Freight train formation scheme and freight rate optimization based on bounded rationality behavior

Abstract

The application provides a freight train operation scheme and freight rate collaborative optimization method based on limited rational behavior, comprising: obtaining utility coefficients and prospect theory parameters affecting the decision-making behavior of shippers; using a freight rate discount coefficient, a freight volume interval breakpoint, and a railway transportation time coding particle position, and initializing a particle swarm; calculating the prospect value of each particle by using a limited rational freight volume distribution model with the goal of maximizing operating income, and outputting the distributed freight volume and railway operating income; inputting the distributed freight volume into a freight train operation scheme compilation model with the goal of minimizing operating cost, and outputting railway transportation time and freight train operation scheme by using a CPLEX solver; feeding back the railway transportation time to the limited rational freight volume distribution model, and updating the position of each particle by taking railway operating income as particle fitness until the maximum income is reached, and outputting the freight train operation scheme. The method can significantly improve the accuracy of demand prediction while optimizing the overall operation and income level.

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 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:

[0005] Firstly, in the aspect of behavior modeling, the existing methods have defects in modeling the path selection behavior of the shippers. They generally implicitly or explicitly assume "perfect rationality" based on the idealized assumption, adopt traditional discrete choice models, and assume 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 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.

[0006] 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 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 isolated optimization leads to the difficulty in balancing the "operation cost-service level-market revenue", and cannot realize the maximization of railway comprehensive benefits while meeting the market multi-demand. SUMMARY

[0007] 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, thereby enhancing the market competitiveness of freight products, and at the same time, optimizing the operation and revenue level as a whole.

[0008] The present application provides a freight train operation scheme and freight rate collaborative optimization method based on bounded rational behavior, comprising:

[0009] S1, collecting freight transport demand information, path and operation related information in the planning period, and obtaining utility coefficients and prospect theory parameters affecting the consignor's decision-making behavior;

[0010] S2, setting the freight rate discount coefficient, the freight volume interval breakpoint and the railway transport time as the first decision variable, using the first decision variable to encode the particle position, and initializing the particle swarm;

[0011] S3, based on the first decision variable of each particle, using the bounded rational freight volume allocation model with the goal of maximizing the operation revenue to calculate the prospect value of each particle, and outputting the allocated freight volume and the corresponding railway operation revenue;

[0012] 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 allocated 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;

[0013] S5, feeding back the railway transport time to the bounded rational freight volume allocation 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.

[0014] Further, the freight transport demand information in the planning period at least includes: freight batch, transport demand volume, origin-destination point information, applicable railway benchmark freight rate;

[0015] The path and the running related information at least includes: the composition of each optional path, the transportation time and the transportation price of the highway and the waterway, the hanging station on the path, the alternative train running line, the technical operation time standard of each station, and the train operation cost parameter.

[0016] Further, the utility coefficient and the prospect theory parameter affecting the decision behavior of the shipper are obtained by the following way:

[0017] A virtual transportation scene with different transportation price and transportation time combinations is designed, the shipper is asked to make path selection, and the transportation price utility coefficient and the transportation time utility coefficient affecting the decision behavior of the shipper are calibrated through analysis of historical operation data or market survey data;

[0018] An experiment including risk decision tasks is designed by using experimental economics method to observe the selection behavior of the shipper under uncertainty, the prospect theory parameters affecting the decision behavior of the shipper, i.e. the risk sensitivity coefficient, the loss aversion coefficient and the probability deviation 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.

[0019] Further, the finite rational freight volume allocation model of the S3 is constructed by the following way:

[0020] 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, and a finite rational freight volume allocation model is constructed with the goal of maximizing the railway operation revenue.

