Congestion endogenous and multi-dimensional overlapping driven multimodal freight path optimization method

Abstract

The application discloses a multi-modal freight transport path optimization method driven by endogenous congestion and multi-dimensional overlap, aiming to solve the technical problem that the existing model cannot simultaneously process multi-dimensional endogenous correlation such as link congestion feedback, hub transfer bottleneck, path physical overlap and mode perception similarity. The application constructs a multi-layer directed multi-modal transport network and generates a candidate path set; establishes a generalized path cost function containing road section and hub endogenous congestion; constructs a road space correlation penalty term based on shared length and a mode similarity penalty term based on hub betweenness centrality; incorporates the above elements into a multi-objective optimization framework based on maximum entropy, and converts it into an improved nested fixed point equation; uses instrumental variable substitution method to solve the endogeneity problem in parameter estimation, and obtains network equilibrium flow through iterative solution. The application breaks through the independent and irrelevant assumption of the traditional model, and significantly improves the accuracy and behavior explanation ability of freight flow prediction in a complex multi-modal transport network.

Description

Technical Field

[0001] This application relates to the field of transportation planning and logistics engineering technology, specifically to a multimodal freight route optimization method driven by endogenous congestion and multidimensional overlap. Background Technology

[0002] In the field of industrial equipment fault diagnosis, and under the national strategy of building a strong transportation nation, multimodal transport, as a core tool for optimizing transportation structure, reducing social logistics costs, and improving overall transportation efficiency, has become a top priority in the construction of a modern comprehensive transportation system. The "National Comprehensive Three-Dimensional Transportation Network Planning Outline" clearly proposes to accelerate the development of multimodal transport, promote the shift of bulk cargo and medium-to-long-distance freight from road to rail and water, and improve the collaborative efficiency of comprehensive transportation corridors. Freight multimodal transport integrates various modes of transport such as road, rail, and waterway to achieve integrated "door-to-door" transportation of goods. Its core lies in achieving optimal allocation of transportation resources and maximizing system efficiency through scientific route selection and flow distribution.

[0003] Freight route selection is a core foundation for the operation and planning of multimodal transport networks. The accuracy of its modeling directly determines the accuracy of network traffic forecasting, the rationality of transport organization schemes, and the reliability of related policy evaluations. Existing research on freight route selection largely draws on the mature stochastic utility theory framework from the passenger transport field, with the Multinomial Logit Model (MNL) and the traditional Nested Logit Model (NL) being the most widely used. The MNL model, based on the assumption of maximizing stochastic utility and using the independent and identically distributed error term of the Gumbel distribution as its core assumption, has advantages such as simple mathematical form, convenient solution, and easy interpretation, and has been widely applied in the field of transportation route selection. The NL model, by nesting similar alternatives, relaxes the independent and identically distributed assumption of the MNL model to some extent, and can characterize the substitution correlation of alternatives within the same nest, thus being extended to multimodal transport selection scenarios. However, in the complex scenario of integrated freight multimodal transport, existing route selection methods based on MNL, NL, and their improved models still have insurmountable technical defects. They cannot adapt to the topological characteristics of multimodal transport networks, the inherent laws of freight behavior, and the dynamic feedback characteristics of congestion. Specifically, these defects are reflected in the following aspects:

[0004] First, the IIA (Independence from Irrelevant Alternatives) assumption of the traditional MNL (Multimodal Transport Neighborhood) model fails to capture the differences in substitution relationships resulting from the high degree of overlap between candidate multimodal transport routes. The IIA assumption requires that the ratio of the selection probabilities of any two alternatives depends only on the utility of those two alternatives themselves, and is independent of other alternatives. This assumption becomes severely biased when there are many shared links between routes, leading to the classic "red bus - blue bus" paradox. In multimodal transport scenarios, most intermodal routes share urban road transport links, and candidate routes for the same origin-destination (OD) pair often have extremely high physical link overlap. The IIA assumption of the traditional MNL model leads to severely distorted estimations of the substitution elasticity of overlapping routes, failing to accurately characterize the shipper's choice behavior between overlapping routes, and consequently causing a significant deviation between the traffic allocation results and the actual situation. Existing improved models such as C-Logit and Path Size Logit (PSL) only penalize path utility through exogenous correction terms for path overlap, which cannot dynamically reflect the impact of traffic changes on path substitution relationships, and thus have limited correction effects.

[0005] Second, existing path relevance correction methods only focus on the geometric overlap of physical paths, failing to fully reflect the multidimensional relevance across modes in multimodal transport scenarios. Multimodal transport path selection is influenced not only by physical link overlap but also by transshipment hubs, mode link combinations, and transport organization methods. Specifically, even if two intermodal transport paths have low physical link overlap, if they share a core transshipment hub and use similar mode combination sequences, shippers' perceived similarity will significantly increase, creating a strong substitution relationship between the two paths. For example, two road-rail intermodal transport paths using different railway trunk lines but sharing the same railway hub for transshipment will be considered highly similar alternatives in shippers' decision-making. Existing correction methods based solely on physical link overlap completely fail to capture this cross-dimensional relevance based on hubs and modes, resulting in a fundamental flaw in the model's characterization of the substitution patterns of multimodal transport paths.

[0006] Third, the tree-like structure of traditional multimodal transport (NL) models cannot adapt to the complex cross-nesting and overlapping scenarios in multimodal transport networks, resulting in a serious "experience-unidentifiable" problem. Traditional NL models require that the nested structure be a non-overlapping tree structure, meaning that an alternative can only belong to one nest and cannot belong to multiple nests simultaneously. However, in multimodal transport scenarios, pure road routes can be nested as independent transport modes or as collection and distribution links in road-rail or road-water intermodal transport routes, exhibiting inherent cross-nesting and overlapping characteristics. Simultaneously, different mode routes sharing the same hub also exhibit cross-nesting correlations. Forcing the use of the non-overlapping nested structure of traditional NL models leads to the inability to effectively identify the model's coverage parameters, resulting in statistically insignificant parameters and signs that contradict economic expectations—a "experience-unidentifiable" problem that renders the model completely devoid of explanatory and predictive value. While existing improved generalized nested Logit models (GNL) allow cross-nested structures, they suffer from drawbacks such as high difficulty in parameter estimation, poor convergence, and high engineering implementation difficulty in high-dimensional path sets of multimodal transport scenarios, making them unsuitable for simulating freight networks at the meso-scale and above.

