A method for optimizing a schedule and a speed curve considering passenger flow

Abstract

The application discloses a kind of schedule and speed curve optimization method considering passenger flow.The method steps are as follows: clustering analysis is carried out to historical section passenger flow to divide passenger flow time characteristics, and a neural network passenger flow prediction model is established;Based on the running condition between single vehicles, according to the kinetic formula, the improved simulated annealing algorithm is used to optimize the working condition conversion point in the driving process of train speed curve, so that the final single section meets the conditions of accurate train stopping, minimum energy consumption and the like;For the running process between multiple trains and multiple stations, an operation time and stopping time schedule optimization model is established, and the simulated annealing algorithm is used to solve the problem with the minimum train traction total energy consumption and passenger waiting time as the optimization objective.The method of the application comprehensively considers the bidirectional optimization of single train speed curve and schedule under passenger flow, maximally reduces the total train traction energy consumption, total operation energy consumption and passenger waiting time of the whole line, and has high use value and application prospect.

Description

Technical Field

[0001] The present invention relates to the technical field of urban rail transit, and in particular to a method for optimizing a timetable and a speed curve taking passenger flow into consideration. Background Art

[0002] With the rapid development of urban rail transit, due to its convenience, punctuality, and efficiency, it has become the preferred mode of transportation in many cities. This has led to a gradual increase in urban rail passenger volume. As the number of urban rail transit lines, operating mileage, and passenger volume increase, operating energy consumption is also increasing. Faced with such enormous energy consumption and growing passenger demand, how to effectively reduce train traction energy consumption and improve passenger service quality has become a key research issue.

[0003] Reducing train traction energy consumption mainly involves the following three aspects:

[0004] 1) Considering the actual route: Optimizing train routes, such as energy-saving slopes;

[0005] 2) Considering the actual equipment: adding inter-station energy storage and absorption devices, optimizing vehicle body materials to reduce vehicle weight, etc.

[0006] 3) Consider the operation mode: optimize the speed curve, train operation plan, timetable optimization, etc.

[0007] From the three perspectives of optimizing energy consumption mentioned above, 1) for existing rail lines, optimization solution 1) is obviously unrealistic, and it is impossible to rebuild the line on the existing line; 2) energy storage devices are currently in use on some domestic subway lines, but they cannot be promoted on a large scale due to cost and technical constraints; compared with the first two optimization methods, 3) only needs to change the train operation plan or operation mode to reduce the energy consumption of a single vehicle. In addition, the optimization of stop time and departure interval can also greatly improve the absorption efficiency of regenerative braking energy consumption of urban rail transit trains, which has little impact on train operation and passenger capacity while being low in cost.

[0008] Improving the quality of passenger service mainly includes several aspects such as passenger comfort, passenger travel mode and passenger waiting time. Passenger comfort mainly reflects the changes in the acceleration of the train during operation, and avoids sudden braking or acceleration as much as possible, which is related to the speed curve of the train. The travel choice of passengers is generally affected by subway planning, including nearby construction and development and line intersections, and the improvement is limited. The waiting time of passengers is related to the planned train schedule, including the departure intervals, running time and stop time between trains.

[0009] Therefore, comprehensive consideration of train operations and passengers to optimize train travel modes and operation plans, namely, passenger flow-based train speed curve optimization and passenger flow-based timetable adjustment, are currently major issues in rail transit energy-saving technology. Summary of the Invention

[0010] The purpose of the present invention is to provide a timetable and speed curve optimization method that takes passenger flow into consideration, so as to maximize the reduction of the total traction energy consumption of trains on the entire line and reduce passenger waiting time while meeting the conditions of passenger comfort, safe train operation and normal operation scheduling.

[0011] The technical solution for achieving the purpose of the present invention is: a method for optimizing a timetable and speed curve taking into account passenger flow, comprising the following steps:

[0012] Step 1: Obtain historical cross-section passenger flow data of the route and perform cluster analysis;

[0013] Step 2: Based on the cluster analysis results, a neural network short-term passenger flow prediction model is established to predict the passenger flow data for the day;

[0014] Step 3: Obtain basic line data, electrical data, section data, and timetable information of rail trains;

[0015] Step 4: Based on the operation of a single train car, a dynamic model is built according to the train line data and electrical data. Taking the punctuality rate, passenger comfort, running time, and traction energy consumption of the actual train operation as the optimization objectives, a single-interval speed curve optimization model based on the parallel simulated annealing algorithm is established;

[0016] Step 5: Based on the coordinated operation of multiple trains, a data module for energy-saving timetable analysis and calculation is established. Minimizing the total traction energy consumption of trains on the entire line and passenger waiting time is optimized. Combined with the speed curve optimization model established for the single-section operation scenario, an integrated timetable and speed curve optimization model is established. Using a parallel simulated annealing algorithm, the speed curve is optimized simultaneously with the timetable's running time and stop time.

[0017] Step 6: Output the optimized results, i.e., the interval energy-saving speed curve and the optimal train schedule for the entire line.

