Freight train opening scheme and freight rate collaborative optimization method based on bounded rationality behaviors

Abstract

The invention provides a freight train opening scheme and freight rate collaborative optimization method based on a finite rationality behavior. The method comprises the steps of obtaining a utility coefficient and a foreground theoretical parameter which influence a shipper decision-making behavior; coding particle positions by using a freight rate discount coefficient, a cargo volume area discontinuity point and railway transportation time, and initializing a particle swarm; calculating a foreground value of each particle by using a finite rationality cargo quantity distribution model with operation income maximization as a target, and outputting distribution cargo quantity and railway operation income; inputting the distributed cargo quantity into a freight train operation scheme compilation model taking the operation cost minimization as a target, and outputting the railway transportation time and a freight train operation scheme by using a CPLEX solver; and feeding back the railway transportation time to the finite rationality cargo quantity distribution model, updating the position of each particle by taking the railway operation income as the particle fitness, and outputting a freight train operation scheme until the maximum income is reached. According to the method, the operation and income level can be integrally optimized while the demand prediction accuracy can be remarkably improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of railway freight organization optimization, and particularly relates to a freight train formation scheme and freight rate collaborative optimization method based on limited rational behavior. BACKGROUND

[0002] In the technical field of railway freight organization optimization, the freight train formation scheme (including formation frequency, marshalling quantity and time arrangement, etc.) is the core basis for organizing transportation production, and its scientificity and rationality is directly related to the operation benefit and market competitiveness of the railway.

[0003] At present, the formulation of the railway freight train formation scheme mostly relies on historical operation data, industry expert experience and mathematical programming models with the target of minimizing railway cost. This kind of method is essentially a "supply-oriented" or "operation-oriented" freight organization optimization idea. However, the freight demand is not fixed, but is determined by the shippers after selecting different freight lines and schemes according to the transportation time, freight rate and other freight service attributes. The transportation path selection behavior of the shippers directly determines the actual freight demand that the railway can obtain, and is a key market factor affecting the economic benefit and operation efficiency of the train formation scheme.

[0004] The existing patent technologies mainly optimize the train formation scheme from the following aspects: train formation scheme compilation technology, dynamic adjustment and automatic generation technology of the running diagram, which focuses on the optimization target of operation efficiency, evaluation and optimization method of the fixed freight formation scheme, and work optimization solution in the marshalling station. Although the above existing technologies have made progress in their respective directions, they have not solved the fundamental problem of collaborative decision-making of the freight demand side (shippers' behavior) and the supply side (formation scheme and pricing). The technical limitations mainly lie in the following two aspects: Firstly, in the aspect of behavior modeling, the existing methods have defects in modeling the path selection behavior of the shippers. The traditional discrete choice model is generally based on the idealized assumption of "completely rational person", assuming that the shippers can accurately perceive the objective utility of all paths and make utility maximization decisions. However, in practice, the shippers are influenced by factors such as information asymmetry and risk preference, and their decision-making behavior shows significant characteristics of limited rationality. Ignoring this realistic psychology leads to systematic deviation between the freight volume predicted based on the traditional model and the actual situation, and the formation scheme formulated accordingly is difficult to accurately match the real market demand from the root.

[0005] Secondly, in the system optimization level, the existing technology generally adopts the step-by-step or isolated optimization paradigm. Usually, the train operation scheme (dominant transport service attribute) and the freight rate strategy are optimized separately as two independent decision-making links. However, the transport time and the freight rate jointly constitute the core basis for the consignor's selection behavior, and they are deeply coupled and mutually restricted. The separate optimization leads to the difficulty in balancing the "operation cost-service level-market revenue", and it is impossible to maximize the comprehensive benefits of the railway while meeting the diversified market demand. SUMMARY

[0006] Therefore, the purpose of the present application is to provide a freight train operation scheme and freight rate collaborative optimization method based on bounded rational behavior, which can significantly improve the demand prediction accuracy and enhance the market competitiveness of freight products, while optimizing the operation and revenue level as a whole.

