A method for optimizing group train tracking operations considering communication latency

Abstract

This invention discloses a group train tracking operation optimization method considering communication delay, comprising the following steps: establishing a heavy-haul railway train group with a "leader-follower" topology; constructing a multi-objective optimization model based on vehicle characteristic constraints, speed limits, and safety distance constraints; generating random communication delays in the model, calculating the time steps corresponding to the delays, and having the following train make control decisions based on the state information of the preceding train at the previous time step; and solving for the running speed of the following train in the multi-objective optimization model using a particle swarm optimization algorithm. This group train tracking operation optimization method effectively solves the problems of uncertainty and dynamic response lag caused by communication delays during the tracking operation of heavy-haul railway train groups. It can not only significantly reduce tracking errors between trains and improve speed synchronization, but also effectively reduce distance fluctuations during acceleration and deceleration phases, ensuring stable train spacing.

Description

Technical Field

[0001] This invention relates to the field of rail transit control technology, specifically to a group train tracking operation optimization method that takes into account communication delays, applicable to scenarios requiring multi-train coordinated operation such as heavy-haul railways, high-speed railways, and urban rail transit. Background Technology

[0002] With the rapid development of rail transit systems, train operation density and speed are constantly increasing, making it difficult for traditional train operation control methods to meet the needs of modern rail transit systems. Especially in scenarios involving multiple trains operating collaboratively, problems such as communication delays and inaccurate information transmission between trains can lead to decreased train operation efficiency and increased safety hazards. Most existing train operation optimization methods are based on idealized communication conditions, assuming that information transmission between trains is instantaneous and accurate, ignoring the delays and uncertainties present in actual communication systems.

[0003] In actual operation, communication delays between trains can be caused by various factors, such as network congestion, signal interference, and equipment failure. These delays can lead to lag in the information received by the train control system, thus affecting the train's operational decisions. For example, if a train ahead suddenly decelerates, a following train may not be able to obtain the information in time due to communication delays, resulting in an excessively close following distance and increasing the risk of collision. Furthermore, existing train operation optimization methods typically only consider the operational efficiency of a single train, lacking overall optimization for the coordinated operation of multiple trains, making it difficult to achieve global optimization.

[0004] Implementing train group control technology on heavy-haul railways still faces many challenges: First, the requirements of communication and control technology. Train group control requires high-precision, low-latency inter-train communication (such as T2T communication) to ensure real-time train coordination. However, the stability and coverage of communication signals place severe demands on complex terrain and weather conditions. Second, the problem of heterogeneous train dynamics. Heavy-haul trains are composed of different train sets with uneven distribution of traction, braking force, and weight, resulting in significant differences in dynamic characteristics. This makes coordinated control of train group operations complex and prone to fluctuations in speed and train spacing, threatening transportation safety and efficiency. Third, ensuring the safety of train group control systems. While train group control shortens the train tracking distance and improves efficiency, it also increases safety risks. If the communication or control system fails, the following train will have difficulty obtaining the status of the preceding train in time, which can easily lead to serious rear-end collisions. There is an urgent need to build a robust fault detection and emergency response mechanism. Fourth, balancing energy consumption and economy. Frequent dynamic adjustments of the train group control system to adapt to the preceding train increase energy consumption. Moreover, the high costs of technology research and development and initial deployment, including control system design and line modification, put heavy pressure on operators' economic decisions.

[0005] Therefore, there is an urgent need for a group train tracking operation optimization method that can effectively take into account communication delays in order to improve the safety, efficiency and reliability of train operation. Summary of the Invention

[0006] The purpose of this invention is to provide a group train tracking operation optimization method that takes into account communication delay. This method is based on real-time communication information and collaborative control between trains, and optimizes factors such as train speed, position, and acceleration to ensure safe intervals and efficient operation between trains.

[0007] To achieve the above objectives, the present invention provides a method for optimizing group train tracking operations considering communication delays, comprising the following steps:

[0008] Step 1: Establish a heavy-haul railway train group with a "leader-follower" topology;

[0009] Step 2: Based on the constraints of the vehicle's own characteristics, speed limits, and safe distance constraints, construct a multi-objective optimization model with the objectives of minimizing the speed difference between the preceding and following trains and minimizing the difference between the target distance and the actual tracking distance;

[0010] Step 3: Generate random communication delays in the multi-objective optimization model, calculate the time steps corresponding to the delays, and make control decisions based on the state information of the preceding train in the previous time step.