[0018] Compared with the existing technology, the present invention has the following significant advantages: (1) cluster analysis is performed on the historical section passenger flow, and the passenger flow period of the whole day is divided into categories. Based on the divided passenger flow categories, the historical section passenger flow is predicted using a neural network as a data source for speed curve optimization and timetable optimization. (2) The present invention comprehensively considers the energy-saving operation of a single train and the energy-saving operation of multiple trains, that is, the timetable is adjusted by combining the energy-saving optimization method of the speed curve of a single train with the collaborative optimization method of multiple trains, and the simulated annealing algorithm is used to optimize the train stop time and departure interval under the consideration of passenger flow, and the simulated annealing algorithm is improved in parallel to increase the number of unimproved times, in order to accelerate the convergence speed and prevent falling into the local optimal solution. Ultimately, the total traction energy consumption of the train and the waiting time of passengers are reduced; (3) The present invention only adjusts the train's running speed and time, and fine-tunes the stop time to achieve the effect of reducing energy consumption, while keeping the original planned time unchanged. It is simple and easy to implement. (4) The present invention does not require the investment of additional equipment and does not set up an energy storage device, which can save a lot of costs. It is highly feasible and practical. (5) It has strong applicability. The present invention adjusts the speed curve and operation schedule of the train to strictly meet the passenger comfort index, train safety operation index, train operation scheduling index, etc. (6) The relevant optimization algorithm designed by the present invention is based on the improved simulated annealing algorithm, which has a fast optimization speed, effectively improves the calculation efficiency and prevents the algorithm from falling into the local optimal solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is an overall schematic diagram of a comprehensive energy-saving optimization method for train speed curves and timetables taking passenger flow into consideration in the present invention.

[0020] Figure 2 This is a neural network cross-section passenger flow prediction model diagram in the present invention.

[0021] Figure 3 This is a flow chart for solving the single train speed curve optimization model based on the improved simulated annealing algorithm in the present invention.

[0022] Figure 4 This is a flow chart for solving a schedule optimization model based on an improved simulated annealing algorithm in the present invention. DETAILED DESCRIPTION

[0023] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments to enable a better understanding of the functions and features of the present invention. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the scope of protection of the present invention is not limited to the following embodiments.

[0024] Combine Figure 1The present invention implements a timetable and speed curve optimization method considering passenger flow, which mainly includes three main modules: a neural network passenger flow prediction module, a single train speed curve optimization module, and a multi-train collaborative timetable optimization module. The specific steps are as follows:

[0025] Step 1: Obtain historical passenger flow data for the route section and perform cluster analysis. The specific sub-steps are as follows;

[0026] (1) Generate sample set. Assume that the operation statistics period is 06:00-23:00, statistics are collected every 15 minutes, and each time period corresponds to d intervals. Therefore, the sample set is divided into D = {D1, D2, D3, ... D m}, where m is the sample size, D i This means that the passenger flow data of all intervals in the current time period is stored, and then:

[0027]

[0028] (2) Randomly select k sample objects μ1, μ2, …μ in the sample set D k As the initial center of each category, the sample k is selected using the elbow method according to the degree of change of the sum of squared errors (SSE) of the clustering.

[0029]

[0030] Where G i is the i-th cluster, p is G i Sample points, m i It is cluster G i The center point of , SSE is the clustering error result of all samples, which represents the quality of the clustering result;

[0031] (3) Calculate the Euclidean distance dist between samples and use it to classify them into the category to which the category center is closest. The calculation formula is as follows:

[0032]

[0033]

[0034] In the formula u=(u1,u2,…,u n ),v=(v1,v2,…,v n ) is represented as a vector of two samples. label represents the category label to which it belongs;

[0035] (4) Update the center point u of each sample category j , using mean value instead, the formula is as follows:

[0036]

[0037] (5) Calculate the objective function E after this iteration. If the difference between the function value calculated this time and the function calculated last time is within the set threshold range, it indicates that the classification is completed and the K-means algorithm is terminated. Otherwise, repeat steps (3) to (5). The calculation formula is as follows:

[0038]

[0039] |E k -E k-1 |≤ε

[0040] Step 2: Based on the cluster analysis results, a neural network short-term passenger flow prediction model is established to predict the passenger flow data for the day;

[0041] Combine Figure 2 The flow chart of the cross-section passenger flow prediction model shown in the figure uses a neural network to predict historical cross-section passenger flow and obtain the passenger flow data for the day. Step 2 specifically includes the following sub-steps:

[0042] (1) Sample data preprocessing: merge the data sets of the section passenger flow data at each moment according to the clustering category to increase the correlation between the data, and use the merged data set as input;

[0043] (2) Initialize the network parameters, including the weights w of the input layer and the hidden layer ij , the weight from the hidden layer to the output layer, and the output threshold θ j 、a k , w ij ,z ij ,θ j ,a k ∈[0,1]; convergence accuracy ε=0.01, adaptive learning rate adjustment factors λ1=1.5,λ2=0.5;

[0044] (3) Calculate the input net of the jth node hidden layer according to the following formula j , the output of the hidden layer h j , the input net of the kth node in the output layer k , the output o of the kth node in the output layer k ;

[0045]

[0046]

[0047]

[0048]