[0007] The present application provides a freight train operation scheme and freight rate collaborative optimization method based on bounded rational behavior, comprising: S1, collecting the freight transport demand information, path and operation related information in the planning period, and obtaining the utility coefficient and prospect theory parameters affecting the consignor's decision-making behavior; S2, setting the freight rate discount coefficient, freight volume interval breakpoint and railway transport time as the first decision variable, using the first decision variable to encode the particle position, and initializing the particle swarm; S3, based on the first decision variable of each particle, using the bounded rational freight volume distribution model with the goal of maximizing the operation revenue to calculate the prospect value of each particle, and outputting the distributed freight volume and the corresponding railway operation revenue; S4, setting the train operation frequency, the number of marshalling vehicles and the arrival and departure time of each station as the second decision variable, and inputting the distributed freight volume into the freight train operation scheme compilation model with the goal of minimizing the operation cost, using the CPLEX solver to output the railway transport time and the corresponding freight train operation scheme; S5, feeding back the railway transport time to the bounded rational freight volume distribution model, taking the railway operation revenue as the particle fitness, updating the particle position based on the inertia of its own motion, the individual optimal position and the group optimal position, until the maximum revenue is reached, and outputting the freight train operation scheme.

[0008] Further, the freight transport demand information in the planning period at least includes: freight batch, transport demand, origin and destination information, applicable railway benchmark freight rate; The path and operation related information at least includes: the composition of each selectable path, the transport time and freight rate of highway and waterway, the stations on the path, the alternative train operation line, the technical operation time standard of each station, and the train operation cost parameters.

[0009] Further, the utility coefficient and the prospect theory parameter affecting the decision-making behavior of the shipper are obtained in the following manner: A virtual transportation scenario with different combinations of freight rates and transportation time is designed, the shipper is asked to make a route selection, and the freight rate utility coefficient and the transportation time utility coefficient affecting the decision-making behavior of the shipper are calibrated by analyzing historical operation data or market survey data; An experiment including a risk decision task is designed to observe the selection behavior of the shipper under uncertainty by using the experimental economics method, the prospect theory parameters affecting the decision-making behavior of the shipper, i.e., the risk sensitivity coefficient, the loss aversion coefficient and the probability distortion coefficient, are back-calculated by fitting the experimental data and the prospect theory model and using the nonlinear least square or maximum likelihood estimation method.

[0010] Further, the limited rationality freight volume allocation model of S3 is constructed in the following manner: S31, based on the first decision variable of each particle and the utility coefficient affecting the decision-making behavior of the shipper, the objective utility of each route to the shipper is calculated to obtain a utility reference point, and based on the prospect theory parameters, the cumulative prospect of each route is calculated, and a limited rationality freight volume allocation model is constructed with the goal of maximizing railway operation revenue.

[0011] Further, S31 specifically includes: S311, based on the interval freight rate discount coefficient and the freight volume interval breakpoint, a segmented linear function relationship between the discounted railway freight rate and the allocated freight volume is established, and the constraint that the railway freight rate decreases with the increase of the allocated freight volume and the discounted railway freight rate is within the specified allowable floating range is set; S312, based on the railway transportation time, the full-route freight rate and transportation time of each route including the highway, railway and waterway transportation modes are calculated, and based on the utility coefficient affecting the decision-making behavior of the shipper, the objective utility of each route to the decision-making behavior of the shipper is calculated to obtain a utility reference point; S313, based on the prospect theory parameters affecting the decision-making behavior of the shipper, the subjective utility and the subjective selection probability of each route to the decision-making behavior of the shipper are calculated through the nonlinear value function and the probability weight function to obtain the cumulative prospect of each route, and the all-or-nothing allocation mechanism is used to allocate all the freight volume of each batch of goods to the transportation route with the highest prospect value; S314, considering the limited rationality of the shipper, a limited rationality freight volume allocation model is constructed with the goal of maximizing railway operation revenue.

[0012] Further, the freight train formation scheme compilation model of S4 is constructed in the following manner: S41, set 0 / 1 decision variables to constrain the operation line selection, and based on the second decision variable of each particle, respectively establish the outflow constraint of the starting station, the inflow constraint of the terminal station, the flow balance constraint of the intermediate station, and the connection time constraint of the train at the station, to ensure that the train operation scheme is feasible and economical; S42, establish transportation time limit constraint, minimum load rate constraint, and maximum load constraint, to ensure that the train operation scheme meets the service requirements and physical limitations; S43, take the allocated load as input, based on the fixed cost of train operation and the reorganization operation cost of the station, establish a freight train operation scheme programming model with the minimum railway operation cost as the target under various operation condition constraints.