[0007] Fourth, existing static route selection models fail to capture the endogenous closed-loop feedback between freight traffic and network congestion, leading to distorted generalized cost estimation. Compared to passenger vehicles, freight vehicles have a significant scale effect on road resource usage, and heavy freight vehicles are one of the core influencing factors of congestion on trunk highways and urban access roads. Simultaneously, the loading, unloading, and transshipment capabilities of multimodal transport hubs are subject to rigid constraints; an increase in hub throughput directly leads to a non-linear increase in transshipment waiting time. Shippers' route selection decisions alter the traffic distribution of links and hubs, resulting in dynamic changes in transportation costs. These changes in transportation costs, in turn, influence shippers' route choices, forming a closed-loop feedback mechanism of "selection-congestion-reselection." Most existing freight route selection models treat link travel time and hub transshipment time as exogenously given fixed values, employing a static modeling framework that completely ignores the endogenous impact of freight traffic on congestion, thus failing to characterize the aforementioned closed-loop feedback mechanism. In scenarios with large freight demand and high network congestion, the generalized cost estimation of static models will be seriously biased, resulting in traffic allocation results that are far from the actual equilibrium state, and thus failing to provide reliable quantitative support for network planning and policy making.

[0008] Fifth, existing models struggle to simultaneously model path relevance, mode relevance, and endogenous congestion feedback in a unified manner, failing to adapt to the complex characteristics of multimodal transport networks. Current research primarily addresses one or two of these shortcomings, such as correcting path overlap, balancing endogenous congestion, or optimizing nested structures for mode selection. No technical solution has yet achieved coupled modeling of path-level spatial relevance, mode-level perceived similarity, and flow-congestion endogenous feedback within a unified theoretical framework. Multimodal freight route selection is a complex decision-making process influenced by multiple factors, including transport costs, path overlap, mode similarity, and congestion dynamics. Single-dimensional improvements cannot fundamentally address the systemic deficiencies of existing models, resulting in low goodness of fit, poor prediction accuracy, and weak explanatory power in real-world multimodal transport scenarios, making it difficult to support practical engineering applications and policy evaluations. Summary of the Invention

[0009] The main objective of this application is to provide a multimodal freight route optimization method driven by endogenous congestion and multidimensional overlap, including the following steps:

[0010] Step S1: Construct a multimodal freight hypernetwork model. The hypernetwork model includes a multi-layered directed graph consisting of highways, railways, waterways, and connecting links. The nodes in the multi-layered directed graph include transportation hub nodes and urban centroid nodes. The attributes of the links include free-flow time, design capacity, and the mode of transport to which they belong.

[0011] Step S2: For each origin-destination OD pair, the Dial algorithm is used to generate a set of valid candidate routes from the origin to the destination, and the candidate route set is divided into four non-overlapping nested groups according to the transportation mode contained in the link: pure road, pure rail, road-rail intermodal transport, and road-water intermodal transport.

[0012] Step S3: Establish a generalized path cost function, which includes the endogenous congestion cost dynamically related to link traffic and the hub transfer cost dynamically related to hub transfer volume, wherein the endogenous congestion cost is calculated based on the BPR function and the hub transfer cost is calculated based on the Kingman queuing model.

[0013] Step S4: Construct a multidimensional overlap penalty term reflecting the competitive relationship between candidate paths. The multidimensional overlap penalty term includes a path correlation penalty term based on the shared segment length ratio and a pattern similarity penalty term weighted by the betweenness centrality of transit hubs. Based on the generalized path cost function and the multidimensional overlap penalty term, construct a multi-objective optimization model with the objectives of minimizing the total system cost, maximizing path selection entropy, minimizing road spatial correlation, and minimizing pattern similarity.

[0014] Step S5: Based on the first-order optimality condition of the multi-objective optimization model, derive the improved nested fixed-point equation for path flow; use the path flow obtained by the nested Logit model as an instrumental variable to replace the endogenous flow term on the right side of the improved nested fixed-point equation, construct an estimable maximum likelihood function, and use the maximum likelihood estimation method to calibrate the model parameters.

[0015] Step S6: Based on the calibrated model parameters, iteratively solve the improved nested fixed-point equation until the path flow change meets the preset convergence threshold, and output the final freight flow and transportation mode for each path.

[0016] In one embodiment, the multi-layer directed graph is represented by a directed graph G:=(N,A), where N is the set of network nodes, H⊂N is the set of multimodal transport hubs, which includes railway hubs, inland dry port hubs, and port hubs; M is the set of transport modes, M={road, rail, water transport}; a road connection edge is set between the city centroid and each transport mode network to represent the terminal collection and distribution link; each link in the link set A records the attribute parameters of length, free flow time, unit transport cost, design capacity, and mode to which it belongs, and parallel multimodal links are allowed to be set between the same start and end nodes.

[0017] In one embodiment, the effective candidate path set is defined as a loopless path that is always farther from the starting point and closer to the destination along the link travel direction; the Dial algorithm is used to search for all effective paths, and each path records the link sequence, hub sequence and mode sequence; the nested grouping is divided into the following four categories: the first category is pure road transport mode, the second category is pure rail transport mode, the third category is road-rail intermodal transport mode, and the fourth category is road-water intermodal transport mode.

[0018] In one embodiment, the endogenous congestion cost is constructed using a BPR function, expressed as:

[0019]

[0020] in, Let a be the free-flow travel time of link a. For the freight volume of link a, Design capacity for link a, where α and β are preset parameters of the BPR function;

[0021] Hub transshipment costs are constructed using the Kingman formula, expressed as follows:

[0022]

[0023] in, These are the basic service efficiency parameters for the hub node h. For the processing of freight traffic at hub node h, The design throughput capacity of hub node h is given; the generalized cost of candidate path r is the sum of the operating costs of all links along the path and the transfer costs of all hubs it passes through, and the generalized cost is dynamically updated with the network freight traffic.

[0024] In one embodiment, the path correlation penalty term based on the shared segment length ratio is expressed as:

[0025]

[0026] in, Let ω be the total length of the shared road segment between candidate path r and candidate path q under OD. , Let r and q be the total lengths of path r and path q, respectively; construct the path correlation coefficient for any two candidate paths r and q. , It can be determined by the normalized ratio of the length of the shared road segment between the two paths to the total length of the two paths.

[0027] In one embodiment, a pattern similarity penalty term is applied based on transit hub betweenness centrality weighting:

[0028]

[0029] Introducing the betweenness centrality of hub nodes As used in the calculation of weights, where , These are the sets of hub nodes that path r and path q pass through.

[0030] In one embodiment, based on the generalized path cost function and the multidimensional overlap penalty term, a multi-objective optimization model is constructed with the objectives of minimizing the total system cost, maximizing path selection entropy, minimizing road spatial correlation, and minimizing pattern similarity.

[0031] Minimize the total system link transportation cost:

[0032]

[0033] Minimize the overall hub transfer cost of the system:

[0034]

[0035] Introducing an entropy term to reflect the bounded rationality of decision-makers, the entropy of maximizing path selection is expressed as:

[0036]

[0037] Introducing a road spatial correlation criterion and utilizing a shared length matrix Penalizing physical overlap and minimizing road spatial correlation is expressed as:

[0038]

[0039] Introducing a pattern similarity criterion, utilizing centrality-based weights The hub competition term characterizes pattern correlation, and minimizing pattern similarity is expressed as:

[0040]

[0041] Where W is the set of OD pairs. Let be the set of candidate paths for OD to ω. For freight flow on path r, Let ω be the average freight flow rate for all paths within OD. For OD The total fixed freight demand.