[0021] Further, the S31 specifically includes:

[0022] S311, based on the interval transportation price discount coefficient and the freight volume interval breakpoint, a segmented linear function relationship between the discounted railway transportation price and the allocated freight volume is established, and the constraint that the railway transportation price decreases with the increase of the allocated freight volume and the discounted railway transportation price is within the specified allowable floating range is set;

[0023] S312, based on the railway transportation time, the full transportation price and the transportation time of each path including the highway, the railway and the waterway transportation mode are calculated, and based on the utility coefficient affecting the decision behavior of the shipper, the objective utility of each path to the decision behavior of the shipper is calculated to obtain the utility reference point;

[0024] S313, based on the prospect theory parameters affecting the decision behavior of the shipper, the subjective utility and the subjective selection probability of each path to the decision behavior of the shipper are calculated by the nonlinear value function and the probability weight function to obtain the cumulative prospect of each path, and the all-or-nothing allocation mechanism is adopted to allocate the entire freight volume of each batch of goods to the transportation path with the highest prospect value.

[0025] S314, considering the limited rationality of the consignor, a limited rationality freight allocation model is constructed to maximize the railway operation revenue.

[0026] Further, the S4 freight train formation scheme programming model is constructed in the following manner:

[0027] S41, setting 0 / 1 decision variables to constrain the running line selection, and based on the second decision variable of each particle, respectively 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;

[0028] S42, establishing transportation time limit constraints, minimum load rate constraints, and maximum load constraints to ensure that the formation scheme meets the service requirements and physical limitations;

[0029] S43, taking the allocated freight volume as input, based on the fixed cost of train formation and the reorganization operation cost of the station under various operation condition constraints, establishing a freight train formation scheme programming model to minimize the railway operation cost.

[0030] The freight train formation scheme based on limited rational behavior and the freight price collaborative optimization method provided by the application have the following beneficial effects:

[0031] (1) The demand prediction accuracy is significantly improved. By using the limited rationality freight allocation model based on the 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 formation scheme;

[0032] (2) The market competitiveness of the freight product is enhanced. By constructing a double-layer collaborative optimization mechanism of the freight train formation scheme and the freight price strategy, the target conflict problem caused by the fragmented 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;

[0033] (3) The overall operation and revenue level is optimized. By establishing a joint decision feedback loop, efficient and self-adaptive matching of the transport capacity resource allocation and market demand dynamics is realized, thereby significantly improving the overall revenue level of railway freight under the premise of ensuring the operation feasibility. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 The flowchart of the freight train formation scheme based on limited rational behavior and the freight price collaborative optimization method provided by the embodiment of the application is shown;

[0035] Figure 2 A schematic diagram of a transport network structure and a shipper transport path selection provided by an embodiment of the present application is shown;

[0036] Figure 3 A decision weight and prospect value diagram of a prospect theory provided by an embodiment of the present application is shown;

[0037] Figure 4 A schematic diagram of joint optimization of a freight train formation scheme and a freight rate discount provided by an embodiment of the present application is shown. DETAILED DESCRIPTION

[0038] In order to make the purpose, technical scheme and advantages of the present technical solution more clear and explicit, the present technical solution will be further described in detail below in combination with specific embodiments. It should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present technical solution. Embodiment One

[0039] Please refer to the flowchart of the freight train formation scheme and freight rate collaborative optimization method based on bounded rational behavior as shown in Figure 1 As shown in Figure 1 , the method comprises:

[0040] S1, collect freight transport demand information, path and formation related information in the planning period, and obtain utility coefficients and prospect theory parameters affecting shipper decision-making behavior.

[0041] 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 formation related information at least includes: the composition of each selectable path, the transport time and freight rate of highways and waterways, the stations on the path, the alternative train operating lines, the technical operation time standards of each station, and the train operation cost parameters.

[0042] In specific implementation, the utility coefficients and prospect theory parameters affecting the shipper decision-making behavior can be obtained by the following methods:

[0043] Design virtual transport scenarios with different combinations of freight rates and transport times, ask shippers to make path selections, and through analysis of historical operation data or market survey data, calibrate the freight rate utility coefficient and transport time utility coefficient affecting the shipper decision-making behavior.

[0044] Use experimental economics methods to design experiments containing risk decision-making tasks to observe the selection behavior of shippers under uncertainty, fit experimental data and prospect theory models, and use nonlinear least squares or maximum likelihood estimation methods to back-calculate the prospect theory parameters affecting the shipper decision-making behavior: risk sensitivity coefficient, loss aversion coefficient and probability deviation coefficient.