[0049] Where m is the dimension of the input vector, θ j is the threshold of the jth node in the hidden layer; φ(·) is the activation function of the hidden layer node; n is the number of hidden layer nodes, α k is the threshold of the kth node in the output layer; is the activation function of the output layer node;

[0050] (4) Adjust the change Δz of the output layer weight according to the following formula jk , the output layer threshold change Δα k , the change in hidden layer weight Δw ij , the hidden layer threshold change Δθ j ;

[0051]

[0052]

[0053]

[0054]

[0055] Where E is the total error function of all P training sample data, that is

[0056]

[0057] Substitute it into the above formula to get the adjustment formula:

[0058]

[0059]

[0060]

[0061]

[0062] (5) Update the weights and thresholds of each layer and calculate the total error function E P , if E P If the convergence accuracy standard is reached or the number of iterations is reached, the training ends. Otherwise, the learning rate is adjusted according to the adaptive learning rate and the next round of learning continues until the requirements are met. The adaptive learning rate adjustment formula is:

[0063]

[0064] Step 3: Obtain basic rail train line data, mainly including line slope and curve data; train electrical data mainly includes overhead line unit impedance, track unit impedance, traction substation location, traction substation characteristic parameters, station location, power supply division, and operating parameters, including the number of online trains, and the departure station and departure time of each train.

[0065] Step 4: Build a dynamic model based on train line data and electrical data. Taking into account the on-time performance, passenger comfort, running time, and traction energy consumption during actual train operation as optimization objectives, establish a single-interval speed curve optimization model based on a parallel simulated annealing algorithm.

[0066] Combine Figure 3 The flowchart of the single train speed curve optimization solution model based on the parallel simulated annealing algorithm is shown in FIG. 4 , and step 4 specifically includes the following sub-steps:

[0067] (1) Initialization: Set the control algorithm parameters and initialize M X0 populations, where X0 is the optimization command of the speed curve.

[0068] X i0 ={mod e, s1, s2, s3, s4, s5, s6}i=0, 1,...M

[0069] Since the original simulated annealing algorithm has low search efficiency and is incomplete for speed curves with a wide range of speed commands, it is easy to fall into local optimality. Therefore, in order to improve the efficiency of the algorithm, the improved parallel simulated annealing algorithm is used for search and solution.

[0070] The specific steps are as follows: First, during the initialization process, M initial solution populations are randomly generated, the corresponding objective function values ​​are calculated, and the smallest objective function value is selected as the optimal initial solution. Then, a candidate solution is generated for each initial solution using the state generation function, and the inner loop Metropolis algorithm is executed in sequence until the inner loop ends, forming M populations under the new temperature state. Individuals in the new state population that are better than the previous state population are retained, and then the cooling operation is repeated until the algorithm stops. An optimal solution is selected from the last remaining population as the final global optimal solution.

[0071] Because multiple populations execute their inner loops independently, they can be run in parallel, allowing the Metropolis algorithm to execute multiple populations simultaneously. While this increases the computational complexity compared to single-solution serial optimization, the solution coverage generated by multiple populations is higher, allowing for early exits from local optima and inner loop iterations, thereby improving the overall efficiency of the algorithm.

[0072] Where the maximum acceleration traction - first coasting - second traction - second coasting - first braking - third coasting - second braking mode is used for speed curve optimization, and the mixed mode in the middle contains another two coasting modes and cruise mode, a total of 7 commands can be used for train energy saving and time saving optimization, which are running mode mode, first coasting start point s1, first coasting end point s2, second coasting start point s3, second coasting end point s4, third coasting start point s5, and third coasting end point s6;

[0073] (2) According to the initialized parameter command, the speed curve and power curve under each initial command parameter and the corresponding train running energy consumption data are calculated by using the dynamic train speed reverse derivation formula. The train is regarded as a single point model to simplify the problem, and the train motion conforms to Newton's kinematics law. The force on the train can be divided into five categories: vertical downward gravity G; upward support force F of the track on the train 支 ; train traction force F t , train braking force B b and train running total resistance W o , but the gravity G in the track direction is counteracted by the support force. The formula is as follows:

[0074]

[0075] In the formula, K1, K2, A are constants; m, n, p, q, d, e, f, a, b, c are polynomial coefficients; v1, v2 are the speed conversion points of the constant torque and constant power areas of the train traction and braking characteristics; i is the slope during train travel, which is equivalent to the slope resistance per unit mass; r is the radius of the curve; L s is the length of the tunnel; M c is the net weight of the train, M p is the average net weight of a person, n is the train passenger capacity, γ is the rotational mass coefficient, M eq is the converted mass of the train;

[0076] According to the above formula, the following formula can be derived:

[0077]

[0078] When the train is in traction, the traction force formula F t (v) and the running resistance formula W o (v, i, r) are brought into the above formula to obtain the differential equation about displacement x and time t, as follows:

[0079]

[0080] The running distance and running time of the traction stage can be obtained:

[0081]

[0082] Where v1, v2, v3 are equations

[0083] The three roots of

[0084] Similarly, the running distance and running time of the coasting phase are:

[0085]

[0086] The running distance and running time of the braking phase are:

[0087]