[0042] In one embodiment, the improved expression for the nested fixed-point equation is:

[0043]

[0044] in, For path r, the fixed utility term, This is the cost sensitivity coefficient. Let r be the generalized cost. This is the penalty coefficient for road spatial correlation. This represents the pattern-aware similarity penalty coefficient.

[0045] In one embodiment, the steps of using the path flow obtained from the nested Logit model as an instrumental variable to replace the endogenous flow term on the right-hand side of the improved nested fixed-point equation, constructing an estimable maximum likelihood function, and calibrating the model parameters using the maximum likelihood estimation method include:

[0046] Construct a nested Logit model to calculate the initial traffic for each path. Treat it as an instrumental variable;

[0047] By replacing the endogenous flow term on the right-hand side of the nested fixed-point equation with instrumental variables, the endogeneity problem is transformed into an exogenous variable estimation problem.

[0048] Construct a likelihood function for path selection and update the model parameters using the maximum likelihood estimation method;

[0049] Repeat the above steps until the iterative convergence accuracy of the model parameters reaches the preset threshold, thus completing parameter estimation and significance testing.

[0050] In one embodiment, the step of iteratively solving the improved nested fixed-point equations until the path flow changes meet a preset convergence threshold, and then outputting the final freight flow and transportation mode for each path, includes:

[0051] Initialize the initial freight flow for each path, and set the convergence threshold and maximum number of iterations;

[0052] Based on the current freight flow, calculate the congestion time of each link and the transfer time of each hub, and update the generalized cost of all candidate routes.

[0053] Based on the current path traffic, update the path space relevance aggregation value and the pattern-aware similarity aggregation value;

[0054] Substitute the improved nested fixed-point equation to calculate the selection probability of each path and the updated path flow;

[0055] Determine if the maximum difference in path traffic between two adjacent iterations is less than the convergence threshold. If so, stop the iteration and output the balanced path traffic and transportation mode sharing results. If not, return to initialization and continue iterating until the maximum number of iterations is reached.

[0056] Therefore, this application has the following beneficial effects:

[0057] First, it breaks through the limitations of the IIA assumption in traditional discrete choice models. By introducing a road spatial correlation penalty term based on shared length and a pattern similarity penalty term based on hub betweenness centrality within the same framework, it can accurately characterize the multidimensional path substitution relationship caused by physical link sharing and key hub sharing. This solves the prediction bias problem caused by neglecting such overlap in traditional MNL and NL models, and significantly improves the model's log likelihood and goodness of fit.

[0058] Second, it achieves dynamic coupling feedback between endogenous congestion and route selection. By simultaneously incorporating the BPR segment congestion function and the Kingman hub queuing delay model into the generalized cost function and solving iteratively at fixed points, it fully simulates the closed-loop process of "selection-congestion-reselection," enabling the model to dynamically assess the ripple effect of infrastructure capacity changes on the overall network traffic distribution.

[0059] Third, it effectively solves the parameter identification failure problem of traditional NL models when there is cross-nesting overlap. By replacing the rigid tree-like nested structure with an explicit multidimensional overlap penalty term, it ensures that both the cost perception coefficient and the two types of correlation penalty coefficients can obtain statistically significant estimates that conform to economic expectations, thus enhancing the engineering practicality of the model.

[0060] Fourth, by introducing hub betweenness centrality as a weighting factor for pattern similarity, this study distinguishes for the first time the differences in the impact of sharing hubs of different importance on cargo owners' choice behavior, captures a deeper level of "pattern-hub" dependency heterogeneity, and improves the granularity of the model's behavioral explanation. Attached Figure Description

[0061] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0062] Figure 1 This is a system flowchart of a multimodal freight route optimization method driven by endogenous congestion and multidimensional overlap.

[0063] Figure 2 This is a schematic diagram of candidate route generation and nested grouping in a multimodal freight route optimization method driven by endogenous congestion and multidimensional overlap. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0065] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this application.

[0066] To address the shortcomings of existing technologies, this application provides a multimodal freight route optimization method driven by endogenous congestion and multidimensional overlap. The method first constructs a multi-layered directed hypernetwork containing highways, railways, waterways, and connecting links, and generates candidate route nesting groups based on transportation modes. Second, it establishes a generalized path cost function comprising segment endogenous congestion costs based on the Bureau of Public Roads Function (BPR) and hub transfer costs based on the Kingman queuing model. Third, it constructs a path relevance penalty term based on the shared segment length ratio and a pattern similarity penalty term weighted by hub betweenness centrality, incorporating both into a multi-objective optimization framework along with the entropy maximization criterion. An improved nested fixed-point equation is derived through first-order optimality conditions, and the flow rate of the basic nested Logit model is used as an instrumental variable to solve the endogeneity problem, achieving unbiased parameter estimation. Finally, the network equilibrium flow rate is obtained through iterative solution. This method overcomes the limitations of the IIA assumption in traditional models, achieves dynamic coupling between congestion and choice, and effectively solves the parameter identification failure problem when there is cross-nested overlap.

[0067] This application provides a multimodal freight route optimization method driven by endogenous congestion and multidimensional overlap, including steps S1-S5, as described above. Figure 1 , Figure 1 This is a system flowchart of a multimodal freight route optimization method driven by endogenous congestion and multidimensional overlap.

[0068] Step S1: Construct a multimodal freight hypernetwork model. The hypernetwork model includes a multi-layered directed graph consisting of highways, railways, waterways, and connecting links. The nodes in the multi-layered directed graph include transportation hub nodes and urban centroid nodes. The attributes of the links include free-flow time, design capacity, and the mode of transport to which they belong.

[0069] Step S2: For each origin-destination OD pair, the Dial algorithm is used to generate a set of valid candidate routes from the origin to the destination, and the candidate route set is divided into four non-overlapping nested groups according to the transportation mode contained in the link: pure road, pure rail, road-rail intermodal transport, and road-water intermodal transport.

[0070] Step S3: Establish a generalized path cost function, which includes the endogenous congestion cost dynamically related to link traffic and the hub transfer cost dynamically related to hub transfer volume, wherein the endogenous congestion cost is calculated based on the BPR function and the hub transfer cost is calculated based on the Kingman queuing model.

[0071] Step S4: Construct a multidimensional overlap penalty term reflecting the competitive relationship between candidate paths. The multidimensional overlap penalty term includes a path correlation penalty term based on the shared segment length ratio and a pattern similarity penalty term weighted by the betweenness centrality of transit hubs. Based on the generalized path cost function and the multidimensional overlap penalty term, construct a multi-objective optimization model with the objectives of minimizing the total system cost, maximizing path selection entropy, minimizing road spatial correlation, and minimizing pattern similarity.