[0045] Here, the shipper behavior survey can be implemented in the form of a questionnaire to characterize the key parameters of the shipper decision-making behavior. In order to improve the implementation efficiency and applicability of the method, the above-mentioned parameters can also be obtained by using other ways, which can be determined based on historical operation data through reverse fitting, or directly using typical parameter values verified by the industry, and the present application does not make any limitation. In addition, the above-mentioned parameters can also be dynamically updated according to the actual operation data, so that the technical solution of the present application has self-adaptive optimization capability.

[0046] 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.

[0047] In this step, the present application is expected to use the particle swarm optimization algorithm embedded with the CPLEX solver to solve the coupled bounded 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 jointly coded by the first decision variable. This coding method can uniformly map the nonlinear decision variables (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.

[0048] As an example, the particle coding 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.

[0049] Table 1, particle coding table

[0050]

[0051] S3, based on the first decision variable of each particle, the prospect value of each particle is calculated by using the bounded rationality freight volume distribution model with the goal of maximizing the operation revenue, and the distribution freight volume and the corresponding railway operation revenue are output.

[0052] In specific implementation, the bounded rationality freight volume distribution model can be constructed in the following way:

[0053] S31, based on the first decision variable of each particle and the utility coefficient affecting the shipper decision-making behavior, 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 bounded rationality freight volume distribution model with the goal of maximizing the railway operation revenue.

[0054] 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. The model identifies the perceived gains and losses of the shipper to different path schemes by setting a transportation utility reference point, describes the loss aversion and sensitivity decreasing psychological characteristics by using a value function, and corrects the subjective cognitive bias of the shipper to the objective probability by using a probability weight function. Finally, by calculating the cumulative prospect value of each path, the model allocates all the freight volume of the large shipper to the path with the highest prospect value based on the deterministic decision-making characteristics of the large shipper under bounded rationality, and outputs the determined allocation result of the freight volume.

[0055] Specifically, the following steps are included:

[0056] 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 railway freight rate is constrained to decrease with the increase of the allocated freight volume, and the discounted railway freight rate is within the specified allowable floating range.

[0057] The railway freight rate is calculated as follows:

[0058] ;

[0059] 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 the freight; The constraint that the long-distance freight rate is higher than the short-distance freight rate is:

[0060] ;

[0061] ;

[0062] In the formula, is the railway freight rate of the freight, is the railway freight rate of the freight, is the railway mileage of the freight; The continuous segmented function between the discounted railway freight rate and the allocated freight volume is established as:

[0063] ;

[0064] ;

[0065] In the formula, is the discounted railway freight rate of the freight, is the discounted railway freight rate of the freight, is the discounted railway freight rate of the freight, ​​​​The allocation of goods, decision variables For interval The freight rate discount factor, For cargo volume range Quantity discount breakpoint, A collection of freight rate discounts;

[0066] The more freight volume is allocated under the constraint, the greater the railway freight rate discount will be.

[0067] ;

[0068] Based on the maximum 15% increase in freight rates, the following restrictions apply to discounted railway freight rates:

[0069] ;

[0070] In the formula, This is the minimum discount requirement for railway freight rates.

[0071] 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.

[0072] 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.

[0073] Calculate the total freight cost including road, rail, and water transport:

[0074] ;

[0075] In the formula, For goods The total freight rate For goods Highway freight rates, For goods Waterway freight rates;

[0076] Calculate the total transportation time, including road, rail, and waterway transport:

[0077] ;

[0078] 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;

[0079] Calculate the objective utility of each route on shippers' decision-making behavior under the influence of freight rates and transit time:

[0080] ;

[0081] 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.

[0082] Calculate the objective probability of shippers' decision-making behavior for each route under the influence of freight rates and transit time:

[0083] ;

[0084] In the formula, For goods The objective probability of choosing its own path. Represents an exponential function. For goods For other paths Objective utility (label 0 represents its own path). A set of paths;

[0085] Calculate the average of the objective utility of all routes for the shipper's decision-making behavior as a utility reference point:

[0086] ;

[0087] In the formula, For goods The utility reference point.

[0088] Here, by receiving railway transport times from the freight train operation plan, together with freight rates, a complete freight service product is formed. Freight rates, freight volume, and operation plans form a two-way coupled, closed-loop feedback collaborative optimization loop, achieving a dynamic balance between market response and transport capacity supply.