[0088] Combining the above formula, we can get the total running time and running distance:

[0089]

[0090] According to the speed data provided by the subway company, there is a speed point every 0.1s. Therefore, when calculating the power and energy consumption of the train, we calculate point by point with Δt = 0.1, and we have:

[0091]

[0092] (3) According to the above steps, the interval speed, power, displacement, time and energy consumption values ​​under the initial parameter command can be obtained. Then the following measurement indicators are added to judge the optimization effect:

[0093] Fixed-point parking index constraint function:

[0094]

[0095] Punctuality index constraint function:

[0096]

[0097] Passenger comfort function:

[0098]

[0099] Energy-saving constraint index function:

[0100]

[0101] Finally, the fitness function F expression is obtained:

[0102]

[0103] (4) According to the dynamic model and formula, calculate the objective function value of each initial population and save the optimal solution P of each population best And the global optimal solution g best Since the parallel simulated annealing algorithm increases the number of populations, the solution coverage rate generated in multiple populations is larger, but the amount of calculation is increased. In order to jump out of the local optimum and the inner and outer loop iterations in advance, the inner and outer loop iterations are improved;

[0104] The specific implementation is as follows: at the beginning of each temperature T, a local solution counter num and the number of times it has not been improved are set and initialized to 0. If the target value calculated by the next new solution is improved compared to the previous solution value, num is reset to 0, otherwise num is increased by 1, that is, num = num + 1; when num > L, the Metropolis algorithm for the current temperature T is exited;

[0105] (5) External loop setting: While(T>T e &&NUM<N), judge whether the current annealing temperature is greater than the set termination temperature, and whether the number of times the outer loop global solution is maintained is less than the set value. If not satisfied, jump out of the outer loop and terminate the algorithm;

[0106] (6) Start traversing M populations for (i = 1; i <= M; i++), and before traversing, set the local solution counter num and the number of times the inner loop has not been improved K, set the inner loop termination condition While (l < L && num < K), and judge whether the number of inner loop iterations has reached the set number and whether the number of times it has not been improved is less than the set value K;

[0107] (7) Generate a candidate solution X′ in the result within the current solution domain, and calculate the fitness function value F according to the above dynamic formula. In order to accept the optimized solution, set the min[1, exp(-ΔC / t] state acceptance function, which is generally given in the form of probability. The design principle of the state acceptance probability is that when the temperature is fixed, the acceptance probability of the solution set that makes the objective function value decrease is greater than the acceptance probability of the solution set that makes the objective function value increase; when the temperature decreases, the acceptance probability of the solution that makes the objective function value increase should be reduced; and when the temperature tends to zero, only the solution with the objective function value decreasing can be accepted. The value generated by min[1, exp(-ΔC / t] is used to determine whether to accept the new value;

[0108] (8) Calculate the increment ΔF = F(X′) - F(X). If ΔF > 0, reset num = 0; otherwise, reset num = num + 1. Determine whether the current number of executions or the number of times the solution has not been improved meets the inner loop conditions.

[0109] (9) Determine whether each population has a historical optimal solution and update the local optimal solution P best and the global optimal solution gbest , if the global solution has not been updated NUM = NUM ​​+ 1; otherwise NUM = 0;

[0110] (10) Perform the cooling operation to determine whether the current temperature is equal to or lower than the termination temperature, or if the global value has not been updated for NUM times > N, then exit the current loop;

[0111] (11) Find the optimal solution for each population in the M memory arrays, and then find the optimal solution for all populations, which is the global optimal solution. Bring the output command into the dynamic calculation model to generate the final optimized speed curve, power curve and corresponding energy consumption value;

[0112] (12) Output the result and the algorithm ends, that is, the optimal speed curve optimization result in the single interval offline case is obtained.

[0113] Step 5: Based on the coordinated operation of multiple trains, a data module for energy-saving timetable analysis and calculation is established. Minimizing the total traction energy consumption of trains on the entire line and passenger waiting time is optimized. Combined with the speed curve optimization model established for the single-section operation scenario, an integrated timetable and speed curve optimization model is established. Using a parallel simulated annealing algorithm, the speed curve is optimized simultaneously with the timetable's running time and stop time.

[0114] Combine Figure 4 The flowchart of solving the schedule optimization model based on the improved simulated annealing algorithm, the main sub-steps of step 5 are as follows:

[0115] (1) Import the basic data module for energy-saving timetable analysis and calculation in step 3;

[0116] The data modules available for energy-saving timetable analysis and calculation include a train operation data module, a track line data module, and an operating timetable data module. The train operation data module includes the time-power data generated by the train when running in each section, which can be calculated from the energy-saving speed curves of each section at different operating times obtained by optimization in step 4. The track line data module includes data information such as overhead line unit impedance, track unit impedance, traction substation location, traction substation characteristic parameters, station location, and power supply partitioning. The operating timetable data provides the arrival and departure times of trains at various stations, including train formation, number of trains online, number of standby trains, and the departure station and departure time of each train.

