally, the two-stage model yields a sea-rail train recovery transport scheme based on the new container sea-rail intermodal transport demand under critical section disruptions. The calculation method for the new container sea-rail intermodal transport demand is as follows:

[0096]

[0097] In the formula:

[0098] In the interrupted state, does train k with period t start from node s, where s∈S?

[0099] In the interrupted state, does train k with period t end at node s, where s∈S?

[0100]

[0101] The objective function for the two-stage model is set as follows:

[0102] The traditional definition of logistics network resilience is its ability to recover to normal transport levels after disruptions or reduced transport capacity caused by disturbances. Therefore, to enhance the resilience of the container sea-rail intermodal transport network under critical segment disruptions, the objective function of the second-stage model is designed to minimize the increase in losses from the recovery transport plan compared to the original transport plan. This increase in losses consists of two parts: the first part is the increase in transport costs for containers restored through route reconfiguration, and the second part is the total value loss of containers whose transport was interrupted. It can be expressed by the following formula:

[0103]

[0104] The constraints for the two-stage model are set as follows:

[0105] Train transport status constraints. If a sea-rail intermodal train k fails to resume operation through route reconstruction during cycle t, it must be marked as interrupted.

[0106]

[0107] Path connectivity constraints. All transport paths used in the recovery transport plan must not contain any interrupted sections.

[0108]

[0109] Inter-section capacity constraints. The total number of sea-rail intermodal freight trains passing through each link (railway section) within a cycle cannot exceed the capacity limit of that section.

[0110]

[0111] Station capacity constraints. The total number of sea-rail intermodal freight trains passing through each node within a cycle cannot exceed the capacity limit of that node;

[0112]

[0113] Decision variable constraints.

[0114]

[0115] To quantify the resilience enhancement effect of the recovery transport plan formulated in this model on the container sea-rail intermodal transport network under different critical segment disruptions, this invention designs a resilience enhancement effect evaluation index. The calculation method of the index χ is as follows:

[0116]

[0117] In this calculation method This represents the total cost of the recovery transportation plan after a disruption in the critical section. This represents the total cost of the original transportation plan before the critical section was disrupted. The cost increase rate of the recovery transportation plan represents the loss compared to the original transportation plan. Therefore, the complement of the cost increase rate is used as the resilience enhancement effect evaluation index χ to evaluate the resilience level of the resilience optimization strategy.

[0118] To verify the effectiveness of the proposed two-stage model in resilience optimization under uncertain failure risk, this invention uses a sea-rail intermodal transport network of a certain land-sea corridor for case analysis. Information on sea-rail freight trains of this land-sea corridor is shown in Table 4:

[0119] Table 4

[0120] Serial Number Train number loading station unloading station port Train brand Transportation methods 1 X9592 Xi'an International Port Qinzhou Port East Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 2 X9591 Xi'an International Port Qinzhou Port East Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 3 X9574 Qinzhou Port East Chengxiang Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 4 X9573 Qinzhou Port East Chengxiang Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 5 X9585 Qinzhou Port East Chengxiang Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 6 X9586 Qinzhou Port East Chengxiang Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 7 X9590 Qinzhou Port East Unity Village Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 8 X9611 Fangchenggang Bookstore Fangchenggang New International Land-Sea Trade Corridor Full vehicles, containers 9 X9612 Fangchenggang Bookstore Fangchenggang New International Land-Sea Trade Corridor Full vehicles, containers 10 X9570 Chengxiang Qinzhou Port East Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 11 X9569 Chengxiang Qinzhou Port East Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 12 X9571 Unity Village Qinzhou Port East Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 13 X9572 Unity Village Qinzhou Port East Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 14 X9575 Chengxiang Qinzhou Port East Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 15 X9576 Chengxiang Qinzhou Port East Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 16 X9579 Unity Village Qinzhou Port East Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 17 X9588 Xiaonanya Qinzhou Port East Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 18 X9587 Xiaonanya Qinzhou Port East Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 19 X9589 Unity Village Qinzhou Port East Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 20 X9603 Bookstore Fangchenggang Fangchenggang New International Land-Sea Trade Corridor Full vehicles, containers 21 X9604 Bookstore Fangchenggang Fangchenggang New International Land-Sea Trade Corridor Full vehicles, containers 22 X9608 Wangjiaying West Qinzhou Port East Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers 23 X9607 Wangjiaying West Qinzhou Port East Qinzhou Port New International Land-Sea Trade Corridor Full vehicles, containers

[0121] Analysis of results from the first-stage model:

[0122] The railway freight hub nodes in the New International Land-Sea Trade Corridor's sea-rail intermodal transport network include Chengxiang Station, Tuanjiecun Station, Dushupu Station, Xi'an International Port, Xiaonanya Station, and Wangjiaying West Station, while the seaport hub nodes include Qinzhou Port and Fangcheng Port. This invention selects Chengxiang Station and Qinzhou Port, which have the highest number of freight trains operating, from the inland railway freight station end and the seaport end respectively, for joint interruption. The alternative node sets for Chengxiang Station and Qinzhou Port are shown in Table 5.