[0013] The freight train operation scheme based on limited rational behavior and the freight price collaborative optimization method provided by the application have the following beneficial effects: (1) The demand prediction accuracy is significantly improved. By using the limited rational load allocation model based on prospect theory, the inherent prediction bias of the traditional "complete rationality" assumption model is effectively overcome, thereby significantly improving the accuracy of freight demand prediction, and providing scientific and reliable market data support for the formulation of the freight train operation scheme; (2) The market competitiveness of the freight product is enhanced. By constructing a double-layer collaborative optimization mechanism of the freight train operation scheme and the freight price strategy, the target conflict problem caused by the separate optimization of the two is solved, and a freight product that is comprehensive optimal in terms of transportation service level and freight price strategy can be generated, thereby effectively enhancing the market competitiveness; (3) The operation and revenue level are overall optimized. By establishing a joint decision feedback loop, efficient and self-adaptive matching of the transport capacity resource allocation and market demand is realized, thereby significantly improving the overall revenue level of railway freight under the premise of ensuring the operation feasibility. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 A flowchart of the freight train operation scheme based on limited rational behavior and the freight price collaborative optimization method provided by the embodiment of the application is shown; Figure 2 A transportation network structure and shipper transportation path selection schematic diagram provided by the embodiment of the application is shown; Figure 3 A decision weight and prospect value diagram of the prospect theory provided by the embodiment of the application is shown; Figure 4 A joint optimization schematic diagram of the freight train operation scheme and the freight price discount provided by the embodiment of the application is shown. DETAILED DESCRIPTION

[0015] To make the objectives, technical solutions, and advantages of this technical solution clearer, the following detailed description, in conjunction with specific embodiments, further illustrates this technical solution. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of this technical solution. Example 1

[0016] Please see as follows Figure 1 The flowchart shown illustrates a freight train operation plan and freight rate co-optimization method based on bounded rationality behavior. Figure 1 As shown, the method includes: S1. Collect information on cargo transportation demand, routes, and operation information during the planning period, as well as obtain utility coefficients and prospect theory parameters that influence shippers' decision-making behavior.

[0017] The freight transport demand information during the planning period includes at least: freight batches, transport demand volume, origin and destination information, and applicable railway benchmark freight rates; the route and operation-related information includes at least: the composition of each optional route, the transport time and freight rates of road and waterway, the stations along the route, alternative train operating lines, the technical operation time standards of each station, and train operation cost parameters.

[0018] In practical implementation, the utility coefficients and prospect theory parameters that influence shippers' decision-making behavior can be obtained through the following methods: Design virtual transportation scenarios with different combinations of freight rates and transportation times, ask shippers to choose routes, and through analysis of historical operating data or market survey data, identify the freight rate utility coefficient and transportation time utility coefficient that affect shippers' decision-making behavior.

[0019] Using experimental economics methods, experiments involving risk decision-making tasks were designed to observe shippers' choice behavior under uncertainty. By fitting experimental data and prospect theory models, nonlinear least squares or maximum likelihood estimation methods were used to deduce the prospect theory parameters that affect shippers' decision-making behavior: risk sensitivity coefficient, loss aversion coefficient, and probability bias coefficient.

[0020] Here, a questionnaire survey can be used to investigate shipper behavior and characterize key parameters of shipper decision-making. To improve the efficiency and applicability of the method, other methods can also be used to obtain the above parameters. These parameters can be determined by backfitting based on historical operating data, or by directly using typical parameter values ​​that have been validated in the industry. This application does not impose any limitations on these methods. Furthermore, the above parameters can be dynamically updated based on actual operating data to enable the technical solution of this application to have adaptive optimization capabilities.

[0021] S2, set the freight rate discount coefficient, the freight volume interval breakpoint and the railway transportation time as the first decision variable, encode the particle position using the first decision variable, and initialize the particle swarm.