[0117] (2) Decision variable setting: Using real number coding, the stop time of each station and the running time adjustment amount Δt between each station are input as decision variables in turn. Let n be the number of platforms from the starting station to the terminal station, then the corresponding number of running intervals is n-1, and the number of decision variables is 4n-2, including uplink and downlink. The decision variable form is: x = [Δt1, Δt2,···,Δt i ,···,Δt 4n-2 ];

[0118] (3) Objective function setting: For the coordinated optimization of multiple trains in the timetable, the total traction energy consumption of the entire line and the waiting time of passengers are minimized, and the timetable running time and stop time are optimized;

[0119] (a) Calculation formula for total traction energy consumption of trains on the entire line:

[0120] Assume that T_start is the simulation start time, T_end is the simulation end time, and Δt is the simulation step size;

[0121] The current simulation time is T_start+nΔt, where n is the number of simulation counts. According to the current simulation time and the passenger flow prediction results of step 2, the passenger flow data p of the current operating interval can be known. i ; According to the initialized decision variables x=[Δt1,Δt2,···,Δt i ,···,Δt 4n-2 ], then the running time of the current interval optimization is t i +Δt i , the current section passenger flow data and the optimization score running time are used as the input of the single vehicle speed curve optimization in step 4, and the optimized speed curve and power curve of the current section and the energy consumption value E of the single section are obtained. i , then the total traction energy consumption value E of the entire line is:

[0122]

[0123] Where T_start is the simulation start time, T_end is the simulation end time, n is the number of all online trains, and m is the number of all current sections;

[0124] (b) Passenger waiting time calculation formula

[0125] The changes of passengers on the platform can be divided into three parts: the time when train i arrives at platform n, the time when passengers wait for the train screen door to open and the time when passengers on the train get off D n ρ nThe change in the number of passengers at platform n is gradually increasing. Another part is the change in the number of passengers in the station when passengers start to board the train, which is gradually decreasing. Another part is the change in the number of passengers stranded due to train capacity limitations during the period from the departure of train i to the arrival of the next train at the platform, and the change in the new passenger flow during this period is gradually increasing.

[0126] When train i arrives at station n, the number of passengers on the platform is equal to the sum of the number of new passengers arriving during the departure interval and the number of passengers stranded at the previous station, satisfying the following formula:

[0127]

[0128] In the formula is the number of passengers when the i-th vehicle arrives at platform n; α n is the passenger arrival rate at the current platform, which can be obtained from passenger flow data; The number of passengers boarding the bus at the previous station;

[0129] According to the actual operation of urban rail transit, when the passenger flow is large, due to the limitation of train capacity, passengers may be stranded. Therefore, the specific number of passengers boarding train i at platform n is is the minimum value of the remaining train capacity and the current number of platforms, satisfying the following formula:

[0130]

[0131] Where C is the train capacity, which is a fixed value for each train; represents the number of passengers in the train when train i arrives at platform n. The passenger flow of each section at each moment can be obtained through the passenger flow forecast data in step 2, which is the number of existing passengers in the train; is the number of passengers getting off the train at platform n, satisfying the following formula:

[0132]

[0133] Where λ n is the passenger getting-off rate at station n, which can be obtained through passenger flow data;

[0134] Therefore, the waiting time of passengers at platform n is the sum of the areas of the three parts, which can be obtained using the following formulas:

[0135]

[0136]

[0137]

[0138] The waiting time of passengers from the time when train i arrives at station n to the time when train i+1 arrives at station n is as follows:

[0139]

[0140] In summary, we can get that the total waiting time for a passenger at a given running time [T_start, T_end] is:

[0141]

[0142] The dimension of passenger waiting time is person-seconds, and the dimension of energy consumption is KWh. Since the solution scales of energy and time are different, the objective function needs to be normalized to make them consistent in dimension, that is:

[0143]

[0144] Among them E min and E max represents the normalized minimum and maximum values ​​of the energy consumption objective function E(x); S min and S max represents the normalized minimum and maximum values ​​of the passenger waiting time objective function S(t); in order to find a solution that satisfies both objective functions, a compromise objective function is formulated as shown below:

[0145]

[0146] Where c1 and c2 represent the weight coefficients of the two objects respectively;

[0147] (4) Setting of relevant constraints: The adjustment of decision variables and the initialization of random generation need to meet certain constraints:

[0148] (a) Turnaround time constraint: Optimize the inter-station running time and stop time without changing the turnaround time. The specific constraint form is as follows:

[0149]

[0150] Where N is the number of platforms, x n is the train's stop time at station n, tr (n,n+1) is the running time of the train from station n to station n+1, t z , t z' is the turning time of the train at the turning stations at both ends, Tz up 、Tz down is the uplink and downlink turnover time;

[0151] (b) Inter-station operating time constraints: This includes the operating time constraints between individual stations and the total operating time constraints between all stations. The specific form is as follows:

[0152]

[0153] in, and The upper and lower limits of the running time between stations n and n+1, and The upper and lower limits of the total running time between all upstream stations, and The upper and lower limits of the total running time between all downstream stations;

[0154] (c) Stop time constraints: This includes the stop time constraints for a single station and the total stop time constraints for all stations. The specific forms are as follows:

[0155]