[0072] Step S5: Based on the first-order optimality condition of the multi-objective optimization model, derive the improved nested fixed-point equation for path flow; use the path flow obtained by the nested Logit model as an instrumental variable to replace the endogenous flow term on the right side of the improved nested fixed-point equation, construct an estimable maximum likelihood function, and use the maximum likelihood estimation method to calibrate the model parameters.

[0073] Step S6: Based on the calibrated model parameters, iteratively solve the improved nested fixed-point equation until the path flow change meets the preset convergence threshold, and output the final freight flow and transportation mode for each path.

[0074] Specifically, the multimodal freight route optimization method driven by endogenous congestion and multidimensional overlap provided in this embodiment forms a closed-loop technical process through six core steps, achieving precise route optimization and balanced traffic distribution in the multimodal freight network. The specific implementation process is as follows:

[0075] Step S1 involves constructing a multimodal freight hypernetwork model, building a multi-layered directed graph covering road, rail, waterway and connecting links, clarifying the hierarchical division of transportation hub nodes and urban centroid nodes, and configuring core attributes such as free flow time, design capacity, and transportation mode for each link, providing a standardized physical network foundation for full-process modeling.

[0076] Step S2 uses the Dial algorithm to generate a set of candidate routes that meet the definition of a valid route for each origin-destination OD pair, eliminating unreasonable routes such as detours and backtracking. At the same time, according to the characteristics of the route transportation mode, the candidate routes are divided into four non-overlapping nested groups: pure road, pure rail, road-rail intermodal transport, and road-water intermodal transport, to adapt to the mode classification characteristics of multimodal transport.

[0077] Step S3 establishes a dynamic generalized path cost function, incorporating endogenous congestion costs calculated based on the BPR function and dynamically related to link traffic, as well as hub transfer costs calculated based on the Kingman queuing model and dynamically related to hub transfer volume, to accurately capture the endogenous closed-loop feedback mechanism of freight "selection-congestion-reselection".

[0078] Step S4 constructs a multidimensional overlap double penalty term, including a path correlation penalty term based on the shared segment length ratio and a pattern similarity penalty term weighted by the betweenness centrality of transfer hubs, simultaneously characterizing the competitive substitution relationship brought about by path physical overlap and pattern hub similarity; combined with the generalized cost function, a multi-objective optimization model is constructed to minimize the total cost of the coupled system, maximize the path selection entropy, and minimize the double penalty term.

[0079] Step S5 derives the improved nested fixed-point equation for path flow by using the first-order optimality condition of the multi-objective optimization model; the path flow obtained by the nested Logit model is used as an instrumental variable to replace the endogenous flow term on the right side of the equation, constructing an estimable maximum likelihood function, completing the accurate calibration of the model parameters, and solving the parameter estimation bias problem caused by endogeneity.

[0080] Step S6, based on the calibrated model parameters, iteratively solves the improved nested fixed-point equation until the path flow changes in adjacent iterations meet the preset convergence threshold. Finally, it outputs the freight flow and transport mode share results for each path, providing reliable quantitative support for multimodal transport network planning and policy evaluation.

[0081] Figure 2 This diagram illustrates the candidate path generation and nested grouping of a multimodal freight route optimization method driven by endogenous congestion and multidimensional overlap. Taking the Suzhou-Ningbo-Zhoushan Port OD pair in the Yangtze River Delta as an example, it inputs a set of infrastructure nodes such as trunk highways and railways, and a set of transportation hub nodes such as Shanghai Port and Suzhou West Railway Hub to construct a comprehensive transportation network node set. A shortest path algorithm is used to generate initial candidate paths for single-mode and multi-mode transport, including pure highway, road-rail intermodal, and road-rail-water intermodal transport. A nested Logit model is used to construct a two-layer selection structure: first, the transport mode decision is completed at the mode selection layer, and then the specific path decision is completed at the path selection layer under the same mode. Finally, the selection probability of each path is output, providing core input for subsequent balanced traffic allocation.

[0082] In one embodiment, the multi-layer directed graph is represented by a directed graph G:=(N,A), where N is the set of network nodes, H⊂N is the set of multimodal transport hubs, which includes railway hubs, inland dry port hubs, and port hubs; M is the set of transport modes, M={road, rail, water transport}; a road connection edge is set between the city centroid and each transport mode network to represent the terminal collection and distribution link; each link in the link set A records the attribute parameters of length, free flow time, unit transport cost, design capacity, and mode to which it belongs, and parallel multimodal links are allowed to be set between the same start and end nodes.

[0083] Specifically, in this embodiment, to accurately depict the multi-level and multi-modal topological features of the intermodal freight transportation network, a standardized and computable multi-layer directed graph network model is constructed. The network is mathematically characterized by a multi-layer directed graph G := (N, A), which comprehensively covers the core network elements of the entire intermodal transportation chain. Here, N is the set of network nodes, including three types of core nodes: urban centroid nodes, nodes along the transportation network, and intermodal transportation hub nodes; H ⊂ N is the set of intermodal transportation hubs, specifically including three types of nodes: railway hubs, inland dry ports, and port hubs, which respectively undertake the functions of cargo transshipment and transfer connection between different transportation modes and are the core carriers for realizing cross-modal transportation. M is the set of transportation modes, set as M = {highway, railway, waterway}, covering the core mainline transportation modes of domestic freight intermodal transportation and adapting to the mainstream scenario requirements of medium- and long-distance transportation of bulk goods. To achieve seamless connection between the urban end and the trunk network, dedicated highway connection edges are set between the urban centroid nodes and the access nodes of each transportation mode network, accurately representing the first and last mile collection and distribution links of the "door-to-door" cargo transportation, and filling the gap in the description of the last mile distribution link in the traditional network model. The link set A is the set of directed links in the network. Each link completely records five core attribute parameters: length, free flow time, unit transportation cost, design capacity, and the mode it belongs to, providing complete basic data support for subsequent cost modeling and path generation; at the same time, multiple parallel multi-modal links are allowed to be set between the same starting and ending nodes, fully restoring the network characteristics of multi-modal parallelism between the same origin and destination in the intermodal transportation scenario and completely retaining the differential selection space of different transportation modes.

[0084] The multi-layer directed graph is formally expressed by the directed graph G := (N, A). In this embodiment, specifically, there are three urban centroid nodes A, B, and C, one railway hub node H1, and one inland river port hub node H2. The hub subset H = {H1, H2} ⊂ N, where H1 represents a railway freight hub with both railway marshalling and container loading / unloading functions, and H2 represents a port hub with the ability of water-road-rail intermodal transfer. The transportation mode set M = {highway, railway, waterway} covers all typical transportation modes in the regional intermodal transportation network.