[0123] Table 5 Set of Alternate Nodes

[0124] Node Name Alternate Nodes Chengxiang Guangyuan South, Puxing, Xiantan, Tuanjie Village, Yuzui, Qingbaijiang, Dawang Town, Gongxing Qinzhou Port Fangchenggang, Guangzhou Port, Shenzhen Port

[0125] Table 6 shows the loading and unloading capacity of interrupted hub nodes, the number of trains with initial load in one cycle, and the number of containers loaded on each train in the stochastic programming model of dynamic load redistribution in the sea-rail intermodal transport network under the first-stage uncertainty cascade failure.

[0126] Table 6 Interruption Node Information

[0127]

[0128] Table 7 shows the loading and unloading capacity of the alternative nodes at Chengxiang Station and Qinzhou Port, the number of trains with initial load in a cycle, and the number of containers loaded on each train.

[0129] Table 7 Information on Alternate Nodes

[0130]

[0131]

[0132] This invention selects a scenario where the Chengxiang Station and Qinzhou Port, two hub nodes, are jointly interrupted. A load redistribution scheme is generated through a dynamic load redistribution model, and the load redistribution scheme is shown in Table 8:

[0133] Table 8 Load Redistribution Scheme

[0134]

[0135]

[0136] To verify the effectiveness and advancement of the constructed load redistribution model, this invention compares the load distribution results using the constructed model with those using load redistribution strategies without a load redistribution strategy and with three traditional cascading failure models. The results are shown in Table 9.

[0137] Table 9 Comparison of Load Redistribution Results

[0138]

[0139]

[0140] As shown in Table 9, compared with the expected total loss from not using load redistribution and using the three traditional load redistribution strategies, the load redistribution strategy proposed in this invention reduces the expected total loss by 85.93%, 94.87%, 87.15%, and 90.40% at Chengxiang Station, and by 99.16%, 99.69%, 57.78%, and 99.35% at Qinzhou Port, respectively. These results demonstrate that the load redistribution model proposed in this invention can significantly reduce the losses caused by the cascading failures resulting from hub node interruptions, enabling the sea-rail intermodal transport network to recover to normal operating levels more quickly and improving network resilience. In addition to reducing losses, the load redistribution strategy proposed in this invention also effectively controls the probability of cascading failures. As shown in Table 9, for the 10 alternative nodes at Chengxiang Station and Qinzhou Port, the failure probability of all alternative nodes is controlled below 70% when using the load redistribution strategy proposed in this invention, which is an acceptable threshold during resilience recovery. The traditional redistribution strategy results in a failure probability exceeding 70% for 40% of the alternative nodes, with 26.67% of the alternative nodes having a 100% failure probability. This indicates that the traditional strategy leads to large-scale cascading failures, posing a significant challenge to the resilience of the sea-rail intermodal transport network.

[0141] Two-stage model results analysis:

[0142] Based on the optimal load redistribution scheme generated by the first-stage model, the new operating demand for 17 sea-rail intermodal freight trains under the simulated joint interruption of Chengxiang Station and Qinzhou Port can be determined. The operating demand for the freight trains is shown in Table 10.

[0143] Table 10 Demand for Sea-Rail Freight Trains

[0144]

[0145]

[0146] In the absence of section disruptions, a sea-rail intermodal transport network organization optimization model is used to obtain the regular sea-rail freight train transport plan under new demand. Based on the regular transport plan, the number of sea-rail freight trains passing through each section can be counted. Then, the section between Longchang Station and Fuji Station, one of the railway sections with the most passing trains, is selected for disruption analysis. Among the 17 train operation demands, 7 trains are affected by section disruptions. Applying the sea-rail intermodal transport network organization optimization model for key section disruptions proposed in this invention, new feasible recovery transport schemes are generated for all 7 trains through route reconstruction, as shown in Table 11.

[0147] Table 11 Transportation Recovery Plan

[0148]

[0149]

[0150] The resilience evaluation index χ = 85.81% for this recovery transportation scheme. This proves that the model proposed in this invention can exhibit strong resilience even when critical sections are disrupted.