[0156] in, and are the upper and lower limits of the stop time at station n, and The upper and lower limits of the total stop time at all stations on the upward route, and The upper and lower limits of the total stop time at all stations on the downlink direction;

[0157] (5) Set the initialization parameters: the initial population M solutions x=[Δt1,Δt2,···,Δt i ,···,Δt 4n-2 ], initial temperature T0, final temperature T e , the maximum number of times the outer loop is not improved is N, the number of iterations of the inner loop is L, and the maximum number of times the inner loop is not improved is K;

[0158] (6) According to the total traction energy consumption calculation formula and the passenger waiting time calculation formula, calculate the objective function value of each initial population and save the optimal solution P of each population. best And the global optimal solution g best ;

[0159] (7) External loop setting: While(T>T e &&NUM<N), judge whether the current annealing temperature is greater than the set termination temperature, and whether the number of times the outer loop global solution is maintained is less than the set value. If not satisfied, jump out of the outer loop and terminate the algorithm;

[0160] (8) Start traversing M populations for (i=1; i<=M; i++), and before traversing, set the local solution counter num and the number of times the inner loop has not been improved K. Set the inner loop termination condition While(l<L&&num<K) to determine whether the number of inner loop iterations has reached the set number and whether the number of times it has not been improved is less than the set value K;

[0161] (9) Generate a candidate solution X′ from the results within the current solution domain, and calculate the fitness function value F based on the above total traction energy consumption calculation formula and the passenger waiting time calculation formula. Determine whether to accept the new value based on the value generated by min[1, exp(-ΔC / t);

[0162] (10) Calculate the increment ΔF = F(X′) - F(X). If ΔF > 0, reset num = 0; otherwise, reset num = num + 1. Determine whether the current number of executions or the number of times the solution has not been improved meets the inner loop condition.

[0163] (11) Determine whether each population has a historical optimal solution and update the local optimal solution P best and the global optimal solution g best , if the global solution has not been updated NUM = NUM ​​+ 1; otherwise NUM = 0;

[0164] (12) Perform the cooling operation to determine whether the current temperature is equal to or lower than the termination temperature, or if the global value has not been updated NUM times>N, then exit the current loop;

[0165] (13) Find the optimal solution of each population in the M memory arrays, and then find the optimal solution of all populations, which is the global optimal solution;

[0166] (14) The algorithm ends with the output result, which is the optimal adjustment between the stopping time at each station and the running time between stations, including both upstream and downstream.

[0167] Step 6: Output the energy-saving optimization results and determine the optimal adjustment strategy for energy-saving operation of trains on the entire line;

[0168] Among them, the optimal adjustment strategy for energy-saving operation of trains on the entire line includes the train energy-saving operation timetable and its corresponding energy-saving speed curve.

[0169] In summary, the method of the present invention adopts software simulation and, from the perspective of urban rail transit operation, makes minor adjustments to the train timetable and operating speed curve taking into account passenger flow fluctuations while meeting passenger comfort indicators, train safety operation indicators, train operation scheduling indicators, etc., thereby significantly reducing the total traction energy consumption of trains on the entire line and passenger waiting time, and has high use value and application prospects.