[0011] Step 4: Solve the running speed of the following train in the multi-objective optimization model based on the particle swarm optimization algorithm.

[0012] Furthermore, in step 2, the optimization objectives are to minimize the difference between the actual distance between the preceding train and the following train and the target distance, and to minimize the speed difference between the two trains; wherein:

[0013] Speed ​​difference index Represented as:

[0014] ;

[0015] Distance index Represented as:

[0016] ;

[0017] in, and These are the speeds of the train in front and the train following; and These are the positions of the preceding train and the following train, respectively. It is the length of the train that is moving forward. It is the expected distance between the two trains.

[0018] Furthermore, in step 2, based on the constraints of the multi-objective optimization model, the mathematical model for the optimization problem of group train tracking operation is established as follows:

[0019] (1)

[0020] (2)

[0021] (3)

[0022] (4)

[0023] (5)

[0024] (6)

[0025] In equations (1)-(6) above, For unit train control quantities. This is the maximum deceleration; This is the maximum acceleration; For unit train speed; The safety clearance is related to the train positioning error margin; The length of a single train unit; Minimum train spacing, safety buffer distance; For position Speed ​​limit at the location.

[0026] Furthermore, in step 3, the following train obtains the status information of the preceding train through onboard equipment, and uses it as input to the algorithm to calculate the target tracking speed of the following train at the next time step according to step 4.

[0027] Furthermore, the specific steps of step 4 are as follows:

[0028] Step 4.1 Initialize the particle swarm: Set the total simulation time T and divide it into multiple time steps. ,Right now , , , , At each time step Initialize and generate several particles Each particle represents an acceleration control strategy for that time step, which is randomly initialized in the range [-1, 1] to ensure that the particle swarm is widely distributed in the search space;

[0029] Step 4.2: Simulate the dynamic movement of the following vehicle; for the current time step... Each particle corresponds to an acceleration control strategy. The position of the following train in the current time step is calculated using a train dynamics model. ,speed and acceleration Randomly generate a delay time to calculate the state of the preceding vehicle with the lag, and calculate the fitness function value;

[0030] Step 4.3: Update the particle swarm state; adjust the particle velocity and position using the standard particle swarm update formula to ensure that the particle acceleration control variable is within a reasonable range.

[0031] Step 4.4: Update the individual optimal and global optimal solutions: During the iteration process, compare the current fitness value of each particle with its historical best fitness. If the current fitness is smaller, update the individual optimal solution of that particle. Compare the individual optimal solutions of all particles. If the fitness of a particle is better than the current global optimal solution, then update the global optimal solution. ;

[0032] Step 4.5, Time Step Advancement: If the current time step... Before reaching T, let the optimal acceleration be... As the following vehicle enters the next time step Input variables; proceed to the next time step. Repeat steps 4.2-4.4 to continue optimizing the acceleration strategy for subsequent time steps;

[0033] Step 4.6: When the simulation time step reaches T or the termination condition is met, stop the algorithm; output the optimal acceleration trajectory of the entire time series for the dynamic control of the following vehicle.

[0034] Furthermore, the simulation time step termination condition in step 4.6 is: the global optimal solution converges, or the maximum number of iterations of 100 is reached.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] (1) This invention employs a lead-follower topology adapted to the operating characteristics of virtual train formations. By acquiring the real-time status of the preceding train and the global objectives of the lead train, a balance between local safety and global coordination is achieved. This structure reduces communication complexity and dependence on high bandwidth, improves system robustness, and simplifies the construction of the collaborative optimization model and the implementation of the distributed control algorithm. When dealing with uncertain interferences such as communication delays and traction fluctuations, the lead-follower topology exhibits advantages such as strong formation stability and high scalability, making it suitable for the complex operating scenarios of heavy-haul freight trains.