[0151] like Figure 2 As shown, this invention further identifies 864 key sections in the regular sea-rail intermodal transport plan through which trains pass, and conducts a full-scenario interruption analysis on each of these 864 key sections. Using the sea-rail intermodal transport network transport organization optimization model designed in this invention under key section interruptions, recovery transport schemes are obtained under different section interruptions. Finally, the resilience indices of all recovery transport schemes are statistically analyzed, and the histogram of resilience index distribution for the 864 key sections is shown below. Figure 2 As shown.

[0152] from Figure 2 As can be seen, the resilience level of all outage scenarios is higher than 85.8%, a threshold that meets the network outage resilience requirements of real-world operational scenarios. Among these, 76.62% of the outage scenarios have a resilience level higher than 98%, indicating that the resilience optimization model proposed in this invention can intelligently shield damaged paths and implement path reconstruction after an inter-regional outage, enabling the sea-rail intermodal transport network to possess strong recovery performance within the outage period and greatly improving the overall resilience of the network under different outage scenarios.

[0153] Based on the above analysis of the sea-rail intermodal transport network of a certain land-sea new corridor, the following conclusions can be drawn:

[0154] First, in hub node outage scenarios, the one-stage dynamic load redistribution model, constrained by reliability theory, successfully controlled the failure probability of alternative nodes to within a preset threshold of 70%. This result is significantly better than the traditional strategy's scenario where 26.67% of alternative nodes completely fail, while reducing losses by more than 57.78%, effectively suppressing the risk of cascading failures. In critical section outage scenarios, the two-stage transport organization optimization model, relying on path reconstruction strategies, maintained the resilience level of 864 outage scenarios above 85.8%, with 76.62% of the section outage scenarios having a resilience level above 98%, verifying the strong support capability of the restorative transport plan for network connectivity and operational efficiency.

[0155] Secondly, this invention constructs a resilience optimization model of "failure risk control-recovery strategy synergy" through interdisciplinary theoretical transplantation. This invention breaks through the limitations of traditional deterministic resilience optimization models and establishes a risk quantification mechanism for load-capacity stochastic interference; through two-stage dynamic connection, it provides an operable decision-making tool for multimodal transport networks to cope with compound interruptions.

[0156] Third, this invention provides a new methodology for complex logistics systems to cope with uncertainty risks, and has important practical significance for enhancing the resilience of international multimodal transport networks.

[0157] The above description is merely a preferred embodiment of the present invention and does not limit the scope of the invention. All equivalent structural changes made using the contents of this invention and its accompanying drawings are included within the scope of the present invention.

[0158] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

Claims

1. A two-stage sea-rail intermodal transport network resilience optimization method under uncertain cascading failure, characterized in that, include: Step S1: Obtain the failed hub node, and generate a container operation load redistribution scheme based on the dynamic load redistribution stochastic programming model of the sea-rail intermodal network under uncertain cascading failure. The dynamic load redistribution stochastic programming model of the sea-rail intermodal network under uncertain cascading failure aims to minimize the total expected loss of all alternative nodes and the container freight volume that cannot be redistributed, and allocates the original container operation demand of the original failed hub node to the surrounding uninterrupted alternative nodes. Step S2: Use the generated container operation load redistribution scheme as input to the sea-rail intermodal transport network transport organization optimization model under critical section interruption to generate new train operation demand. When the new train operation demand occurs in the critical area, the path is reconstructed through the sea-rail intermodal transport network transport organization optimization model to generate a new feasible recovery transport scheme.

2. The two-stage sea-rail intermodal transport network resilience optimization method under uncertain cascading failure as described in claim 1, characterized in that, The objective function of the stochastic programming model for dynamic load redistribution in the sea-rail intermodal transport network under uncertain cascading failure is: Where: Φ(·) is the cumulative distribution function of the standard normal distribution, Let be the total demand for container operations at the replacement node a after load redistribution within period t. This indicates whether train k cannot be assigned during period t. The value is 1 if it cannot be assigned, and 0 if it can be assigned. Let O be the container freight volume of train k in period t, and let O be the set of interruption nodes. o μ is the set of alternative nodes that can be used to distribute load for interrupt node o. a To replace the rated container handling capacity of node a for one cycle, σ a To replace the standard deviation of the freight handling capacity of node a over one cycle, To replace the standard deviation of the total load of node a during period t, The set of trains with interruption node o as the starting or ending point within period t.