Claims

1. A method for optimizing timetables and speed curves taking into account passenger flow, characterized in that: The following steps are involved: Step 1: Obtain historical cross-section passenger flow data of the route and perform cluster analysis; Step 2: Based on the cluster analysis results, a neural network short-term passenger flow prediction model is established to predict the passenger flow data for the day; Step 3: Obtain basic line data of rail trains, mainly including line slope and curve data and train electrical data; Step 4: Based on the single-section operation, a dynamic model is built using train line data and electrical data. Taking into account the punctuality rate, passenger comfort, operating time, and traction energy consumption during actual train operation as optimization objectives, a speed curve optimization model based on a parallel simulated annealing algorithm is established to obtain the energy-saving operating speed curve for different operating times between each station. Step 5: Establish a data module for energy-saving timetable analysis and calculation. Under the condition of coordinated operation of multiple trains, minimize the total traction energy consumption of all trains on the entire line and minimize the waiting time of passengers. Combined with the speed curve optimization model established for the single-section operation, an integrated timetable and speed curve optimization model is established. Using a parallel simulated annealing algorithm, the speed curve is optimized simultaneously with the timetable running time and stop time. The data module for energy-saving timetable analysis and calculation described in step 5 is established. Under the condition of coordinated operation of multiple trains, the total traction energy consumption of the entire line and the waiting time of passengers are minimized as the optimization objectives. Combined with the speed curve optimization model established under the single-section operation condition above, an integrated optimization model of timetable and speed curve is established. Using a parallel simulated annealing algorithm, the speed curve is optimized simultaneously with the timetable running time and the stop time. Step 5.1, import the basic data module for energy-saving timetable analysis and calculation in step 3; The data modules available for energy-saving timetable analysis and calculation include a train operation data module, a track line data module, and an operating timetable data module. The train operation data module includes the time-power data generated by the train when running in each section, which can be calculated from the energy-saving speed curves of each section at different operating times obtained by optimization in step 4. The track line data module includes data information such as overhead line unit impedance, track unit impedance, traction substation location, traction substation characteristic parameters, station location, and power supply partitioning. The operating timetable data provides the arrival and departure times of trains at various stations, including train formation, number of trains online, number of standby trains, and the departure station and departure time of each train. Step 5.2, decision variable setting: Use real number coding, and input the stop time of each station and the running time adjustment amount Δt between each station as decision variables. Let n be the number of platforms from the starting station to the terminal station, then the corresponding number of running intervals is n-1, and the number of decision variables is 4n-2, including uplink and downlink. The decision variable form is: x = [Δt1, Δt2,···,Δt i ,···,Δt 4n-2 ]; Step 5.3, objective function setting: Optimize the timetable running time and stop time by minimizing the total traction energy consumption of trains on the entire line and the waiting time of passengers. Step 5.3.1, the formula for calculating the total traction energy consumption of trains on the entire line is: Assume that T_start is the simulation start time, T_end is the simulation end time, and Δt is the simulation step size; The current simulation time is T_start+nΔt, where n is the number of simulation counts. According to the current simulation time and the passenger flow prediction results of step 2, the passenger flow data p of the current operating interval can be known. i ; According to the initialized decision variables x=[Δt1,Δt2,···,Δt i ,···,Δt 4n-2 ], then the running time of the current interval optimization is t i +Δt i , the current section passenger flow data and the optimization score running time are used as the input of the single vehicle speed curve optimization in step 4, and the optimized speed curve and power curve of the current section and the energy consumption value E of the single section are obtained. i , then the total traction energy consumption value E of the entire line is: Where T_start is the simulation start time, T_end is the simulation end time, n is the number of all online trains, and m is the number of all current sections; Step 5.3.2, Passenger waiting time calculation formula: The changes of passengers on the platform can be divided into three parts: the time when train i arrives at platform n, the time when passengers wait for the train screen door to open and the time when passengers on the train get off D n ρ n The change in the number of passengers at platform n is gradually increasing. Another part is the change in the number of passengers in the station when passengers start to board the train, which is gradually decreasing. Another part is the change in the number of passengers stranded due to train capacity limitations during the period from the departure of train i to the arrival of the next train at the platform, and the change in the new passenger flow during this period is gradually increasing. When train i arrives at station n, the number of passengers on the platform is equal to the sum of the number of new passengers arriving during the departure interval and the number of passengers stranded at the previous station, satisfying the following formula: In the formula is the number of passengers when the i-th vehicle arrives at platform n; α n is the passenger arrival rate at the current platform, obtained from passenger flow data; The number of passengers boarding the bus at the previous station; According to the actual operation of urban rail transit, when the passenger flow is large, due to the limitation of train capacity, passengers may be stranded. Therefore, the specific number of passengers boarding train i at platform n is is the minimum value of the remaining train capacity and the current number of platforms, satisfying the following formula: Where C is the train capacity, which is a fixed value for each train; represents the number of passengers in the train when train i arrives at platform n. The passenger flow of each section at each moment is obtained through the passenger flow forecast data in step 2, which is the number of passengers currently in the train. is the number of passengers getting off the train at platform n, satisfying the following formula: Where λ n is the passenger alighting rate at station n, obtained through passenger flow data; Therefore, the waiting time of passengers at platform n is the sum of the areas of the three parts, which can be obtained by the following formulas: The waiting time of passengers from the time train i arrives at station n to the time train i+1 arrives at station n is as follows: In summary, we can get that the total waiting time for a passenger at a given running time [T_start, T_end] is: The dimension of passenger waiting time is person-seconds, and the dimension of energy consumption is KWh. Since the solution scales of energy and time are different, the objective function needs to be normalized to make them consistent in dimension, that is: Among them E min and E max represents the normalized minimum and maximum values ​​of the energy consumption objective function E(x); S min and S max represents the normalized minimum and maximum values ​​of the passenger waiting time objective function S(t); in order to find a solution that satisfies both objective functions, a compromise objective function is formulated as shown below: Where c1 and c2 represent the weight coefficients of the two objects respectively; Step 5.4, setting of relevant constraints. The adjustment of decision variables and initialization of random generation need to meet certain constraints: Step 5.4.1, Turnaround time constraint: Optimize the inter-station running time and stop time without changing the turnaround time. The specific constraint form is as follows: Where N is the number of platforms, x n is the train's stop time at station n, tr (n,n+1) is the running time of the train from station n to station n+1, t z , t z' is the turning time of the train at the turning stations at both ends, Tz up 、Tz down is the uplink and downlink turnover time; Step 5.4.2, inter-station operating time constraints: This includes the operating time constraints between individual stations and the total operating time constraints between all stations. The specific form is as follows: in, and The upper and lower limits of the running time between stations n and n+1, and The upper and lower limits of the total running time between all upstream stations, and The upper and lower limits of the total running time between all downstream stations; Step 5.4.3, stop time constraints: This includes the stop time constraints for a single station and the total stop time constraints for all stations. The specific form is as follows: in, and are the upper and lower limits of the stop time at station n, and The upper and lower limits of the total stop time at all stations on the upward route, and The upper and lower limits of the total stop time at all stations on the downlink direction; Step 5.5, set the initialization parameters: the initial population M solutions x=[Δt1,Δt2,···,Δt i ,···,Δt 4n-2 ], initial temperature T0, final temperature T e , the maximum number of times the outer loop is not improved is N, the number of iterations of the inner loop is L, and the maximum number of times the inner loop is not improved is K; Step 5.6: Calculate the objective function value of each initial population and save the optimal solution P for each population based on the total traction energy consumption calculation formula and the passenger waiting time calculation formula. best And the global optimal solution g best ; Step 5.7, outer loop setting: While(T>T e &&NUM<N), judge whether the current annealing temperature is greater than the set termination temperature, and whether the number of times the outer loop global solution is maintained is less than the set value. If not satisfied, jump out of the outer loop and terminate the algorithm; Step 5.8, start traversing M populations for (i=1; i<=M; i++), and before traversing, set the local solution counter num and the number of times the inner loop has not been improved K, set the inner loop termination condition While(l<L&&num<K), and determine whether the number of inner loop iterations has reached the set number and whether the number of times it has not been improved is less than the set value K; Step 5.9: Generate a candidate solution X′ from the results within the current solution domain, and calculate the fitness function value F based on the above total traction energy consumption calculation formula and the passenger waiting time calculation formula. Determine whether to accept the new value based on the value generated by min[1, exp(-ΔC / t); Step 5.10, calculate the increment ΔF = F(X′) - F(X). If ΔF > 0, reset num = 0; otherwise, reset num = num + 1. Determine whether the current number of executions or the number of times the solution has not been improved meets the inner loop conditions. Step 5.11: Determine whether each population has a historical optimal solution and update the local optimal solution P best and the global optimal solution g best , if the global solution has not been updated NUM = NUM ​​+ 1; otherwise NUM = 0; Step 5.12, perform the cooling operation to determine whether the current temperature is equal to or lower than the termination temperature, or if the global unupdated times NUM>N, then jump out of the current loop; Step 5.13: Find the optimal solution for each population in the M memory arrays, and then find the optimal solution for all populations, which is the global optimal solution. Step 5.14, output the result, and the algorithm ends, that is, the optimal adjustment of the stop time at each station and the running time between stations, including up and down; Step 6: Output the optimized results, i.e., the interval energy-saving speed curve and the optimal train schedule for the entire line.