[0022] In this step, the application is expected to use a particle swarm optimization algorithm embedded in a CPLEX solver to solve the coupled finite rationality freight volume distribution model and the freight train formation model. Among them, the particle swarm optimization algorithm is responsible for intelligent search of the first decision variable in the global range, and the particle position is encoded by the first decision variable. This encoding method can uniformly map the nonlinear decision variable (freight rate discount coefficient, freight volume interval breakpoint) and railway transportation time to the particle search space, so that the particle swarm optimization algorithm can represent the whole collaborative optimization system for global exploration.

[0023] As an example, the particle encoding table is as follows: in particle 1, the freight volume less than 20 corresponds to the freight rate discount coefficient of 0.95, the freight volume interval of 20-30 corresponds to the freight rate discount coefficient of 0.9, and the freight volume interval of 50-75 corresponds to the freight rate discount coefficient of 0.8; the railway transportation time of freight 1 is 120h, and the railway transportation time of freight 2 is 70h.

[0024] Table 1, particle encoding table

[0025] S3, based on the first decision variable of each particle, the prospect value of each particle is calculated by using the finite rationality freight volume distribution model with the goal of maximizing the operating income, and the distribution freight volume and the corresponding railway operating income are output.

[0026] In specific implementation, the finite rationality freight volume distribution model can be constructed in the following way: S31, based on the first decision variable of each particle and the utility coefficient affecting the decision behavior of the shipper, the objective utility of each path to the shipper is calculated to obtain the utility reference point, and based on the prospect theory parameters, the cumulative prospect of each path is calculated to construct the finite rationality freight volume distribution model with the goal of maximizing the railway operating income.

[0027] In this step, a shipper path selection behavior model is constructed based on the prospect theory in behavioral economics to replace the complete rationality assumption in traditional theory. This model identifies the perceived gains and losses of shippers to different path schemes by setting a transportation utility reference point, uses a value function to depict the psychological characteristics of loss aversion and decreasing sensitivity, and uses a probability weight function to correct the subjective cognitive bias of the objective probability. Finally, by calculating the cumulative prospect value of each path, based on the deterministic decision-making characteristics of large shippers under limited rationality, all the freight volume is allocated to the path with the highest prospect value, thereby outputting the determined distribution freight volume result.

[0028] Specifically comprising the following steps: S311, based on the interval freight discount coefficient and the freight volume interval breakpoint, establishing a segmented linear function relationship between the discounted railway freight and the allocated freight volume, and a constraint that the railway freight decreases with the increase of the allocated freight volume, and the discounted railway freight is within the specified allowed floating range.

[0029] The railway freight is calculated as follows: ;

[0030] In the formula, is the railway base price one of the freight ; is the railway base price two of the freight ; is the railway mileage of the freight ; is the set of freight; The constraint that the long-distance freight is higher than the short-distance freight is: ; In the formula, is the railway freight of the freight ; is the railway freight of the freight ; is the railway mileage of the freight ; The continuous segmented function between the discounted railway freight and the allocated freight volume is established as: ; In the formula, is the discounted railway freight of the freight ; is the allocated freight volume of the freight, decision variable is the freight discount coefficient of the interval ; is the quantity discount breakpoint of the freight volume interval ; is the set of freight discount; The constraint that the more the allocated freight volume, the greater the railway freight discount is: ; According to the freight adjustment range of the highest 15% floating, the discounted railway freight is limited as follows: ; In the formula, is the minimum discount requirement of the railway freight.

[0031] ​Here, a piecewise linear price discount function is introduced as a linkage mechanism. This function uses the allocation of freight volume ranges and the corresponding freight rate discount coefficients as core decision variables, and incorporates pricing rule constraints to ensure that the discounted freight rates comply with railway operation policies. By dynamically adjusting freight rate discounts, the market attractiveness of railway services and freight volume allocation are directly affected.

[0032] S312. Based on railway transportation time, calculate the total freight rate and transportation time for each route, including road, rail, and waterway transportation. Then, based on the utility coefficients that affect the shipper's decision-making behavior, calculate the objective utility of each route on the shipper's decision-making behavior to obtain a utility reference point.