[0037] (2) The group train tracking operation optimization method of the present invention effectively solves the problems of uncertainty and dynamic response lag caused by communication delay during the tracking operation of heavy-haul railway group trains. It can not only significantly reduce the tracking error between trains and improve speed synchronization, but also effectively reduce distance fluctuations during acceleration and deceleration, ensuring stable train spacing. By introducing a dynamic safety distance penalty term and acceleration smoothness constraints, the anti-interference ability of the system can be improved and the train following performance can be optimized. The present invention not only helps to improve the safety and efficiency of train operation, but also enhances the overall transport capacity and operational stability of railway transportation in complex dynamic environments.

[0038] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0039] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:

[0040] Figure 1 This is a flowchart illustrating a group train tracking operation optimization method that takes into account communication delay, according to the present invention.

[0041] Figure 2 This is a schematic diagram of the train force analysis in the group train tracking operation optimization method of the present invention;

[0042] Figure 3 This is a schematic diagram of the safe braking model of a group train in the group train tracking operation optimization method of the present invention;

[0043] Figure 4 This is a flowchart of the particle swarm optimization algorithm in the group train tracking operation optimization method of the present invention;

[0044] Figure 5 These are the optimized speed-time (vt) and speed difference-time curves of the preceding and following trains in this invention; wherein: (a) is the optimized speed-time (vt) curve of the preceding and following trains; (b) is the optimized speed difference-time curve of the preceding and following trains;

[0045] Figure 6 These are the distance difference-time curves before and after optimization in this invention; where: (a) is the distance difference-time curve before optimization, and (b) is the distance difference-time curve after optimization. Detailed Implementation

[0046] The present invention will now be described in detail with reference to the embodiments shown in the accompanying drawings. However, it should be noted that these embodiments are not intended to limit the present invention. Equivalent transformations or substitutions in function, method, or structure made by those skilled in the art based on these embodiments are all within the scope of protection of the present invention.

[0047] Please see Figures 1 to 6 This invention provides a method for optimizing group train tracking operations considering communication latency, comprising the following steps:

[0048] Step 1: Establish a heavy-haul railway train group with a "leader-follower" topology;

[0049] Establishing a dynamic model for a group of trains: To achieve speed tracking control of a group of trains, establishing an accurate train dynamic model is the primary prerequisite. The dynamic model of a single train is... Figure 2 As shown.

[0050] During operation, a train is primarily subjected to traction, braking force, basic resistance, and additional resistance. Traction and braking force determine the train's acceleration or deceleration, while resistance always acts in the opposite direction to the train's motion. Additional resistance includes gradient resistance and curve resistance. Gradient resistance is generated by the component of gravity, while curve resistance is caused by the centrifugal force of the train on a curved path.

[0051] The dynamic equations of a train during operation can be expressed as:

[0052]

[0053] In the formula, For train quality; For train traction, For the braking force of the train, For air resistance, To add resistance, Add resistance to the curve, where T and B are traction and braking states (Boolean variables of 0 or 1).

[0054] Step 2: Based on the constraints of vehicle characteristics, speed limits, and safety distance, a multi-objective optimization model is constructed with the objectives of minimizing the speed difference between preceding and following trains and minimizing the difference between the target distance and the actual tracking distance. This step analyzes and establishes a mathematical optimization model for group train tracking operation, taking minimizing train spacing error and speed difference as optimization objectives, while considering constraints such as train dynamics characteristics, maximum traction force limits, braking force limits, and safety distance. Specifically:

[0055] 1. Model optimization objective:

[0056] Based on the actual operation of heavy-haul railway group control, the optimization objectives are to minimize the difference between the actual distance and the target distance between the preceding and following trains, and to minimize the speed difference between the two trains. Speed ​​difference index Represented as: Distance index Represented as: ;in, and These are the speeds of the train in front and the train following; and These are the positions of the preceding train and the following train, respectively. It is the length of the train that is moving forward. This is the expected distance between the two trains. The smaller the distance indicator, the closer the distance between the two trains is to the expected distance.

[0057] The model is based on the optimization of tracking operations between two trains, assuming that each train can be analyzed independently, without considering complex global network interference or interactions. It focuses on the operational adjustments of adjacent trains, thus being suitable for local optima, but may not find a global optimum in multi-train scenarios. It is suitable for relatively simple scenarios such as tracking operations and alternating scheduling, but its performance is insufficient for complex scenarios such as dense train formations or cross-scheduling. Optimization of multiple trains requires considering a broader decision space, which may lead to slower model convergence or getting trapped in local optima.

