Rail transit train cooperative scheduling method

Abstract

The invention discloses a rail transit train cooperative scheduling method, and belongs to the technical field of train scheduling. The method comprises the following steps: firstly, constructing a single-train local objective function and constraint containing elements such as net power and punctuality error, and then, establishing a multi-train total objective function and constraint according to the single-train local objective function and constraint; decomposing the total objective function to obtain a global coordination item, and fusing the global coordination item into a local objective function to form a local sub-problem; and finally, solving a local sub-problem and sending a prediction trajectory, checking trajectory conflicts by a signal coordinator, and updating a global variable and a Lagrangian multiplier vector until convergence to realize multi-objective optimization and line global energy consumption optimization.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of train scheduling, in particular to a rail transit train cooperative scheduling method. BACKGROUND

[0002] In the field of rail transit, with the expansion of the operation scale and the upgrading of green transportation demand, train energy saving has become the core research direction of the industry, and the research focus has gradually shifted from single train energy optimization to multi-train cooperative energy saving in the past 20 years. Currently, the industry has formed a certain technical foundation: on the one hand, single train energy saving is mainly achieved by optimizing the ATO (Automatic Train Operation) system operation curve and adjusting the traction and braking strategy combined with the train dynamics model; on the other hand, in the multi-train cooperative research, some schemes introduce model predictive control (MPC) algorithm to try to optimize the running state, or based on the principle of regenerative braking to recover braking energy and store it in the energy pool, while there are also technical explorations to optimize train control and cooperative driving strategy through reinforcement learning, distributed model predictive control, etc. to balance the energy saving effect and basic operation needs.

[0003] However, the existing technology still has key bottlenecks in the multi-train cooperative energy saving scenario: the existing schemes are difficult to simultaneously meet the multi-train operation safety constraints (including the safety distance constraint of the same direction, the signal blocking time window constraint of the opposite direction or the crossing turnout area), the operation index constraints (on-time rate, accurate parking, comfort), and the efficient allocation and utilization of regenerative braking energy in a unified optimization framework. Specifically, most schemes focus only on single train energy optimization, ignoring the coupling constraints between multiple trains; or although they consider multi-train cooperation, they do not include the capacity limit of the regenerative braking energy pool, energy transmission and storage loss into the global optimization objective, resulting in low utilization rate of regenerative energy; in addition, some schemes involving multi-objective optimization lack an engineering coupling constraint solving path, making it difficult to balance optimization solving efficiency and control accuracy under complex line conditions, and unable to achieve global energy optimization of the line, which is a core obstacle to the application of rail transit multi-train cooperative energy saving technology. SUMMARY

[0004] In view of the above deficiencies in the prior art, the rail transit train cooperative scheduling method provided by the present application solves the problem that the prior art scheme cannot simultaneously consider the multi-train operation safety constraints (safety distance, signal blocking time window), operation index constraints (on-time rate, accurate parking, comfort) and efficient utilization of regenerative braking energy in a unified optimization framework, and lacks an engineering coupling constraint solving path under multi-train coupling constraints, and cannot achieve global energy optimization of the line.

[0005] In order to achieve the above application purposes, the technical scheme adopted by the present application is as follows: a rail transit train cooperative scheduling method, comprising the following steps: S1. Based on the net power, punctuality error penalty, acceleration change penalty, and endpoint state deviation of each train, establish a local objective function for each train and set constraints on the local objective function. S2. Based on the local objective function of a single train, establish the overall objective function for multiple trains, and set constraints on the overall objective function; S3. Decompose the overall objective function to obtain the global coordination term, and add the global coordination term to the local objective function to obtain the local subproblems; S4. Solve the local subproblems of a single train under the constraints of the local objective function and send the predicted trajectory. The signal coordinator checks the predicted trajectories of each train based on the constraints of the overall objective function. If there is a conflict, update the global common variables and the Lagrange multiplier vector until convergence.

[0006] Furthermore, the expression for the local objective function in S1 is: , Wherein, J(μ) i,k Let be the local objective function of the i-th train at time k, where α is the weight of net power, β is the weight of punctuality error penalty, Υ is the weight of acceleration change penalty, and ρ is the weight of final state deviation. Let be the net power of the i-th train at time k. Let $\frac{i}{i}$ be the penalty for the punctuality error of the $i$-th train at time $k$. For the penalty term of acceleration change, Let represent the endpoint state deviation of the i-th train, where i is the train number, k is the time number, and N is the prediction time domain length.