[0033] Calculate the total freight cost including road, rail, and waterway transportation: ; In the formula, For goods The total freight rate For goods Highway freight rates, For goods Waterway freight rates; Calculate the total transportation time, including road, rail, and waterway transport: ; In the formula, For goods The total transportation time For goods Road transport time, decision variables For goods The railway transport time is determined by the train operation plan development model. For goods Waterway transportation time; Calculate the objective utility of each route on shippers' decision-making behavior under the influence of freight rates and transit time: ; In the formula, For goods The objective utility of its own path, This is the freight utility coefficient. This is the transportation time utility coefficient. The random utility coefficients of the discrete choice model follow an independent and identically distributed Gumbel distribution, and are used to characterize the degree of randomness of unobserved factors in the shipper's decision-making. Calculate the objective probability of shippers' decision-making behavior for each route under the influence of freight rates and transit time: ; In the formula, for the goods the objective selection probability of the path, representing an exponential function, for the goods for other paths the objective utility of the path (label 0 represents the self-path), for the set of paths; calculate the average value of the objective utility of all paths to the decision-making behavior of the shipper as the utility reference point: ; wherein, for the goods the utility reference point.

[0034] Here, the railway transportation time from the freight train formation scheme output is received to form a complete freight service product together with the freight rate. The freight rate, freight volume, and formation scheme form a synergistic optimization loop with bidirectional coupling and closed-loop feedback, realizing the dynamic balance of market response and transport supply.

[0035] S313, based on the prospect theory parameters affecting the decision-making behavior of the shipper, the subjective utility and subjective selection probability of each path to the decision-making behavior of the shipper are calculated through a nonlinear value function and a probability weight function, to obtain the cumulative prospect of each path, and a whole-or-nothing allocation mechanism is adopted to allocate all the freight volume of each batch of goods to the transportation path with the highest prospect value.

[0036] Calculate the gain or loss value of each path compared to the utility reference point: ; wherein, for the goods for other paths the utility gain or loss value of the path (label 0 represents the self-path); Based on the gain or loss of each path, the subjective utility of each path to the decision-making behavior of the shipper is calculated: ; wherein, for the goods for the path the subjective utility obtained by the value function, the risk sensitivity coefficient affecting the decision-making behavior of the shipper, the loss aversion coefficient; According to the gain or loss of each path, the subjective selection probability of each path to the decision-making behavior of the shipper is calculated: ; wherein, for the goods subjective selection probability of path , objective selection probability of path , probability offset coefficient; based on the subjective utility and the subjective selection probability of each path to the shipper's decision-making behavior, the cumulative prospect of each path is calculated: ; wherein, prospect value of path for goods ; The "all-or-nothing" allocation mechanism is adopted to allocate the entire transport volume of each batch of goods to the transport path with the highest cumulative prospect: ; wherein, allocated goods volume of path for goods

[0037] Here, the "all-or-nothing" allocation mechanism is mainly considered for railway freight transport, which has large single transport volume, strong planning, and shippers are mostly large shippers who need to make a unique decision. Therefore, the "all-or-nothing" allocation mechanism is actually a direct simulation of the unique deterministic path selection behavior of large shippers under bounded rationality. This mechanism is consistent with the actual behavior logic and can provide stable freight flow input for the freight train formation scheme programming model, effectively ensuring the solvability and stability of the mixed integer programming solution.

[0038] S314, considering the limited rationality of shippers, a freight allocation mechanism is adopted to maximize the railway operating revenue and build a bounded rationality freight allocation model.

[0039] The bounded rationality freight allocation model is: ; wherein, railway operating revenue, the product of the allocated freight volume of all goods and the railway freight rate, railway operating cost determined by the freight train formation scheme programming model.

[0040] S4, set the train formation frequency, the number of cars in the train formation, and the arrival and departure time of each station as the second decision variable, and input the allocated freight volume into the freight train formation scheme programming model with the objective of minimizing the operating cost, and use the CPLEX solver to output the railway transport time and the corresponding freight train formation scheme.

[0041] ​In this step, the CPLEX solver is responsible for fine evaluation of each search point given by the particle swarm optimization algorithm. The freight train formation model takes the allocated freight volume from the upper model as the core input, integrates the flow conservation constraint, station operation capacity constraint, train connection constraint, and load capacity constraint, etc., so as to generate a technically feasible and economically optimal train formation scheme under the premise of meeting all the operation conditions. The transport time determined by the scheme will be fed back to the upper model as a key service parameter.