[0089] S313, based on the prospect theory parameters affecting the consignor's decision-making behavior, the subjective utility and subjective selection probability of each path on the consignor's decision-making behavior are calculated through the nonlinear value function and probability weight function, so as to obtain the cumulative prospect of each path, and the all-or-nothing allocation mechanism is adopted to allocate all the freight volume of each batch of goods to the transport path with the highest prospect value.

[0090] The gain or loss value of each path compared with the utility reference point is calculated:

[0091] ;

[0092] In the formula, is the utility of the goods to the path ;

[0093] Based on the gain or loss of each path, the subjective utility of each path on the consignor's decision-making behavior is calculated:

[0094] ;

[0095] In the formula, is the subjective utility of the goods to the path , is the risk sensitivity coefficient affecting the consignor's decision-making behavior, is the loss aversion coefficient;

[0096] According to the gain or loss of each path, the subjective selection probability of each path on the consignor's decision-making behavior is calculated:

[0097] ;

[0098] In the formula, is the subjective selection probability of the goods to the path , is the objective selection probability of the goods to the path , is the probability offset coefficient;

[0099] Based on the subjective utility and subjective selection probability of each path on the consignor's decision-making behavior, the cumulative prospect of each path is calculated:

[0100] ;

[0101] In the formula, is the prospect value of the goods to the path ;

[0102] The "all or nothing" allocation mechanism is adopted to allocate the entire volume of each batch of goods to the transport path with the highest cumulative prospect:

[0103]

[0104] In the formula, The goods The allocated volume of the goods on the path.

[0105] Here, the "all or nothing" allocation mechanism is adopted mainly considering that railway freight transport has large single volume, strong planning, and most of the shippers are large shippers who need to make a unique decision. Therefore, this mechanism is 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.

[0106] S314, considering the limited rationality of the shipper, a limited rationality freight volume allocation model is constructed to maximize the railway operation revenue.

[0107] The limited rationality freight volume allocation model is:

[0108]

[0109] In the formula, The railway operation revenue, The product of the allocated volume of all goods and the railway freight rate, The railway operation cost determined by the freight train formation scheme programming model.

[0110] S4, set the train formation frequency, the number of cars in the formation, and the arrival and departure time of each station as the second decision variable, input the allocated volume into the freight train formation scheme programming model with the objective of minimizing the operation cost, and use the CPLEX solver to output the railway transport time and the corresponding freight train formation scheme.

[0111] 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 scheme programming model takes the allocated volume output by the upper model as the core input, integrates flow conservation constraints, station operation capacity constraints, train connection constraints, and load capacity constraints, etc., so as to generate a technically feasible and economically optimal train formation scheme under the premise of meeting all operation conditions. The transport time determined by the scheme will be fed back to the upper model as a key service parameter.

[0112] In specific implementation, the freight train formation scheme programming model can be constructed in the following way: ​​

[0113] S41, set 0 / 1 decision variables to constrain the running 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.

[0114] The outflow constraint of the starting station is established as:

[0115] ;

[0116] In the formula, is a 0 / 1 decision variable, used to decide whether the freight is selected to run on the running line , if the running line is selected, , is a set of stations on the path, is a set of arrival running lines of the station , is a set of departure running lines of the station ; The inflow constraint of the terminal station is established as:

[0117]

[0118] ;

[0119] According to the same batch of freight, when passing through the intermediate station, the arrival and departure running lines must be matched at the same time, the flow balance constraint of the intermediate station is established as:

[0120] ;

[0121] According to the difference between the departure time and the arrival time meeting the minimum technical operation time standard, the connection time constraint of the train at the station is established as:

[0122] ;

[0123] 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 .

[0124] S42, establish transportation time limit constraint, minimum load rate constraint, maximum load constraint, to ensure that the train operation scheme meets the service requirements and physical limitations.