[0007] Furthermore, the constraints of the local objective function in S1 include: safety clearance constraints, signal blocking time window constraints, and regenerative braking energy distribution constraints.

[0008] Furthermore, the expression for the safety clearance constraint is: Among them, s i-1 (k) represents the position of the (i-1)th train at time k, s i (k) represents the position of the i-th train at time k, D0 is the basic safety distance between trains, τ is the time interval, and v i (k) represents the speed of the i-th train at time k, where i is the train number and k is the time number; The signal blocking time window constraint includes: A1. Define the set of available time for the defined segment; A2. Predict the time it will take for the train to enter the target section; A3. Limit the entry time of a single train to the set of available times; A4. Limit the time interval between multiple trains entering the same section; Regenerative braking energy distribution constraints include: B1. Limitation of energy pool capacity; B2. Determine the energy pool's absorption power; B3. Calculate the energy loss based on the regeneration power and the energy in the energy pool; B4. Calculate the energy of the energy pool at the next moment based on the energy loss, the energy of the energy pool, the regeneration power, and the absorption power.

[0009] Furthermore, the overall objective function in S2 is the minimum of the sum of the local objective functions of all trains; The constraints of the overall objective function include: train spacing coupling constraints, energy pool constraints, and section time window constraints.

[0010] Furthermore, the expression for the local subproblem in S3 is: , Where, μ i,m+1 Let μ be the acceleration vector of the i-th train in the (m+1)-th iteration at local location. i,m Let J(μ) be the acceleration vector of the i-th train in the m-th iteration at the local location. i,m Let be the local objective function of the i-th train in the m-th iteration, and argmin be the value of finding μ that minimizes the expression. i,m U i Let A be the set of possible accelerations for the i-th train at all times, θ be the penalty parameter, and A be the set of possible accelerations for the i-th train at all times. i Extract the coupling state matrix for the i-th train, z m Let λ be the global public variable in the local m-th iteration. i,m Let |i| be the Lagrange multiplier vector of the i-th train in the m-th iteration at local location, and |i| be the L2 norm. The global coordination term, where m is the number of the local iteration and i is the train number.

[0011] Furthermore, S4 includes the following sub-steps: S41. Solve the local subproblems of a single train within the constraints of the local objective function to obtain the predicted trajectory, and send the predicted trajectory to the signal coordinator. S42. On the signal coordinator, the predicted trajectories of each train are checked according to the constraints of the overall objective function, and the global common variables are updated when conflicts exist. S43. Update the Lagrange multiplier vectors based on the updated global public variables. S44. Based on the updated global common variables, determine whether convergence has occurred. If convergence has occurred, send the current acceleration vector to the train. If convergence has not occurred, feed back the updated global common variables and Lagrange multiplier vectors to each train and jump to step S41.

[0012] Furthermore, the formula for updating the global public variable in S42 is: Among them, z l+1 For the (l+1)th iteration of the signal coordinator, For the projection operator of common variables, A i Extract the coupling state matrix for the i-th train, μ i,l+1 Let λ be the acceleration vector of the i-th train on the signal coordinator in the (l+1)th iteration. i,l Let be the Lagrange multiplier vector of the i-th train on the signal coordinator in the l-th iteration, where l is the iteration number on the signal coordinator, i is the train number, and M is the number of trains.

[0013] Furthermore, the formula for updating the Lagrange multiplier vector in S43 is: , Where, λ i,l+1 Let be the Lagrange multiplier vector of the i-th train in the (l+1)-th iteration on the signal coordinator.

[0014] Furthermore, the first element of the Lagrange multiplier vector is used to control the coupling constraint of train spacing, the second element of the Lagrange multiplier vector is used to control the energy pool constraint, and the third element of the Lagrange multiplier vector is used to control the time window constraint of the section.