[0058] 2. Model constraints:

[0059] Constraints are based on the dynamic characteristics and real-time communication requirements of group trains, and are generally designed under conditions such as maximum traction force, braking force, and safe train distance, while meeting standards for train operation safety and efficiency. The optimization process primarily considers the maximum acceleration limits of trains and the safety constraints on train spacing to ensure that trains can follow stably in different environments, avoid collision risks, and improve system response speed.

[0060] ① Vehicle inherent characteristic constraints: The traction and braking performance of a train is an inherent attribute of the train vehicle, determining the traction and braking force that the train can provide during operation, and playing an important role in the automatic train control. Due to the complexity of the design of the train's traction and braking system, factors such as train resistance, weight, transmission system, and train formation need to be considered for matching design. This invention only considers the output range of traction and braking force of the train affected by the saturation characteristics of the traction motor.

[0061] Considering the traction and braking characteristics of unit trains, the control inputs for unit trains must take into account the following constraints: the traction and braking forces of each unit train are physically limited, and the control system must ensure that the control inputs do not exceed the maximum capacity range. Exceeding this range may result in equipment damage or system malfunction.

[0062] ② Speed ​​Limits: Train operating speed is limited by the maximum permissible speed under track conditions, the ATP protection speed, and the maximum safe operating speed calculated based on the train's own performance. Train speed constraints mean that the train speed must not exceed the maximum permissible speed under the track curvature radius and train formation requirements. The speed of each unit train must meet the speed limits caused by track or environmental conditions (such as terrain, weather, track conditions, etc.). For each unit train, the following speed limits must be met. Track speed limits may be caused by factors such as curves, gradients, and platforms. During group train tracking, each train must always meet the speed limit conditions; otherwise, unsafe situations may occur (such as derailment or inability to stop in time).

[0063] ③ In addition, train tracking must also meet the constraints of safe distance:

[0064] To ensure the actual relative distance between unit trains is kept within a reasonable range, a safety constraint is added to maintain the relative distance between units within a safe range. This is achieved by using a minimum running distance. To prevent rear-end collisions during operation or braking, it is necessary to ensure that the minimum safe distance between adjacent trains meets certain physical conditions. (Unit train) The minimum distance relative to the vehicle in front is constrained by the principle of relative braking distance.

[0065] Based on the above analysis, the mathematical model for the optimization problem of group train tracking operation is established as follows:

[0066] (1)

[0067] (2)

[0068] (3)

[0069] (4)

[0070] (5)

[0071] (6)

[0072] In equations (1)-(6) above, For unit train control quantities. This is the maximum deceleration; This is the maximum acceleration; For unit train speed; The safety clearance is related to the train positioning error margin; The length of a single train unit; Minimum train spacing, safety buffer distance; For position Speed ​​limit at the location.

[0073] like Figure 3 This is a schematic diagram of a group train safety braking model. The scenario of "the leading train has the most favorable braking opportunity, and the following train has the most unfavorable braking opportunity" represents the most unfavorable scenario for group train safety braking. Based on this scenario, a group train safety braking model is established. The minimum safe distance between unit trains within the group under the most unfavorable scenario can be expressed as:

[0074] (7)

[0075] In equation (7), This represents the distance traveled by the following vehicle from the moment the preceding vehicle begins braking to the moment the following vehicle begins braking. Its value is affected by equipment response time, communication delay, and train operation speed. This indicates the braking distance of the following vehicle under the most unfavorable conditions; This indicates the braking distance of the vehicle in front under the most favorable conditions. This indicates the safe distance between trains.

[0076] Step 3: Generate random communication delays in the multi-objective optimization model, calculate the time steps corresponding to the delays, and make control decisions based on the state information of the preceding train in the previous time step. The following train obtains the state information of the preceding train through onboard equipment and also knows its own state information. It uses this information as input to the algorithm to calculate the target tracking speed of the following train in the next time step according to Step 4.