[0085] Highway mode connection edges are set between the urban centroid nodes A, B, and C and the actual transportation network to represent the last mile collection and distribution links of the cargo from the departure place to the hub or from the hub to the destination. The introduction of the connection edges ensures the seamless connection between the starting and ending points and the actual physical transportation network, avoiding the loss of accessibility caused by the abstraction of the centroid.

[0086] In one embodiment, the effective candidate path set is defined as a loopless path that is always farther from the starting point and closer to the destination along the link travel direction; the Dial algorithm is used to search for all effective paths, and each path records the link sequence, hub sequence and mode sequence; the nested grouping is divided into the following four categories: the first category is pure road transport mode, the second category is pure rail transport mode, the third category is road-rail intermodal transport mode, and the fourth category is road-water intermodal transport mode.

[0087] Specifically, in this embodiment, the generation of the effective candidate path set follows strict topology screening criteria. An effective path is defined as an acyclic path that is always farther from the starting point and closer to the destination along the link's travel direction. This definition effectively eliminates unreasonable paths such as detours and backtracking, which are not adopted in actual freight decision-making, reducing the size of the candidate set and improving subsequent solution efficiency. Path search uses the Dial algorithm, which expands only along directions that increase the impedance from the node to the starting point and decrease the impedance to the destination, based on node labels, ensuring that every generated path is an effective acyclic path. Taking the OD pair A→B as an example, the starting point is the city centroid node A, and the destination is the city centroid node B. The network includes railway hub H1 and port hub H2. The Dial algorithm starts from node A, calculates the minimum impedance from each adjacent node to A and the minimum impedance to B, and only includes an adjacent node that satisfies the condition of "farther from A and closer to B" in the effective edge set, continuing the search forward. During this process, a node can be visited multiple times, but edges cannot be reused, thus traversing all link combinations that meet the conditions. Five candidate paths, r1 to r5, are ultimately generated. Each path fully records its link sequence, transshipment hub sequence, and transport mode sequence. After generation, the five paths are divided into four non-overlapping nested groups according to their mode sequences: path r1 is assigned to the pure road transport mode; path r2 to the pure rail transport mode; path r3 to the road-rail intermodal transport mode; and paths r4 and r5 to the road-water intermodal transport mode. This grouping provides a hierarchical framework for the subsequent calculation of mode selection probabilities under the nested Logit structure.

[0088] In one embodiment, the endogenous congestion cost is constructed using a BPR function, expressed as:

[0089]

[0090] in, Let a be the free-flow travel time of link a. For the freight volume of link a, Design capacity for link a, where α and β are preset parameters of the BPR function;

[0091] Hub transshipment costs are constructed using the Kingman formula, expressed as follows:

[0092]

[0093] in, These are the basic service efficiency parameters for the hub node h. For the processing of freight traffic at hub node h, The design throughput capacity of hub node h is given; the generalized cost of candidate path r is the sum of the operating costs of all links along the path and the transfer costs of all hubs it passes through, and the generalized cost is dynamically updated with the network freight traffic.

[0094] Specifically, in this embodiment, to address the core deficiency of existing static route selection models that treat transportation costs as exogenous and fail to capture the endogenous closed-loop feedback of freight "selection-congestion-reselection," a generalized cost function coupling dynamic congestion on links and rigid bottlenecks at hubs is constructed to achieve real-time dynamic updates of transportation costs based on network freight traffic. The endogenous congestion cost is constructed using the BPR function, with the expression:

[0095]

[0096] in, Let a be the free-flow travel time of link a. For the freight volume of link a, The design capacity for link 'a' is defined, with α and β being preset parameters for the BPR function. For highway scenarios, the recommended national standard values ​​of α=0.15 and β=4 are used; for railway and waterway links, these values ​​can be adjusted based on operational characteristics. This function accurately characterizes the non-linear growth characteristics of congestion delays caused by the scale effect of freight vehicles. When the link traffic approaches its design capacity, the travel time increases exponentially, perfectly conforming to the actual evolution of traffic flow.

[0097] Hub transshipment costs are constructed using the Kingman formula, expressed as follows:

[0098]

[0099] in, These are the basic service efficiency parameters for the hub node h. For the processing of freight traffic at hub node h, The design throughput capacity of hub node h is given; the generalized cost of candidate path r is the sum of the operating costs of all links along the path and the transfer costs of all hubs it passes through, and the generalized cost is dynamically updated with the network freight traffic.

[0100] This formula accurately reflects the rigid constraints of the transshipment capacity of multimodal transport hubs. When the hub's traffic volume approaches its design capacity, the transshipment waiting time increases dramatically, fully demonstrating the decisive impact of hub bottlenecks on transportation efficiency. The generalized cost of candidate path r is the sum of the operating costs of all links along the route and the transshipment costs of all hubs it passes through. It is dynamically updated with the network's freight traffic volume, fundamentally solving the problem of distorted cost estimation in traditional static models and providing a reliable cost basis for subsequent balanced traffic allocation.

[0101] In one embodiment, the path correlation penalty term based on the shared segment length ratio is expressed as:

[0102]

[0103] in, Let ω be the total length of the shared road segment between candidate path r and candidate path q under OD. , Let r and q be the total lengths of path r and path q, respectively; construct the path correlation coefficient for any two candidate paths r and q. , It can be determined by the normalized ratio of the length of the shared road segment between the two paths to the total length of the two paths;

[0104] Specifically, in this embodiment, to address the issue that the independent and identically distributed (IIA) assumption of the traditional multinomial Logit MNL model cannot characterize the distortion of substitution relationships caused by the high degree of overlap in multimodal transport routes, a path spatial correlation coefficient based on the shared segment length ratio is constructed. As the core calculation basis for the path correlation penalty term, it accurately quantifies the degree of physical overlap and spatial substitution correlation between any two candidate paths. The path correlation coefficient is constructed using a geometric mean normalization method, and its expression is:

[0105]

[0106] in Let ω be the total length of the shared road segment between candidate path r and candidate path q under OD. , Let r and q be the total lengths of paths r and q, respectively. Unlike traditional arithmetic mean normalization, the geometric mean method effectively eliminates the bias caused by differences in path lengths, avoiding misjudgment of high correlation when short and long paths share a small number of road segments, thus ensuring the objectivity and accuracy of the correlation coefficient calculation. The correlation coefficient is strictly limited to the range [0,1]: a value of 0 indicates that the two paths have no shared road segments and there is no spatial substitution relationship; the closer the value is to 1, the higher the physical overlap between the two paths, and the stronger the perceived substitution correlation for the freight owner. For example, two road-rail intermodal transport paths that share more than 80% of the urban collection and distribution links will have a correlation coefficient close to 0.9, and will be considered highly similar alternatives in the freight owner's decision-making.