[0015] The beneficial effects of this invention are as follows: This invention addresses the challenge of simultaneously addressing the constraints of multi-train operation safety, operational performance indicators, and efficient utilization of regenerative braking energy within a unified optimization framework. It establishes a local objective function for each train, incorporating factors such as net power (related to regenerative braking energy utilization and energy consumption), punctuality error penalty (corresponding to punctuality rate constraints), acceleration change penalty (corresponding to comfort constraints), and endpoint state deviation, and sets corresponding constraints. Based on this, a comprehensive objective function for multiple trains is constructed, using multi-train operation safety constraints as constraints. This approach comprehensively addresses various needs from a global perspective, achieving a balance between multi-train operation safety, operational performance indicators, and efficient utilization of regenerative braking energy within a unified optimization framework.

[0016] This invention addresses the problem of lacking an engineering-based solution path and failing to achieve optimal global energy consumption for a train under multi-train coupling constraints. The invention first decomposes the overall objective function to obtain a global coordination term. This global coordination term is then added to the local objective function to obtain local subproblems. Each train solves its own local subproblem and sends its predicted trajectory under its corresponding constraints. Subsequently, with the help of a signal coordinator, the predicted trajectories of each train are checked based on the constraints of the overall objective function. If conflicts exist, the global common variables and Lagrange multiplier vectors are updated. This iterative process continues until convergence, forming an engineering-based optimization solution path that effectively handles the coupling constraints of multiple trains and ultimately achieves optimal global energy consumption for the train. Attached Figure Description

[0017] Figure 1 This is a flowchart of a collaborative scheduling method for rail transit trains.

[0018] Figure 2 This is a schematic diagram of the overlapping area of ​​traction and braking stages of different trains within the same power supply zone.

[0019] Figure 3 This is a diagram showing the relative speeds at various levels related to train operation control. Detailed Implementation

[0020] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0021] like Figure 1 As shown, a method for coordinated scheduling of rail transit trains includes the following steps: S1. Based on the net power, punctuality error penalty, acceleration change penalty, and endpoint state deviation of each train, establish a local objective function for each train and set constraints on the local objective function. S2. Based on the local objective function of a single train, establish the overall objective function for multiple trains, and set constraints on the overall objective function; S3. Decompose the overall objective function to obtain the global coordination term, and add the global coordination term to the local objective function to obtain the local subproblems; S4. Solve the local subproblems of a single train under the constraints of the local objective function and send the predicted trajectory. The signal coordinator checks the predicted trajectories of each train based on the constraints of the overall objective function. If there is a conflict, update the global common variables and the Lagrange multiplier vector until convergence.

[0022] In this embodiment, the expression for the local objective function in S1 is: , Wherein, J(μ) i,k Let be the local objective function of the i-th train at time k, where α is the weight of net power, β is the weight of punctuality error penalty, Υ is the weight of acceleration change penalty, and ρ is the weight of final state deviation. Let be the net power of the i-th train at time k. Let $\frac{i}{i}$ be the penalty for the punctuality error of the $i$-th train at time $k$. For the penalty term of acceleration change, Let represent the endpoint state deviation of the i-th train, where i is the train number, k is the time number, and N is the prediction time domain length.

[0023] α, β, Υ, and ρ can be dynamically adjusted according to the operational strategy, with emphasis on punctuality during peak periods and energy consumption during off-peak periods.

[0024] The expression for net power is:

[0025]

[0026] , in, Let be the traction power of the i-th train at time k. Let a be the regenerative power of the i-th train at time k. i (k) represents the acceleration of the i-th train at time k, F res,i (v i (k) represents the running resistance of the i-th train at time k, v i (k) represents the speed of the i-th train at time k, m i Let η be the mass of the i-th train, and max be the maximum of the two values. regen For regenerative braking feedback efficiency.

[0027] During the braking phase, the train generates regenerative braking energy, which is collected and stored in an energy pool, such as... Figure 2 As shown.

[0028] The expression for running resistance is: Among them, C 0,i C is the coefficient of static friction and rolling resistance. 1,i C is the drag coefficient for the first-order velocity term, reflecting a portion of mechanical friction and aerodynamic drag. 2,i This is the drag coefficient for the square of the velocity, reflecting the characteristic that air resistance increases with the square of the velocity.

[0029] The expression for running speed is: , Among them, v i (k-1) represents the speed of the i-th train at time k-1, T s For the sampling period, a i (k-1) represents the acceleration of the i-th train at time k-1.