[0077] Step 4: Solve for the running speed of the following train in the multi-objective optimization model using the particle swarm optimization algorithm; such as... Figure 4 As shown, the specific steps are as follows:

[0078] Step 4.1 Initialize the particle swarm: Set the total simulation time T and divide it into multiple time steps. ,Right now , , , , At each time step Initialize and generate several particles Each particle represents an acceleration control strategy for that time step, which is randomly initialized in the range [-1, 1] to ensure that the particle swarm is widely distributed in the search space;

[0079] Step 4.2: Simulate the dynamic movement of the following vehicle; for the current time step... Each particle corresponds to an acceleration control strategy. The position of the following train in the current time step is calculated using a train dynamics model. ,speed and acceleration Randomly generate a delay time to calculate the state of the preceding vehicle with the lag, and calculate the fitness function value;

[0080] Step 4.3: Update the particle swarm state; adjust the particle velocity and position using the standard particle swarm update formula to ensure that the particle acceleration control variable is within a reasonable range.

[0081] Step 4.4: Update the individual optimal and global optimal solutions: During the iteration process, compare the current fitness value of each particle with its historical best fitness. If the current fitness is smaller, update the individual optimal solution of that particle. Compare the individual optimal solutions of all particles. If the fitness of a particle is better than the current global optimal solution, then update the global optimal solution. ;

[0082] Step 4.5, Time Step Advancement: If the current time step... The total simulation time T has not yet been reached, so let the optimal acceleration be... As the following vehicle enters the next time step Input variables; proceed to the next time step. Repeat steps 4.2-4.4 to continue optimizing the acceleration strategy for subsequent time steps;

[0083] Step 4.6: When the simulation time step reaches T or the termination condition is met (global optimal solution converges, or the maximum number of iterations reaches 100), stop the algorithm; output the optimal acceleration trajectory for the entire time series. It is used for the dynamic control of the following vehicle.

[0084] Example

[0085] A heavy-haul railway trunk line (originating station A - terminating station B) was selected as a case study to verify the effectiveness of the model and algorithm. A scenario was considered where two trains were tracking and optimizing each other on a track with a total length of 2000 meters. The two trains departed simultaneously from their initial positions (200 meters apart). Specific assumptions and operating rules are as follows:

[0086] Each train has a mass of 5000 tons and a maximum operating speed of 20 m / s. The train's power system can provide an acceleration of 1 m / s² during acceleration and a deceleration of 1 m / s² during braking. The time step in the algorithm optimization process is 0.1 seconds.

[0087] The train's journey is divided into three main phases: acceleration, constant speed, and braking.

[0088] During the acceleration phase, the leading train starts from a standstill and gradually accelerates at an acceleration of 1 m / s² until it reaches its maximum speed of 20 m / s. While the leading train is still moving, its acceleration remains at 1 m / s² until it reaches 20 m / s. Once the leading train reaches its maximum speed of 20 m / s, the train enters a constant speed phase, maintaining a steady speed until braking requirements are met. When the train reaches the braking initiation point, it enters the deceleration phase. Specifically, when the leading train's displacement reaches or exceeds 1800 meters, it activates its braking mechanism, decelerating at a maximum rate of 1 m / s² until its speed drops to zero. The following train also activates its deceleration mechanism when its displacement reaches 1600 meters, braking at the same rate to ensure a safe stop and maintain a safe distance between trains to avoid collisions or other safety hazards.

[0089] Table 1 Parameter Information

[0090]

[0091] In vehicle-to-vehicle communication research, communication delay is typically affected by various factors, such as the distance between trains, interference from the surrounding environment, and the performance of communication equipment. Taking into account these factors and the complexities of actual operation, this embodiment defines a representative delay range of 0.2s-0.4s to simulate different delay scenarios that may occur in reality, thereby comprehensively evaluating the performance of the method of this invention in reducing communication delay interference.

[0092] The optimization results for communication delay interference using this model and algorithm are as follows:

[0093] ① The algorithm was programmed using MATLAB and ran on a machine with an R7-8845HS processor at 3.8GHz, 32.0 GB of onboard RAM, and a 64-bit operating system. According to the optimized distance difference-time curve, the tracking distance difference remained consistently between 200 and 204 meters, with significantly reduced fluctuations. During acceleration and deceleration, the tracking distance curve was smoother, and the deviation converged rapidly. During the constant speed phase (20-100 seconds), the tracking distance remained between 203 and 204 meters, with a significant reduction in error.