[0107] In one embodiment, a pattern similarity penalty term is applied based on transit hub betweenness centrality weighting:

[0108]

[0109] Introducing the betweenness centrality of hub nodes As used in the calculation of weights, where , These are the sets of hub nodes that path r and path q pass through.

[0110] Specifically, in this embodiment, to address the core deficiency of existing path relevance correction methods that only focus on physical link overlap and cannot characterize the cross-dimensional similarity between hubs and modes in multimodal transport scenarios, a mode-aware similarity coefficient weighted by the betweenness centrality of transshipment hubs is constructed. This coefficient serves as the core calculation basis for the mode similarity penalty term, accurately quantifying the substitution relevance of any two candidate paths at the level of transshipment hub and mode combination. The expression for the mode-aware similarity coefficient is:

[0111]

[0112] Introducing the betweenness centrality of hub nodes As used in the calculation of weights, where , These are the sets of hub nodes that path r and path q pass through. The betweenness centrality of hub node h represents the degree of hub's transit core in the entire multimodal transport network. Its value is equal to the proportion of all shortest paths in the network that pass through the hub. This embodiment innovatively introduces betweenness centrality as a weight, rather than assigning the same weight to all hubs, which can accurately reflect the dominant role of core hubs in path similarity. The coefficient is strictly limited to the range of [0,1]: a value of 0 indicates that the two paths have no shared hubs and there is no substitution relationship at the mode level; the closer the value is to 1, the more core hubs the two paths share, and the higher the similarity of the mode combination. For example, two road-rail-water intermodal transport paths that use different railway trunk lines but share the core port hub of Shanghai Port can still have a mode similarity coefficient of over 0.5 even if the physical link overlap is low. This is something that traditional correction methods based solely on physical overlap cannot capture at all.

[0113] In one embodiment, based on the generalized path cost function and the multidimensional overlap penalty term, a multi-objective optimization model is constructed with the objectives of minimizing the total system cost, maximizing path selection entropy, minimizing road spatial correlation, and minimizing pattern similarity.

[0114] Minimize the total system link transportation cost:

[0115]

[0116] Minimize the overall hub transfer cost of the system:

[0117]

[0118] Introducing an entropy term to reflect the bounded rationality of decision-makers, the entropy of maximizing path selection is expressed as:

[0119]

[0120] Introducing a road spatial correlation criterion and utilizing a shared length matrix Penalizing physical overlap and minimizing road spatial correlation is expressed as:

[0121]

[0122] Introducing a pattern similarity criterion, utilizing centrality-based weights The hub competition term characterizes pattern correlation, and minimizing pattern similarity is expressed as:

[0123]

[0124] Where W is the set of OD pairs. Let be the set of candidate paths for OD to ω. For freight flow on path r, Let ω be the average freight flow rate for all paths within OD. For OD The total fixed freight demand.

[0125] Specifically, in this embodiment, to address the systemic shortcomings of existing multimodal transport route optimization models that only aim to minimize the cost of a single system and cannot simultaneously consider the bounded rationality of cargo owners, the correlation of route space, and the similarity of patterns, a multi-objective stochastic equilibrium optimization model containing five mutually coupled objectives is constructed based on a dynamic generalized route cost function and a multi-dimensional overlapping double penalty term, thereby achieving unified modeling of system efficiency, user behavior, and network characteristics.

[0126] Based on the generalized path cost function and the multidimensional overlap penalty term, a multi-objective optimization model is constructed with the objectives of minimizing the total system cost, maximizing path selection entropy, minimizing road spatial correlation, and minimizing pattern similarity.

[0127] Minimize the total system link transportation cost:

[0128]

[0129] Minimize the overall hub transfer cost of the system:

[0130]

[0131] Introducing an entropy term to reflect the bounded rationality of decision-makers, the entropy of maximizing path selection is expressed as:

[0132]

[0133] Introducing a road spatial correlation criterion and utilizing a shared length matrix Penalizing physical overlap and minimizing road spatial correlation is expressed as:

[0134]

[0135] Introducing a pattern similarity criterion, utilizing centrality-based weights The hub competition term characterizes pattern correlation, and minimizing pattern similarity is expressed as:

[0136]

[0137] Where W is the set of OD pairs. Let be the set of candidate paths for OD to ω. For freight flow on path r, Let ω be the average freight flow rate for all paths within OD. For OD The total fixed freight demand.

[0138] Objective function 1 aims to minimize the total system link transportation cost. This is achieved by accumulating the traffic-weighted operating costs of all links across the entire network, thus optimizing the overall efficiency of the trunk transportation link. The core principle is to incorporate the dynamic congestion cost calculated by the BPR function into the system cost accounting, rather than using static fixed costs. This ensures that the model can reflect the endogenous impact of freight traffic changes on link transportation efficiency in real time.

[0139] Objective function 2 aims to minimize the total hub transshipment cost of the system. By accumulating the flow-weighted transshipment costs of all hubs across the entire network, it achieves optimal overall efficiency in the transshipment process. Based on the Kingman formula, its dynamic bottleneck delay cost calculation accurately characterizes the decisive impact of the rigid constraints on the transshipment capacity of multimodal transport hubs on system costs, thus addressing the shortcomings of traditional models in characterizing the hub bottleneck effect.

[0140] Objective function 3 is to minimize the bounded rationality term based on maximum entropy, which is equivalent to maximizing the path selection entropy. It is used to characterize the bounded rationality and perceived randomness of cargo owners in complex decision-making environments. It breaks through the limitations of the traditional assumption of perfect rationality and makes the model more consistent with the information asymmetry and behavioral bias characteristics in actual freight decision-making.

[0141] Objective function 4 is to minimize the spatial correlation of roads. By weighting the spatial correlation coefficient of the paths, highly overlapping paths with traffic flow deviating from the average level are dynamically penalized, and the traffic distribution ratio of overlapping paths is automatically adjusted, which fundamentally solves the "red bus - blue bus" paradox caused by the IIA assumption of the traditional MNL model.

[0142] Objective function 5 is to minimize pattern similarity. By using the pattern similarity coefficient weighted by hub betweenness centrality, traffic penalties are imposed on paths sharing core hubs, which accurately characterizes the path competition relationship caused by hub bottlenecks. At the same time, it breaks through the constraints of the non-intersecting tree structure of the traditional nested Logit model and solves the problem of parameter unidentification caused by cross-nesting overlap.

[0143] In one embodiment, the improved expression for the nested fixed-point equation is:

[0144]

[0145] in, For path r, the fixed utility term, This is the cost sensitivity coefficient. Let r be the generalized cost. This is the penalty coefficient for road spatial correlation. This represents the pattern-aware similarity penalty coefficient.