[0030] Set an emergency braking speed limit for the operating speed: v i (k) < V, V = [v] e,1 , …, v e,R ], where V is the emergency braking speed limit vector, v e,1 To limit the speed at orbital position 1, v e,R The speed limit is set at position R on the track, where R is the number of speed limits. Since subways have track conditions (curves, gradients, etc.), the specific emergency braking speed limit needs to be found based on the specific location on the track.

[0031] In situations where the operating speed needs to be lower than the emergency braking speed limit, such as... Figure 3 As shown, Figure 3 The ATP system speed limit is a speed limit set by the Automatic Train Protection (ATP) system to ensure train operation safety and prevent speeding. The ATO operating speed represents the actual operating speed under the control of the Automatic Train Operation (ATO) system. It is the ATP system emergency braking trigger speed. If the actual speed of the train reaches this value, the ATP system will forcibly trigger emergency braking to ensure that the train stops within a safe distance.

[0032] The expression for the punctuality error penalty is: Where max represents the maximum of the two values. Let be the predicted arrival time of the i-th train. Let be the planned arrival time of the i-th train.

[0033] Predicted arrival time setting The predicted time point is calculated using the velocity-position relationship formula, which is: , Among them, s i (k) represents the position of the i-th train at time k, s i (k-1) represents the position of the i-th train at time k-1, T s For the sampling period, a i (k-1) represents the acceleration of the i-th train at time k-1.

[0034] The expression for the penalty term for the change in acceleration is: , Among them, a i(k) represents the acceleration of the i-th train at time k, a i (k-1) represents the acceleration of the i-th train at time k; Penalties for changes in acceleration are related to passenger comfort; setting penalties for changes in acceleration can improve passenger comfort.

[0035] The destination state deviation, also known as the arrival position deviation, is expressed as follows:

[0036] , Among them, s arr,pre To predict the arrival distance of the train after it travels according to the planned time, s is the target position where the train should stop precisely, and s0 is the initial distance. Let a be the scheduled arrival time of the i-th train. i (k) represents the acceleration of the i-th train at time k.

[0037] In this embodiment, the constraints of the local objective function in S1 include: safety distance constraint, signal blocking time window constraint, and regenerative braking energy allocation constraint.

[0038] In this embodiment, the expression for the safety distance constraint is: , Among them, s i-1 (k) represents the position of the (i-1)th train at time k, s i (k) represents the position of the i-th train at time k, D0 is the basic safety distance between trains, τ is the time interval, and v i (k) represents the speed of the i-th train at time k, where i is the train number and k is the time number.

[0039] τ determines the dynamic safety distance and is related to the train's current speed.

[0040] Safety distance constraints can only solve the problem of safe rear-end collisions between trains running on the same track and traveling in the same direction, while signal block time window constraints essentially solve the problem of resource conflicts based on the same location within the same time period, such as scenarios where trains running in opposite directions or trains traveling in a straight line and laterally enter the same turnout area.

[0041] The signal blocking time window constraint includes: A1. Define the available time set for the segment: Where W is the set of available time, t 1,min t represents the entry time of the first segment. 1,max t is the clearing time for the first segment. j,min Let t be the entry time of the j-th segment. j,max Let t be the clearing time of the j-th segment.n,min Let t be the entry time of the nth segment. n,max Let be the clearing time of the nth segment, ∪ be the union, j be the segment number, and n be the number of segments; A2. Predict the time when the train will enter the target section: , in, Let s be the estimated arrival time of the i-th train in the j-th section. j Let s be the entry point of the j-th segment. 0 t represents the current position of the train. unc To account for the time factors of error and system transmission delay, t0 is the current time, v avg,i To predict the average speed before entering the section; A3. Limit the entry time of a single train within the available time set: in, Let be the estimated entry time of the i-th train in the j-th section, where j is the number of the block section selected from the n sections; A4. Restrict the time interval between multiple trains entering the same section: i and r, , Where, is the i-th vehicle The estimated arrival time of the train in section j. Let be the estimated arrival time of the r-th train in the j-th section. The minimum time required to clear the confirmation, where r is another train.

[0042] The regenerative braking energy of the train needs to be reasonably distributed on the line. That is, within a certain period of time, the total regenerative energy must not exceed the battery capacity and absorption capacity, and the energy distribution in the battery must meet the requirements.