[0042] In specific implementation, the freight train formation model can be constructed in the following manner: S41, set 0 / 1 decision variables to constrain the selection of running lines, and based on the second decision variables of each particle, establish the outflow constraint of the starting station, the inflow constraint of the terminal station, the flow balance constraint of the intermediate station, and the connection time constraint of the train at the station, so as to ensure the feasibility and economy of the formation scheme.

[0043] The outflow constraint of the starting station is established as follows: ; In the formula, is a 0 / 1 decision variable, which is used to decide whether the freight is selected to run on the line , and if the line is selected, , is the set of stations on the path, is the set of arrival running lines of the station , is the set of departure running lines of the station ; The inflow constraint of the terminal station is established as follows: ; According to the same batch of freight when passing through the intermediate station, the departure and arrival running lines must be matched at the same time, and the flow balance constraint of the intermediate station is established as follows: ; According to the difference between the departure time and the arrival time satisfying the minimum technical operation time standard, the connection time constraint of the train at the station is established as follows: ; In the formula, is the departure time of the running line , is the arrival time of the running line , is the minimum technical operation time standard of the station .

[0044] S42, establish a transport time limit constraint, a minimum load constraint, and a maximum load constraint to ensure that the train scheduling scheme meets service requirements and physical limitations.

[0045] To reserve a reasonable buffer on the basis of the arrival time of goods determined by the running line to meet the overall time requirement, the transport time limit constraint is established as: ; In the formula, is the time margin of railway transportation, is the departure station arrival time of the goods ; To ensure that the selected running line meets the minimum load requirement, the minimum load constraint is established as: ; In the formula, is the maximum number of groupings, is the load limit; The total amount of goods carried by any running line must not exceed its rated load capacity, and the maximum load constraint is established as: .

[0046] S43, taking the allocated load as input, under various operating condition constraints, a train scheduling scheme preparation model is established based on the fixed cost of train operation and the reorganization operation cost of the station, with the goal of minimizing railway operation cost.

[0047] The freight train scheduling scheme preparation model is: ; In the formula, is the railway operation cost, is the fixed cost of the running line , is the unit reorganization operation cost of the station .

[0048] It is worth noting that the limited rational load allocation model (referred to as the upper model) and the freight train scheduling scheme preparation model (referred to as the lower model) constructed in this application are bi-level programming models. Due to its unique structure, it faces significant solution challenges: the upper model presents strong non-linear characteristics due to the inclusion of the non-linear value function and probability weight function in prospect theory, and the lower model is a typical mixed integer linear programming problem; at the same time, there is a close coupling relationship between the upper and lower layers, the pricing decision of the upper model directly affects the load input of the lower model, and the transport time result output by the lower model also reacts to the decision-making process of the upper layer. The complex structure of "non-linear-linear" mixing and bidirectional dependence makes it difficult for traditional optimization methods to directly and efficiently solve it.

[0049] To overcome this technical challenge, this application designs a particle swarm optimization (PSO) algorithm embedding a CPLEX planner. The core of this algorithm lies in transforming the complex two-layer coupled problem into an iterative process where PSO and CPLEX work collaboratively: PSO acts as an "upper-level model explorer," responsible for intelligently searching for upper-level nonlinear decision variables globally; for each set of decisions, it solidifies them as parameters and calls CPLEX as a "lower-level model evaluator" to accurately solve the corresponding lower-level mixed-integer programming problem. Finally, the lower-level optimal solution returned by CPLEX (such as operating cost) is fed back to PSO as a direct basis for evaluation and optimization decisions. Through this deep collaborative mechanism, efficient exploration of the solution space is achieved, thereby overcoming the core problem of collaborative optimization.

[0050] S5. Feed the railway transportation time back to the bounded rationality freight volume allocation model, and use the railway operation revenue as the particle fitness. Update the position of each particle based on its own motion inertia, individual optimal position and group optimal position until the maximum revenue is reached, and output the freight train operation plan.

[0051] In this step, care must be taken to ensure that the update speed does not exceed the limit when updating the positions of each particle.