[0146] Specifically, in this embodiment, to address the technical challenge of traditional stochastic user equilibrium models failing to simultaneously couple endogenous congestion feedback, path space correlation, and pattern-aware similarity, an improved nested fixed-point equation is derived using the first-order optimality condition of a multi-objective optimization model. This achieves a unified mathematical expression for the probability of multimodal freight route selection and the equilibrium flow, providing a core theoretical basis for subsequent iterative solutions. The expression of the improved nested fixed-point equation is as follows:

[0147] The improved expression for the nested fixed-point equation is as follows:

[0148]

[0149] in, For path r, the fixed utility term, This is the cost sensitivity coefficient. Let r be the generalized cost. This is the penalty coefficient for road spatial correlation. This represents the pattern-aware similarity penalty coefficient.

[0150] The core feature of this equation is that both its left and right sides contain endogenous path flow variables. This accurately describes the closed-loop feedback mechanism of this application.

[0151] In one embodiment, the steps of using the path flow obtained from the nested Logit model as an instrumental variable to replace the endogenous flow term on the right-hand side of the improved nested fixed-point equation, constructing an estimable maximum likelihood function, and calibrating the model parameters using the maximum likelihood estimation method include:

[0152] Construct a nested Logit model to calculate the initial traffic for each path. Treat it as an instrumental variable;

[0153] By replacing the endogenous flow term on the right-hand side of the nested fixed-point equation with instrumental variables, the endogeneity problem is transformed into an exogenous variable estimation problem.

[0154] Construct a likelihood function for path selection and update the model parameters using the maximum likelihood estimation method;

[0155] Repeat the above steps until the iterative convergence accuracy of the model parameters reaches the preset threshold, thus completing parameter estimation and significance testing.

[0156] Specifically, in this embodiment,

[0157] To address the parameter estimation bias caused by the inclusion of endogenous flow terms on the right-hand side of the improved nested fixed-point equation, an innovative approach combining instrumental variable substitution with maximum likelihood estimation was adopted to calibrate the model parameters. This fundamentally overcomes the estimation distortion caused by endogeneity and ensures that all core parameters are statistically significant and economically reasonable.

[0158] The first step is to construct a basic nested Logit NL model, which calculates the initial predicted flow for each route based on actual freight route selection observation data, and uses this as an instrumental variable. This instrumental variable is highly correlated with the endogenous flow term, reflecting the true distribution characteristics of the route flow, while being uncorrelated with the model's random error term, fully satisfying the requirements of instrumental variable validity and exogeneity.

[0159] The second step is to replace the endogenous flow term on the right side of the improved nested fixed-point equation with the aforementioned instrumental variables. This transforms the endogeneity estimation problem, which originally had a circular causal relationship, into a standard parameter estimation problem based on exogenous instrumental variables. This cuts off the endogenous loop and eliminates the parameter estimation bias caused by endogeneity.

[0160] The third step involves constructing a log-likelihood function for route selection based on actual observed freight route selection frequency data. A numerical optimization algorithm is then used to maximize this likelihood function, and core model parameters such as cost sensitivity coefficient, road spatial correlation penalty coefficient, and pattern-aware similarity penalty coefficient are updated.

[0161] Fourth, repeat the instrumental variable generation, endogenous term substitution, and parameter update steps mentioned above until the iterative convergence accuracy of the model parameters reaches the preset 0.01% threshold. After completing the parameter estimation, calculate the t-statistic and p-value of each parameter, and perform statistical significance testing to ensure that all core parameters are significant at a significance level of 5% or higher, and that the signs are in line with economic expectations.

[0162] In one embodiment, the step of iteratively solving the improved nested fixed-point equations until the path flow changes meet a preset convergence threshold, and outputting the final freight flow and transport mode share for each path, includes:

[0163] Initialize the initial freight flow for each path, and set the convergence threshold and maximum number of iterations;

[0164] Based on the current freight flow, calculate the congestion time of each link and the transfer time of each hub, and update the generalized cost of all candidate routes.

[0165] Based on the current path traffic, update the path space relevance aggregation value and the pattern-aware similarity aggregation value;

[0166] Substitute the improved nested fixed-point equation to calculate the selection probability of each path and the updated path flow;

[0167] Determine if the maximum difference in path traffic between two adjacent iterations is less than the convergence threshold. If so, stop the iteration and output the balanced path traffic and pattern sharing results. If not, return to initialization and continue iterating until the maximum number of iterations is reached.

[0168] Specifically, in this embodiment, to address the difficulty of directly solving the improved nested fixed-point equations due to endogenous variables, an iterative solution strategy combining the successive averaging method with dynamic step size is adopted. Through multiple iterations, the globally unique equilibrium solution is gradually approximated, ensuring the accuracy and computational efficiency of the flow allocation results.

[0169] The first step is to initialize the initial freight flow for each path, distributing the fixed freight demand of each OD pair evenly across all its candidate paths. Simultaneously, a convergence threshold of 1e-6 and a maximum number of iterations of 1000 are set. Uniform initialization avoids local optima caused by initial value deviations, and the preset parameters ensure both solution accuracy and prevent the occurrence of infinite iterations.

[0170] The second step involves summing the total freight volume of each link and the total processing volume of each hub based on the current iterative path traffic. These are then substituted into the BPR function and Kingman's formula to calculate the dynamic congestion time of each link and the dynamic transfer time of each hub, respectively, thereby updating the generalized cost of all candidate paths. This step is the core of achieving an endogenous closed-loop feedback mechanism of "selection-congestion-reselection," ensuring that cost calculations closely reflect the real-time network status.

[0171] The third step is to calculate the spatial correlation aggregation value and pattern-aware similarity aggregation value of each path with all other paths based on the current path traffic, so as to provide data support for the dynamic correction of path utility.

[0172] The fourth step involves substituting the updated generalized cost and correlation aggregation values ​​into the improved nested fixed-point equation to calculate the selection probability and auxiliary flow of each path. The path flow in the next round is updated using a dynamic step size of 1 / (k+1), which effectively improves the stability and convergence speed of the iteration process.

[0173] The fifth step is to determine whether the maximum absolute difference in path traffic between two adjacent iterations is less than the convergence threshold. If so, the iteration stops, and the freight traffic and transport mode share of each path in equilibrium are output. If the iterations do not converge and the maximum number of iterations has not been reached, the process returns to the cost update step to continue iterating. This process typically converges within 100-200 iterations, combining engineering feasibility with solution accuracy.