[0043] Regenerative braking energy distribution constraints include: B1. Limitation of energy pool capacity: , Among them, E pool (k) represents the energy of the energy pool at time k. This represents the maximum capacity of the energy pool. B2. Determine the energy pool's absorbed power: , in, Let d be the power absorbed by the energy pool at time k. sched Assign weight coefficients to the scheduler, T s For time step; B3. Calculate the energy loss based on the regeneration power and the energy in the energy pool: Among them, L loss (k) represents energy loss. Let λ be the regeneration power of the i-th train at time k, and λ be the storage loss coefficient. B4. Based on the energy loss, the energy pool's energy, the regeneration power, and the absorbed power, calculate the energy pool's energy at the next moment: , Among them, E pool (k+1) represents the energy in the energy pool at time k+1.

[0044] In this embodiment, the overall objective function is the minimum of the sum of the local objective functions of all trains: , Where min represents the minimum value, μ i,k Let J(μ) be the acceleration vector of the i-th train at time k. i,k Let M be the local objective function of the i-th train at time k, and M be the number of trains.

[0045] The constraints of the overall objective function include: train spacing coupling constraints, energy pool constraints, and section time window constraints.

[0046] The expression for the train spacing coupling constraint is: , Among them, g ir (μ i ,μ r D represents the constraint on the coupling of the distance between trains i and r. safe For a safe distance, s i (k) represents the position of the i-th train at time k, s r (k) represents the position of the r-th train at time k, and ε represents the set of trains.

[0047] Train spacing coupling constraints are used to represent train spacing coupling and how to achieve a safe spacing.

[0048] The expression for the energy pool constraint is: , Where h(μ) 1, μ 2,…, μ M (This is a constraint on the energy pool.) Let T be the power absorbed by the energy pool at time k. s For the time step, E pool (k) represents the energy of the energy pool at time k. This represents the maximum capacity of the energy pool.

[0049] The expression for the time window constraint is: ,in, For the time window constraint, t iLet t be the time when the i-th train enters a certain section, t be the time when trains are allowed to enter the section, W be the set of available times, and || be the absolute value.

[0050] μ 1, μ 2,…, μ M There are M acceleration vectors, μ i =[a i (1),…, a i (L)],a i (1) Let a be the first acceleration of the i-th train. i (L) represents the Lth acceleration of the i-th train, where L is the number of accelerations in an acceleration vector.

[0051] In the time window constraint of a section, if the current speed causes the train to enter a certain section when the available time set is not met, the speed will be forcibly reduced until it is met.

[0052] The expression for the local subproblem in S3 is: , Where, μ i,m+1 Let μ be the acceleration vector of the i-th train in the (m+1)-th iteration at local location. i,m Let J(μ) be the acceleration vector of the i-th train in the m-th iteration at the local location. i,m Let be the local objective function of the i-th train in the m-th iteration, and argmin be the value of finding μ that minimizes the expression. i,m U i Let A be the set of possible accelerations for the i-th train at all times, θ be the penalty parameter, and A be the set of possible accelerations for the i-th train at all times. i Extract the coupling state matrix for the i-th train, z m Let λ be the global public variable in the local m-th iteration. i,m Let |i| be the Lagrange multiplier vector of the i-th train in the m-th iteration at local location, and |i| be the L2 norm. For global coordination, m is the number of local iterations, and i is the train number.

[0053] A i μ i,m This represents the "global coupling mapping" of local control variables (may transfer the local control variable μ of train i to the global coupling mapping). i,m This is mapped to the "dimensional of global public variables," such as "time of entering the segment" and "energy request amount," reflecting the impact of local decisions on the global situation.

[0054] Coupled state extraction matrix A i The expression is: , Among them, C s Extracting a submatrix for position-related states, Ct Extracting submatrices for time-window related states, C P Extract submatrices for power-related states, where R is the real number field, L is the length of the acceleration vector, and N... s N represents the dimension of location-related state variables. t N represents the dimension of state quantities related to the time window. P For power-related state variables, the dimension is denoted as .

[0055] N s The value of N is usually taken as 1. t The value of N is usually taken as 1. P The value is usually taken as 1.