[0094] ② The optimized system's average tracking distance is closer to the target distance (200 meters), with reduced error and improved accuracy. The optimization strategy significantly reduces distance deviation during dynamic phases, enhancing stable tracking performance between trains. The optimized mean square distance error is reduced by 1.70%, allowing subsequent trains to respond more quickly and effectively to preceding trains during dynamic tracking, and significantly reducing distance fluctuations during acceleration and deceleration. The optimized mean square speed error is reduced by 60.74%, greatly mitigating the impact of communication delay on speed synchronization. Subsequent trains can quickly adapt to speed changes of preceding trains, ensuring operational stability.

[0095] Table 2 Comparison of Optimization Results

[0096]

[0097] Table 3 Algorithm performance before and after optimization

[0098]

[0099] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A group train tracking operation optimization method considering communication delay, characterized by, Includes the following steps: Step 1: Establish a heavy-haul railway train group with a "leader-follower" topology; Step 2: Based on the constraints of the vehicle's own characteristics, speed limits, and safe distance constraints, construct a multi-objective optimization model with the objectives of minimizing the speed difference between the preceding and following trains and minimizing the difference between the target distance and the actual tracking distance; Step 3: Generate random communication delays in the multi-objective optimization model, calculate the time steps corresponding to the delays, and make control decisions based on the state information of the preceding train in the previous time step. Step 4: Solve for the running speed of the following train in the multi-objective optimization model based on the particle swarm optimization algorithm; the specific steps are as follows: Step 4.1 Initialize the particle swarm: Set the total simulation time T and divide it into multiple time steps. ,Right now , , , , At each time step Initialize and generate several particles Each particle represents an acceleration control strategy for that time step, which is randomly initialized in the range [-1, 1] to ensure that the particle swarm is widely distributed in the search space; Step 4.2: Simulate the dynamic movement of the following vehicle; for the current time step... Each particle corresponds to an acceleration control strategy. The position of the following train in the current time step is calculated using a train dynamics model. ,speed and acceleration Randomly generate a delay time to calculate the state of the preceding vehicle with the lag, and calculate the fitness function value; Step 4.3: Update the particle swarm state; adjust the particle velocity and position using the standard particle swarm update formula to ensure that the particle acceleration control variable is within a reasonable range. Step 4.4: Update the individual optimal and global optimal solutions: During the iteration process, compare the current fitness value of each particle with its historical best fitness. If the current fitness is smaller, update the individual optimal solution of that particle. Compare the individual optimal solutions of all particles. If the fitness of a particle is better than the current global optimal solution, then update the global optimal solution. ; Step 4.5, Time Step Advancement: If the current time step... Before reaching T, let the optimal acceleration be... As the following vehicle enters the next time step Input variables; Enter the next time step Repeat steps 4.2-4.4 to continue optimizing the acceleration strategy for subsequent time steps; Step 4.6: When the simulation time step reaches T or the termination condition is met, stop the algorithm; output the optimal acceleration trajectory of the entire time series for the dynamic control of the following vehicle.

2. The group train tracking operation optimization method according to claim 1, characterized in that, In step 2, the optimization objectives are to minimize the difference between the actual distance between the preceding train and the following train and the target distance, and to minimize the speed difference between the two trains; wherein: Speed ​​difference index Represented as: ； Distance index Represented as: ； in, and These are the speeds of the train in front and the train following; and These are the positions of the preceding train and the following train, respectively. It is the length of the train that is moving forward. This is the expected distance between the two trains; Based on the constraints of the multi-objective optimization model, the mathematical model for the optimization problem of group train tracking operation is established as follows: (1) (2) (3) (4) (5) (6) In equations (1)-(6) above, For unit train control quantities. This is the maximum deceleration; This is the maximum acceleration; For unit train speed; The safety clearance is related to the train positioning error margin; The length of a single train unit; Minimum train spacing, safety buffer distance; For position Speed ​​limit at the location.

3. The group train tracking operation optimization method according to claim 1, characterized in that, In step 3, the following train obtains the status information of the preceding train through onboard equipment, and uses it as input to the algorithm to calculate the target tracking speed of the following train at the next time step according to step 4.

4. The group train tracking operation optimization method according to claim 1, characterized in that, The simulation time step termination condition in step 4.6 is: the global optimal solution converges, or the maximum number of iterations of 100 is reached.

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