[0174] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0175] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0176] It should be particularly noted that, through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, or of course, by hardware. Based on this understanding, the above technical solutions, in essence or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0177] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for optimizing multimodal freight routes driven by endogenous congestion and multidimensional overlap, characterized in that, Includes the following steps: Step S1: Construct a multimodal freight hypernetwork model. The hypernetwork model includes a multi-layered directed graph consisting of highways, railways, waterways, and connecting links. The nodes in the multi-layered directed graph include transportation hub nodes and urban centroid nodes. The attributes of the links include free-flow time, design capacity, and the mode of transport to which they belong. Step S2: For each origin-destination OD pair, the Dial algorithm is used to generate a set of valid candidate routes from the origin to the destination, and the candidate route set is divided into four non-overlapping nested groups according to the transportation mode contained in the link: pure road, pure rail, road-rail intermodal transport, and road-water intermodal transport. Step S3: Establish a generalized path cost function, which includes the endogenous congestion cost dynamically related to link traffic and the hub transfer cost dynamically related to hub transfer volume, wherein the endogenous congestion cost is calculated based on the BPR function and the hub transfer cost is calculated based on the Kingman queuing model. Step S4: Construct a multidimensional overlap penalty term reflecting the competitive relationship between candidate paths. The multidimensional overlap penalty term includes a path correlation penalty term based on the shared segment length ratio and a pattern similarity penalty term weighted by the betweenness centrality of transit hubs. Based on the generalized path cost function and the multidimensional overlap penalty term, construct a multi-objective optimization model with the objectives of minimizing the total system cost, maximizing path selection entropy, minimizing road spatial correlation, and minimizing pattern similarity. Step S5: Based on the first-order optimality condition of the multi-objective optimization model, derive the improved nested fixed-point equation for path flow; use the path flow obtained by the nested Logit model as an instrumental variable to replace the endogenous flow term on the right side of the improved nested fixed-point equation, construct an estimable maximum likelihood function, and use the maximum likelihood estimation method to calibrate the model parameters. Step S6: Based on the calibrated model parameters, iteratively solve the improved nested fixed-point equation until the path flow change meets the preset convergence threshold, and output the final freight flow and transportation mode for each path.

2. The method according to claim 1, characterized in that, In step S1, the multi-layer directed graph is represented by a directed graph G:=(N,A), where N is the set of network nodes, H⊂N is the set of multimodal transport hubs, which includes railway hubs, inland dry port hubs, and port hubs; M is the set of transport modes, M={road, rail, water transport}; and road connection edges are set between the city centroid and each transport mode network to represent the terminal collection and distribution links. Each link in link set A records attribute parameters such as length, free flow time, unit transportation cost, design capacity, and mode. Parallel multi-mode links are allowed between the same start and end nodes.

3. The method according to claim 1, characterized in that, In step S2, the effective candidate path set is defined as a loopless path that is always farther from the starting point and closer to the destination along the link travel direction; the Dial algorithm is used to search for all effective paths, and each path records the link sequence, hub sequence and mode sequence; the nested grouping is divided into the following four categories: the first category is pure road transport mode, the second category is pure rail transport mode, the third category is road-rail intermodal transport mode, and the fourth category is road-water intermodal transport mode.

4. The method according to claim 1, characterized in that, In step S3, the endogenous congestion cost is constructed using the BPR function, and its expression is: ； in, Let a be the free-flow travel time of link a. For the freight volume of link a, Design capacity for link a, where α and β are preset parameters of the BPR function; Hub transshipment costs are constructed using the Kingman formula, expressed as follows: ； in, These are the basic service efficiency parameters for the hub node h. For the processing of freight traffic at hub node h, The design throughput capacity of hub node h is given; the generalized cost of candidate path r is the sum of the operating costs of all links along the path and the transfer costs of all hubs it passes through, and the generalized cost is dynamically updated with the network freight traffic.

5. The method according to claim 1, characterized in that, In step S4, the path correlation penalty term based on the shared segment length ratio is expressed as: ； in, Let ω be the total length of the shared road segment between candidate path r and candidate path q under OD. , Let r and q be the total lengths of path r and path q, respectively; construct the path correlation coefficient for any two candidate paths r and q. , It can be determined by the normalized ratio of the length of the shared road segment between the two paths to the total length of the two paths.

6. The method according to claim 1, characterized in that, In step S4, a pattern similarity penalty term based on the betweenness centrality of transit hubs is applied: ； Introducing the betweenness centrality of hub nodes As used in the calculation of weights, where , These are the sets of hub nodes that path r and path q pass through.

7. The method according to claim 1, characterized in that, In step S5, based on the generalized path cost function and the multidimensional overlap penalty term, a multi-objective optimization model is constructed with the objectives of minimizing the total system cost, maximizing path selection entropy, minimizing road spatial correlation, and minimizing pattern similarity. Minimize the total system link transportation cost: ； Minimize the overall hub transfer cost of the system: ； Introducing an entropy term to reflect the bounded rationality of decision-makers, the entropy of maximizing path selection is expressed as: ； Introducing a road spatial correlation criterion and utilizing a shared length matrix Penalizing physical overlap and minimizing road spatial correlation is expressed as: ； Introducing a pattern similarity criterion, utilizing centrality-based weights The hub competition term characterizes pattern correlation, and minimizing pattern similarity is expressed as: ； Where W is the set of OD pairs. Let be the set of candidate paths for OD to ω. For freight flow on path r, Let ω be the average freight flow rate for all paths within OD. For OD The total fixed freight demand.

8. The method according to claim 1, characterized in that, In step S6, the improved expression for the nested fixed-point equation is as follows: ； in, For path r, the fixed utility term, This is the cost sensitivity coefficient. Let r be the generalized cost. This is the penalty coefficient for road spatial correlation. This represents the pattern-aware similarity penalty coefficient.

9. The method according to claim 1, characterized in that, In step S5, the process of using the path flow obtained from the nested Logit model as an instrumental variable to replace the endogenous flow term on the right-hand side of the improved nested fixed-point equation, constructing an estimable maximum likelihood function, and calibrating the model parameters using the maximum likelihood estimation method includes: Construct a nested Logit model to calculate the initial traffic for each path. Treat it as an instrumental variable; By replacing the endogenous flow term on the right-hand side of the nested fixed-point equation with instrumental variables, the endogeneity problem is transformed into an exogenous variable estimation problem. Construct a likelihood function for path selection and update the model parameters using the maximum likelihood estimation method; Repeat the above steps until the iterative convergence accuracy of the model parameters reaches the preset threshold, thus completing parameter estimation and significance testing.

10. The method according to claim 1, characterized in that, Step S6, which involves iteratively solving the improved nested fixed-point equation until the path flow change meets a preset convergence threshold, and then outputting the final freight flow and transport mode share for each path, includes: Initialize the initial freight flow for each path, and set the convergence threshold and maximum number of iterations; Based on the current freight flow, calculate the congestion time of each link and the transfer time of each hub, and update the generalized cost of all candidate routes. Based on the current path traffic, update the path space relevance aggregation value and the pattern-aware similarity aggregation value; Substitute the improved nested fixed-point equation to calculate the selection probability of each path and the updated path flow; Determine if the maximum difference in path traffic between two adjacent iterations is less than the convergence threshold. If so, stop the iteration and output the balanced path traffic and pattern sharing results. If not, return to initialization and continue iterating until the maximum number of iterations is reached.

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