[0056] Location-related state extraction submatrix C s Used to extract safety-critical locations, its structure is: a row vector (and a sparse vector, i.e., most elements are 0, only critical locations are 1). When L=10 (which can be understood as 10 time steps or data points, each step being 1 second), the vector is [0 0 0 1 ... 0], representing the position s extracted from the train's multi-dimensional location data at the 3rd time step (because the index starts from 0, the 4th element corresponds to this). i (3) This position is a key position involving safety constraints (such as the train needing to meet the safety distance from the train in front at this position). Set 1 in the first row and fourth column of the matrix (because the subscript starts from 0) to indicate that the position of the i-th train at the 3rd second has an impact on the safety distance.

[0057] Time window related state extraction submatrix C t The structure used to extract the braking power of a train is: a sparse row vector. When L=10, the vector is [0 0 0… 1…0]. The matrix is ​​set to 1 in the 1st row and 6th column (since the index starts from 0), indicating that the time window for the i-th train to enter a certain section is not met due to the train speed at the 6th second.

[0058] Power-related state extraction submatrix C P The structure used to extract the braking power of a train is: a sparse row vector. When L=10, the vector is [0 0 0… 0…1]. The value is set to 1 in the 2nd row and 11th column of the matrix (since the subscript starts from 0), indicating that the braking power of the i-th train at the 10th second affects the energy pool constraint.

[0059] Global public variable z m The expression is: ,in, For the secure projection operator, For the projection operator of the time interval, Projection operator for capacity allocation, si (k) represents the position of the i-th train at time k, t i (k) represents the time when the i-th train enters the section at time k. Let M be the regenerative power of the i-th train at time k, and M be the number of trains.

[0060] z m The global common variables at the m-th iteration (such as "unified safety distance constraints", "unified section time window", "global energy allocation scheme", which are "consistent variables" shared by all trains) are represented.

[0061] The safety projection operator is used to enforce vehicle spacing, while the capacity allocation projection operator is used to prevent excessive energy use.

[0062] The expression for the Lagrange multiplier vector is: , Where, λ i,m,1 The first element in the Lagrange multiplier vector is used to control the coupling constraint of train spacing, λ. i,m,2 The second element in the Lagrange multiplier vector is used to control the energy pool constraint, λ. i,m,3 The third element in the Lagrange multiplier vector is used to control the time window constraint of the segment.

[0063] The initial values ​​of the three elements in the Lagrange multiplier vector can be set. For example, the initial value of the first element can be set to 30m, the initial value of the second element can be set to 800kW, and the initial value of the third element can be set to 90s.

[0064] The penalty parameter θ is used to control the "strength of consistency between local decisions and global public variables" - the larger θ is, the more it emphasizes that "local decisions should match global variables".

[0065] In this embodiment, S4 includes the following sub-steps: S41. Solve the local subproblems of a single train within the constraints of the local objective function to obtain the predicted trajectory, and send the predicted trajectory to the signal coordinator. S42. On the signal coordinator, the predicted trajectories of each train are checked according to the constraints of the overall objective function, and the global common variables are updated when conflicts exist. S43. Update the Lagrange multiplier vectors based on the updated global public variables. S44. Based on the updated global common variables, determine whether convergence has occurred. If convergence has occurred, send the current acceleration vector to the train. If convergence has not occurred, feed back the updated global common variables and Lagrange multiplier vectors to each train and jump to step S41.

[0066] In this embodiment, convergence refers to whether the difference between the updated global public variable and the target global public variable reaches a preset range.

[0067] The acceleration vector is the decision vector of the train. The train operation is controlled by adjusting the acceleration. The train's speed and position can also be calculated by the acceleration. Therefore, the predicted trajectory is based on the acceleration vector. Combined with the formulas for speed and position, the multi-dimensional operating state sequence of the train at each time step in the prediction time domain, such as position, speed, traction / braking power, and arrival time, is further derived.

[0068] The formula for updating global public variables is: , Among them, z l+1 For the (l+1)th iteration of the signal coordinator, For the projection operator of common variables, A i Extract the coupling state matrix for the i-th train, μ i,l+1 Let λ be the acceleration vector of the i-th train on the signal coordinator in the (l+1)th iteration. i,l Let be the Lagrange multiplier vector of the i-th train on the signal coordinator in the l-th iteration, where l is the iteration number on the signal coordinator, i is the train number, and M is the number of trains.

[0069] μ i,l+1 Let A be the control variable (e.g., acceleration command) obtained by the i-th train in the (l+1)-th iteration during the "local update" step. i μ i,l+1 λ represents the linear relationship between the control variables of train i and the "global coupling part" (reflecting the association between the train and the common variables). i,l For the l-th iteration, the i-th Lagrange multiplier (used to coordinate consistency between the train and common variables).