[0125] ​​​In order to allow a reasonable buffer based on the cargo arrival time determined by the operating line and to meet the overall time requirements, the transportation time limit constraint is established as follows:

[0126] ;

[0127] In the formula, For the time margin of railway transportation, For goods Origin and arrival times;

[0128] To ensure that all selected operating lines meet the minimum load factor requirement, the minimum load factor constraint is established as follows:

[0129] ;

[0130] In the formula, To the maximum number of groups, Due to cargo load factor restrictions;

[0131] The total amount of goods carried by any operating line shall not exceed its rated cargo capacity, and the maximum cargo capacity constraint shall be established as follows:

[0132] .

[0133] S43. Taking the allocated freight volume as input, and under various operational constraints, based on the fixed cost of train operation and the relocation operation cost of stations, with the goal of minimizing railway operating costs, establish a freight train operation plan preparation model.

[0134] The freight train operation plan development model is as follows:

[0135] ;

[0136] In the formula, For railway operating costs, For the running line Fixed costs, For the station The unit cost of adaptation operations.

[0137] It is worth noting that the bounded rationality freight allocation model (referred to as the upper-level model) and the freight train operation plan formulation model (referred to as the lower-level model) constructed in this application are bi-level programming models. Due to their unique structure, they face significant solution challenges: the upper-level model exhibits strong nonlinear characteristics due to the inclusion of nonlinear value functions and probability weight functions from prospect theory, while the lower-level model is a typical mixed-integer linear programming problem; simultaneously, there is a tight coupling between the upper and lower levels, with the freight rate decisions of the upper-level model directly affecting the freight input of the lower-level model, and the transportation time results output by the lower-level model in turn affecting the decision-making process of the upper level. This complex structure of "nonlinear-linear" hybrid and bi-directional dependence makes it difficult for traditional optimization methods to solve directly and efficiently.

[0138] 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.

[0139] 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.

[0140] 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.

[0141] In practice, particle positions can be updated in the following ways:

[0142] ;

[0143] 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. a learning factor moving towards the individual optimal position and the group optimal position, a random number in the range of [0, 1], denotes the individual optimal position, denotes the position of the i-th particle in the j-th iteration, denotes the position of the i-th particle in the j-th iteration, denotes the position of the i-th particle in the j-th iteration, denotes the group optimal position;

[0144] ;

[0145] in the formula, denotes the position of the i-th particle in the j-th iteration. The specific values of the control parameters such as inertia weight and learning factor 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.

[0146] The first decision variable is optimized and adjusted by updating the particle position. When the termination condition is reached, the approximate optimal solution corresponding to the group optimal position is output. This solution contains the optimal freight discount strategy and train operation scheme, which embodies the final result of the collaborative optimization of the present application.

[0147] 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 rate) is taken as input to affect the prediction result (allocated freight volume) of the bounded-rational freight volume allocation model; the allocated freight volume is taken as input to drive the generation of the scheme of the freight train operation scheme compilation model; 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 volume allocation model for the next round of optimization iteration.

[0148] Embodiment Two:

[0149] Please refer to the transport network structure and shipper transport path selection schematic diagram as shown in .

[0150] 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 volume 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 predicted allocated freight volume of the selected 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. Figure 2 Figure 2

[0151] ​​Please refer to the decision weight and prospect value chart of prospect theory as shown in Figure 3 Figure 3 The working principle of the core limited rationality freight volume allocation model of the present application is illustrated. The schematic diagram specifically depicts the key components of the prospect theory: the value function describes the loss aversion and decreasing sensitivity psychological characteristics of the shipper through its S-shaped curve; the probability weight function reflects the subjective cognitive bias of the shipper to the objective probability through its anti-S-shaped curve. The diagram illustrates how the present application converts the traditional objective utility calculation into more realistic subjective prospect value calculation by introducing the prospect theory, thereby accurately quantifying the limited rationality decision-making behavior.

[0152] Please refer to the joint optimization schematic diagram of the freight train formation scheme and the freight rate discount as shown in Figure 4 Figure 4 The freight train formation scheme and the freight rate collaborative optimization mechanism realized by the present application are shown. The left part of the diagram reveals the closed-loop feedback loop constituted by the freight rate discount collaborative optimization method, the limited rationality freight volume allocation model and the freight train formation scheme compilation model. The closed-loop feedback loop is the core architecture for realizing the collaborative optimization of the freight train formation scheme and the freight rate, and is one of the key innovations of the present application. The right part of the diagram provides an exemplary train working diagram, which specifically shows the output results of the freight train formation scheme compilation model, including the train arrival and departure time arrangement that meets the station operation capacity constraints and the train connection constraints.