[0052] In practice, particle positions can be updated in the following ways: ; In the formula, For the first The particle in the first The speed of each iteration For the first The particle in the first The speed of each iteration The inertial factor that allows particles to maintain their own motion. The learning factor is used to move towards the individual's optimal position and the group's optimal position. A random number in the range [0,1]. This represents the optimal position of an individual. For the first The particle in the first The position of the next iteration. Indicates the optimal position of the group; ; In the formula, For the first The particle in the first The position of the next iteration.

[0053] The specific values of the inertia weight, learning factor and other control parameters in the above formula can be set and adjusted according to the characteristics and size of the actual optimization problem, and the parameter tuning process belongs to the range of common knowledge and routine debugging in the technical field.

[0054] The first decision variable is adjusted and optimized by updating the particle position. When the termination condition is reached, the approximate optimal solution corresponding to the population optimal position is output. The solution contains the optimal freight discount strategy and the train formation scheme, which embodies the final result of the collaborative optimization of the present application.

[0055] The particle swarm optimization (PSO) algorithm embedded with the CPLEX planner designed in the present application forms a closed-loop feedback through the following data flow: the dynamically adjusted freight discount (discounted freight) is taken as input to affect the prediction result (allocated freight) of the bounded rational freight allocation model; the allocated freight is taken as input to drive the generation of the train formation scheme; the transportation time parameter output by the scheme is taken as input to feedback to the freight discount adjustment strategy and the bounded rational freight allocation model for the next round of optimization iteration.

[0056] Embodiment two: Please refer to the transport network structure and shipper transport path selection diagram as shown in Figure 2 . Figure 2 The transport network structure to which the method of the present application is applied is shown. In the transport network, public water intermodal transport (P1, P5), public rail intermodal transport (P2) and highway transport (P3, P4) jointly constitute multiple complete paths, forming the path selection set of shippers. The bounded rational freight allocation model of the present application is based on this network topology to analyze the selection behavior of shippers among the paths, and the output is the allocated freight predicted to select the railway path (railway transport or public rail intermodal transport). The figure clearly defines the input scenario and problem boundary of the technical solution of the present application.

[0057] Please refer to the decision weight and prospect value diagram of prospect theory as shown in Figure 3 . Figure 3 The working principle of the bounded rational freight allocation model, which is the core of the present application, is explained. The diagram specifically depicts the key components of the prospect theory: the value function describes the loss aversion and decreasing sensitivity psychological characteristics of shippers through its S-shaped curve; the probability weight function reflects the subjective cognitive bias of shippers to objective probability through its inverse S-shaped curve. The diagram illustrates how the present application converts the traditional objective utility calculation into a more realistic subjective prospect value calculation by introducing the prospect theory, thereby accurately quantifying the bounded rational decision-making behavior.

[0058] Please refer to the joint optimization diagram of the train formation scheme and the freight discount as shown in Figure 4 . Figure 4The freight train formation scheme and the freight price coordination optimization mechanism realized by the application are shown. The left part of the figure discloses a closed loop feedback loop formed among the freight price discount coordination optimization method, the bounded rationality freight volume distribution model and the freight train formation scheme compilation model. The closed loop feedback loop is the core architecture for realizing the freight train formation scheme and the freight price coordination optimization, and is one of the key innovations of the application. The right part of the figure provides an exemplary train working diagram, and specifically shows the output result of the freight train formation scheme compilation model, which contains train arrival and departure time arrangement satisfying the station operation capacity constraint and the train connection constraint.

[0059] The above is only the preferred embodiment of the application. Based on the technical content, many changes can be made to the specific implementation manner and application range by those skilled in the art without departing from the concept of the application, and all the changes belong to the protection scope of the application.