[0070] In the (l+1)th iteration, the signal coordinator first fuses the "local information (coupling terms + Lagrange multipliers)" of all trains and takes the average. Then, it projects this "averaged result" onto the constraint set Z of the common variables, ultimately obtaining the new common variable z. l+1 The constraint set Z is the set of all "multi-train coordination constraints" that the global public variables must satisfy. , Where, λ i,l+1 Let be the Lagrange multiplier vector of the i-th train in the (l+1)-th iteration on the signal coordinator.

[0071] This invention solves the global optimization problem through a decomposition-coordination strategy. Its core is to transform the coupled constraints into subproblems that each train can solve independently. The process consists of three steps: 1. Train parallel optimization: Each train independently calculates the local optimum and uploads the predicted trajectory; 2. Signal layer coordination and arbitration: Integrate trajectories, check safety / energy constraints, and update common variables; 3. Multiplier correction deviation: Adjust the train control quantity based on the coordination results.

[0072] This invention decomposes the complex multi-train coupled constraint problem into subproblems that can be solved in a distributed manner through a "local optimization-global arbitration-multiplier feedback" loop. Its core lies in replacing direct constraints with quadratic penalty terms, enabling each train to pursue its own energy-saving optimization while also considering global coordination.

[0073] In this embodiment, the solution algorithm adopts ADMM (Alternating Direction Method of Multipliers).

[0074] This invention addresses the challenge of simultaneously addressing the constraints of multi-train operation safety, operational performance indicators, and efficient utilization of regenerative braking energy within a unified optimization framework. It establishes a local objective function for each train, incorporating factors such as net power (related to regenerative braking energy utilization and energy consumption), punctuality error penalty (corresponding to punctuality rate constraints), acceleration change penalty (corresponding to comfort constraints), and endpoint state deviation, and sets corresponding constraints. Based on this, a comprehensive objective function for multiple trains is constructed, using multi-train operation safety constraints as constraints. This approach comprehensively addresses various needs from a global perspective, achieving a balance between multi-train operation safety, operational performance indicators, and efficient utilization of regenerative braking energy within a unified optimization framework.

[0075] This invention addresses the problem of lacking an engineering-based solution path and failing to achieve optimal global energy consumption for a train under multi-train coupling constraints. The invention first decomposes the overall objective function to obtain a global coordination term. This global coordination term is then added to the local objective function to obtain local subproblems. Each train solves its own local subproblem and sends its predicted trajectory under its corresponding constraints. Subsequently, with the help of a signal coordinator, the predicted trajectories of each train are checked based on the constraints of the overall objective function. If conflicts exist, the global common variables and Lagrange multiplier vectors are updated. This iterative process continues until convergence, forming an engineering-based optimization solution path that effectively handles the coupling constraints of multiple trains and ultimately achieves optimal global energy consumption for the train.

[0076] The above are merely preferred embodiments of the present invention and are not intended to limit the present 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 method for coordinated scheduling of rail transit trains, characterized in that, Includes the following steps: S1. Based on the net power, punctuality error penalty, acceleration change penalty, and endpoint state deviation of each train, establish a local objective function for each train and set constraints on the local objective function. S2. Based on the local objective function of a single train, establish the overall objective function for multiple trains, and set constraints on the overall objective function; S3. Decompose the overall objective function to obtain the global coordination term, and add the global coordination term to the local objective function to obtain the local subproblems; S4. Solve the local subproblems of a single train under the constraints of the local objective function and send the predicted trajectory. The signal coordinator checks the predicted trajectories of each train based on the constraints of the overall objective function. If there is a conflict, update the global common variables and the Lagrange multiplier vector until convergence.

2. The rail transit train cooperative scheduling method according to claim 1, characterized in that, The expression for the local objective function in S1 is: , Wherein, J(μ) i,k Let be the local objective function of the i-th train at time k, where α is the weight of net power, β is the weight of punctuality error penalty, Υ is the weight of acceleration change penalty, and ρ is the weight of final state deviation. Let be the net power of the i-th train at time k. Let $\frac{i}{i}$ be the penalty for the punctuality error of the $i$-th train at time $k$. For the penalty term of acceleration change, Let represent the endpoint state deviation of the i-th train, where i is the train number, k is the time number, and N is the prediction time domain length.