[0153] The above is only the preferred embodiment of the present application. For those skilled in the art, many changes can be made to the specific implementation manner and application range according to the technical content of the present application, as long as these changes do not deviate from the concept of the present application, and all belong to the protection scope of the present application.​​

Claims

1. A method for co-optimizing freight train operation schemes and freight rates based on bounded rationality behavior, characterized in that, 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 affect shippers' decision-making behavior; S2. Set the freight rate discount coefficient, the freight volume interval breakpoint and the railway transportation time as the first decision variables, use the first decision variables to encode the particle positions, and initialize the particle swarm; S3. Based on the first decision variable of each particle, calculate the prospect value of each particle using a bounded rationality freight allocation model with the goal of maximizing operating revenue, and output the allocated freight volume and the corresponding railway operating revenue. S4. Set the train frequency, number of cars in the formation, and arrival and departure times of each station as the second decision variables, and input the allocated freight volume into the freight train operation plan preparation model with the goal of minimizing operating costs. Use the CPLEX solver to output the railway transportation time and the corresponding freight train operation plan. 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. The bounded rational quantity allocation model for S3 is constructed as follows: S31. Based on the first decision variables of each particle and the utility coefficients that affect the shipper's decision-making behavior, calculate the objective utility of each path for the shipper to obtain the utility reference point. Then, based on the prospect theory parameters, calculate the cumulative prospect of each path and construct a bounded rationality freight volume allocation model with the goal of maximizing railway operating revenue. S31 specifically includes: S311. Based on the interval freight rate discount coefficient and the freight volume interval breakpoint, establish a piecewise linear function relationship between the discounted railway freight rate and the allocated freight volume, and constrain the railway freight rate to decrease as the allocated freight volume increases, and the discounted railway freight rate is within the prescribed allowable fluctuation range. 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. S313. Based on the prospect theory parameters that affect the shipper's decision-making behavior, the subjective utility and subjective choice probability of each path to the shipper's decision-making behavior are calculated through nonlinear value function and probability weight function to obtain the cumulative prospect of each path. Then, an all-or-nothing allocation mechanism is adopted to allocate the entire volume of each batch of goods to the transportation path with the highest prospect value. S314. Considering the bounded rationality of the shipper in the cargo allocation mechanism, and with the goal of maximizing railway operating revenue, construct a bounded rationality cargo volume allocation model.

2. The method as described in claim 1, characterized in that, The freight transport demand information during the planning period shall include at least: freight batches, transport demand volume, origin and destination information, and applicable railway benchmark freight rates; The route and operation-related information shall include at least: the composition of each optional route, the transportation time and freight rate of road and waterway, the stops along the route, alternative train operating lines, the technical operation time standards of each station, and train operation cost parameters.

3. The method as described in claim 1, characterized in that, The utility coefficients and prospect theory parameters influencing shippers' decision-making behavior are obtained through the following methods: Design virtual transportation scenarios with different combinations of freight rates and transportation times, ask shippers to choose routes, and identify the freight rate utility coefficient and transportation time utility coefficient that affect shippers' decision-making behavior through analysis of historical operating data or market survey data. 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.

4. The method as described in claim 1, characterized in that, The freight train operation plan compilation model for S4 is constructed using the following method: S41. Set 0 / 1 decision variables to constrain the selection of the operating line, and based on the second decision variables of each particle, establish outflow constraints of the starting station, inflow constraints of the terminal station, flow balance constraints of intermediate stations, and train connection time constraints at stations to ensure that the operation plan is feasible and economical. S42. Establish transportation time constraints, minimum load factor constraints, and maximum load capacity constraints to ensure that the operation plan meets service requirements and physical limitations. S43. Taking the allocated freight volume as input, and under various operational constraints, based on the fixed cost of train operation and the relocation operation cost of stations, with the goal of minimizing railway operating costs, establish a freight train operation plan preparation model.

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