Claims

1. A freight train formation scheme and freight rate collaborative optimization method based on bounded rationality behavior, characterized in that, The method comprises: S1, collecting the freight transportation demand information, path and running related information in the planning period, and obtaining the utility coefficient and prospect theory parameters affecting the decision-making behavior of the shipper; S2, setting the freight volume interval breakpoints and railway transportation time as the first decision variable, using the first decision variable to encode the particle position, and initializing the particle swarm; S3, based on the first decision variable of each particle, using the bounded rationality freight volume allocation model with the goal of maximizing operating revenue to calculate the prospect value of each particle, and outputting the allocated freight volume and the corresponding railway operating revenue; S4, setting the train running frequency, the number of marshalling vehicles and the arrival and departure time of each station as the second decision variable, and inputting the allocated freight volume into the freight train formation scheme compilation model with the goal of minimizing operating cost, using the CPLEX solver to output the railway transportation time and the corresponding freight train formation scheme; S5, feeding back the railway transportation time to the bounded rationality freight volume allocation model, taking the railway operating revenue as the particle fitness, updating the particle position based on the inertia of its own motion, the individual optimal position and the group optimal position, until the maximum revenue is reached, and outputting the freight train formation scheme.

2. The method of claim 1, wherein, The freight transportation demand information in the planning period at least includes: freight batch, transportation demand, origin and destination information, and applicable railway benchmark freight rate; The path and running related information at least includes: the composition of each selectable path, the transportation time and freight rate of highways and waterways, the stations on the path, the alternative train operation line, the technical operation time standard of each station, and the train operation cost parameters.

3. The method of claim 1, wherein, The utility coefficient and prospect theory parameters affecting the decision-making behavior of the shipper are obtained by: Designing virtual transportation scenarios with different combinations of freight rates and transportation times, asking the shipper to make path selection, and through analysis of historical operation data or market survey data, the freight rate utility coefficient and transportation time utility coefficient affecting the decision-making behavior of the shipper are calibrated; Using experimental economics method, designing an experiment containing risk decision tasks to observe the selection behavior of the shipper under uncertainty, fitting the experimental data and prospect theory model, and using nonlinear least squares or maximum likelihood estimation method to back-propagate the prospect theory parameters affecting the decision-making behavior of the shipper: risk sensitivity coefficient, loss aversion coefficient and probability deviation coefficient.

4. The method of claim 1, wherein, The bounded rationality freight volume allocation model of S3 is constructed by: S31, based on the first decision variable of each particle and the utility coefficient affecting the decision-making behavior of the shipper, calculating the objective utility of each path to the shipper to obtain the utility reference point, and based on the prospect theory parameters, calculating the cumulative prospect of each path, and constructing the bounded rationality freight volume allocation model with the goal of maximizing railway operating revenue.

5. The method of claim 4, wherein, S31 specifically includes: S311, based on the interval freight rate discount coefficient and the freight volume interval breakpoint, establishing a segmented linear function relationship between the discounted railway freight rate and the allocated freight volume, and constraining the railway freight rate to decrease with the increase of the allocated freight volume, and the discounted railway freight rate to be within the specified allowable floating range; S312, based on the railway transportation time, calculating the full transportation price and transportation time of each path including highway, railway and waterway transportation mode, and based on the utility coefficient affecting the decision-making behavior of the shipper, calculating the objective utility of each path to the decision-making behavior of the shipper to obtain the utility reference point; S313, based on the prospect theory parameters affecting the decision-making behavior of the shipper, calculating the subjective utility and subjective selection probability of each path to the decision-making behavior of the shipper through the nonlinear value function and the probability weight function, to obtain the cumulative prospect of each path, and using the all-or-nothing allocation mechanism to allocate all the freight volume of each batch of goods to the transportation path with the highest prospect value; S314, considering the freight allocation mechanism of the limited rationality of the shipper, building a limited rationality freight allocation model with the goal of maximizing railway operation revenue.

6. The method of claim 1, wherein, The freight train formation scheme programming model of S4 is built in the following way: S41, setting 0 / 1 decision variables to constrain the selection of running lines, and based on the second decision variable of each particle, establishing the outflow constraint of the starting station, the inflow constraint of the terminal station, the flow balance constraint of the intermediate station, and the connection time constraint of the train at the station to ensure that the formation scheme is feasible and economical; S42, establishing transportation time limit constraint, minimum load rate constraint and maximum load constraint to ensure that the formation scheme meets the service requirements and physical limitations; S43, taking the allocated freight volume as input, based on the fixed cost of train formation and the reorganization operation cost of the station, establishing a freight train formation scheme programming model with the goal of minimizing railway operation cost under various operation condition constraints.

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