3. The rail transit train cooperative scheduling method according to claim 1, characterized in that, The constraints of the local objective function in S1 include: safety distance constraints, signal blocking time window constraints, and regenerative braking energy distribution constraints.

4. The rail transit train cooperative scheduling method according to claim 3, characterized in that, The expression for the safety distance constraint is: , Among them, s i-1 (k) represents the position of the (i-1)th train at time k, s i (k) represents the position of the i-th train at time k, D0 is the basic safety distance between trains, τ is the time interval, and v i (k) represents the speed of the i-th train at time k, where i is the train number and k is the time number; The signal blocking time window constraint includes: A1. Define the set of available time for the defined segment; A2. Predict the time it will take for the train to enter the target section; A3. Limit the entry time of a single train to the set of available times; A4. Limit the time interval between multiple trains entering the same section; The regenerative braking energy distribution constraints include: B1. Limitation of energy pool capacity; B2. Determine the energy pool's absorption power; B3. Calculate the energy loss based on the regeneration power and the energy in the energy pool; B4. Calculate the energy of the energy pool at the next moment based on the energy loss, the energy of the energy pool, the regeneration power, and the absorption power.

5. The rail transit train cooperative scheduling method according to claim 1, characterized in that, The overall objective function in S2 is the minimum of the sum of the local objective functions of all trains; The constraints of the overall objective function include: train spacing coupling constraints, energy pool constraints, and section time window constraints.

6. The rail transit train cooperative scheduling method according to claim 1, characterized in that, The expression for the local subproblem in S3 is: , Where, μ i,m+1 Let μ be the acceleration vector of the i-th train in the (m+1)-th iteration at local location. i,m Let J(μ) be the acceleration vector of the i-th train in the m-th iteration at the local location. i,m Let be the local objective function of the i-th train in the m-th iteration, and argmin be the value of finding μ that minimizes the expression. i,m U i Let A be the set of possible accelerations for the i-th train at all times, θ be the penalty parameter, and A be the set of possible accelerations for the i-th train at all times. i Extract the coupling state matrix for the i-th train, z m Let λ be the global public variable in the local m-th iteration. i,m Let |i| be the Lagrange multiplier vector of the i-th train in the m-th iteration at local location, and |i| be the L2 norm. The global coordination term, where m is the number of the local iteration and i is the train number.

7. The rail transit train cooperative scheduling method according to claim 1, characterized in that, S4 includes the following sub-steps: S41. Solve the local subproblems of a single train within the constraints of the local objective function to obtain the predicted trajectory, and send the predicted trajectory to the signal coordinator. S42. On the signal coordinator, the predicted trajectories of each train are checked according to the constraints of the overall objective function, and the global common variables are updated when conflicts exist. S43. Update the Lagrange multiplier vectors based on the updated global public variables. S44. Based on the updated global common variables, determine whether convergence has occurred. If convergence has occurred, send the current acceleration vector to the train. If convergence has not occurred, feed back the updated global common variables and Lagrange multiplier vectors to each train and jump to step S41.

8. The rail transit train cooperative scheduling method according to claim 7, characterized in that, The formula for updating the global public variable in S42 is as follows: , Among them, z l+1 For the (l+1)th iteration of the signal coordinator, For the projection operator of common variables, A i Extract the coupling state matrix for the i-th train, μ i,l+1 Let λ be the acceleration vector of the i-th train on the signal coordinator in the (l+1)th iteration. i,l Let be the Lagrange multiplier vector of the i-th train on the signal coordinator in the l-th iteration, where l is the iteration number on the signal coordinator, i is the train number, and M is the number of trains.

9. The rail transit train cooperative scheduling method according to claim 8, characterized in that, The formula for updating the Lagrange multiplier vector in S43 is as follows: , Where, λ i,l+1 Let be the Lagrange multiplier vector of the i-th train in the (l+1)-th iteration on the signal coordinator.

10. The rail transit train cooperative scheduling method according to claim 7, characterized in that, The first element of the Lagrange multiplier vector is used to control the coupling constraint of train spacing, the second element is used to control the energy pool constraint, and the third element is used to control the time window constraint of the section.

Images