3. The two-stage sea-rail intermodal transport network resilience optimization method under uncertain cascading failure as described in claim 2, characterized in that, The constraints of the stochastic programming model for dynamic load redistribution in the sea-rail intermodal transport network under the uncertainty cascade failure condition include: Load redistribution status constraints for container sea-rail intermodal freight trains: When only one of the origin and destination of a train is interrupted, the train is either assigned to a feasible alternative node or marked as unassigned. When both the origin and destination are interrupted, the train must be assigned to the alternative nodes of its original origin and destination at the same time, otherwise it will be marked as unassigned at the same time. Replacement node failure threshold constraint: in: The maximum allowable failure probability for replacement node a; Alternative node load dynamic update constraints: in: To replace the initial load of node a in period t, This indicates whether the starting point of train k is assigned to a substitute node a during cycle t. If yes, the value is 1; otherwise, the value is 0. Whether the destination of train k is assigned to a substitute node a in cycle t. If yes, the value is 1, otherwise the value is 0. Spatiotemporal reachability constraint: When a train is assigned from the interruption node to the replacement node, the time it takes to travel from the interruption node to the replacement node by road shall not exceed the duration of one cycle. Node capacity constraints: Dynamic Evolution Constraints of Train Reassignment Demand: Train Sets It consists of all trains that departed from interruption node o in cycle t but were not assigned, and all trains originally scheduled to depart from interruption node o in cycle t.

4. The two-stage sea-rail intermodal transport network resilience optimization method under uncertain cascading failure as described in claim 3, characterized in that, The mathematical expression for the load redistribution state constraint of the container sea-rail intermodal freight train is: Where: N is the set of hub nodes that need to be redistributed after the interruption. In non-interrupted operation, whether train k starts from node m is the determining factor. If yes, the value is 1; otherwise, the value is 0. k,m ∈{0,1} indicates whether train k ends at node m in the non-interrupted state. If yes, the value is 1, otherwise the value is 0.

5. The two-stage sea-rail intermodal transport network resilience optimization method under uncertain cascading failure as described in claim 3, characterized in that, The mathematical expression for the spatiotemporal reachability constraint is: Where: d o,a v represents the road transport distance from the interrupted node o to the replacement node a. road Let Δt be the average speed of road transport, and Δt be the length of one period.

6. The two-stage sea-rail intermodal transport network resilience optimization method under uncertain cascading failure as described in claim 1, characterized in that, The objective function of the sea-rail intermodal transport network transportation organization optimization model under the interruption of the critical section is: Where: c transport The transportation cost per unit path length. Path in uninterrupted state Whether it passes through the interval r, if yes, the value is 1, otherwise the value is 0, γ r,p To determine whether path p in the interrupted state passes through interval r, the value is 1 if it does, and 0 otherwise. r Let r be the length of the interval. This parameter determines whether the sea-rail intermodal freight train k selects route p to operate during cycle t. If yes, the value is 1; otherwise, it is 0. r Let c be the length of the interval r. loss The unit value loss for unshipped containers. To determine whether the sea-rail intermodal freight train k is interrupted during cycle t, P k Let R be the set of feasible routes for train k under interrupted conditions, and let R be the set of links in the container sea-rail intermodal transport network.

7. The two-stage sea-rail intermodal transport network resilience optimization method under uncertain cascading failure as described in claim 6, characterized in that, The constraints of the sea-rail intermodal transport network transportation organization optimization model under the condition of interruption in the key section are as follows: Train transport status constraints: If the sea-rail intermodal train k does not resume operation through route reconstruction in period t, it is marked as interrupted transport; Path connectivity constraints: in: This parameter determines whether the sea-rail intermodal freight train k selects route p to operate during cycle t. If yes, the value is 1; otherwise, the value is 0. This indicates whether the interval r is interrupted during the period t. If it is, the value is 1; otherwise, the value is 0. Inter-section capacity limit constraint: The total number of sea-rail intermodal freight trains passing through each link within a cycle cannot exceed the capacity limit of that section; Station capacity constraints: The total number of sea-rail intermodal freight trains passing through each node within a cycle cannot exceed the capacity limit of that node.

8. The two-stage sea-rail intermodal transport network resilience optimization method under uncertain cascading failure as described in claim 4, characterized in that, The method further includes: A resilience evaluation was conducted on the generated feasible recovery transportation schemes, calculating the resilience improvement effect on the container sea-rail intermodal transport network under different critical section disruptions. The resilience evaluation index χ² is: in: The total cost of the recovery transportation plan after the disruption of critical sections. This represents the total cost of the original transportation plan before the critical section was disrupted.

9. A two-stage sea-rail intermodal transport network resilience optimization device under uncertain cascading failure, comprising a memory, a processor, and a program stored in the memory, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1-8.

10. A storage medium having a program stored thereon, characterized in that, When the program is executed, it implements the method as described in any one of claims 1-8.

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