2. A method for optimizing a timetable and speed curve considering passenger flow according to claim 1, characterized in that: The acquisition of cross-sectional passenger flow data and cluster analysis described in step 1 specifically includes the following steps: Step 1.1, generate sample set. Assume that the operation statistics period is 06:00-23:00, statistics are collected every 15 minutes, and each time period corresponds to d intervals. Therefore, the sample set is divided into D = {D1, D2, D3, ... D m }, where m is the sample set size, D i This means that the passenger flow data of all intervals in the current time period is stored, and then: Step 1.2: Randomly select k sample objects μ1, μ2, …μ in the sample set D. k As the initial center of each class, the sample k is selected using the elbow rule according to the degree of change of the sum of squared errors (SSE) of the clustering; Where G i is the i-th cluster, p is G i Sample points, m i It is cluster G i The center point of , SSE is the clustering error result of all samples, which represents the quality of the clustering result; Step 1.3: Calculate the Euclidean distance dist between samples and use it to classify them into the category to which the category center is closest. The calculation formula is as follows: In the formula u=(u1,u2,…,u n ),v=(v1,v2,…,v n ) is represented as a vector of two samples, label represents the category label; Step 1.4, update the center point u of each sample category j , using mean value instead, the formula is as follows: In step 1.5, calculate the objective function E after this iteration. If the difference between the calculated function value and the last calculated function value is within the set threshold, the classification is completed and the K-means algorithm terminates. Otherwise, repeat steps 1.3 to 1.

5. The calculation formula is as follows: |And k -AND k-1 |≤ε。 3. The method for optimizing a timetable and speed curve considering passenger flow according to claim 1, characterized in that: According to the cluster analysis results described in step 2, a neural network short-term passenger flow prediction model is established to predict the passenger flow data for the day. The specific steps are as follows: Step 2.1: Sample data preprocessing: Merge the data sets of the section passenger flow data at each moment according to the clustering category to increase the correlation between the data, and use the merged data set as input; Step 2.2, initialize the network parameters, including the weights w of the input layer and the hidden layer ij , the weight from the hidden layer to the output layer, and the output threshold θ j 、a k , w ij ,z ij ,θ j ,a k ∈[0,1]; convergence accuracy ε=0.01, adaptive learning rate adjustment factors λ1=1.5,λ2=0.5; Step 2.3, calculate the input net of the jth node hidden layer according to the following formula j , the output of the hidden layer h j , the input net of the kth node in the output layer k , the output o of the kth node in the output layer k ; Where m is the dimension of the input vector, θ j is the threshold of the jth node in the hidden layer; φ(·) is the activation function of the hidden layer node; n is the number of hidden layer nodes, α k is the threshold of the kth node in the output layer; is the activation function of the output layer node; Step 2.4: Adjust the change in the output layer weights Δz according to the following formula: jk , the output layer threshold change Δα k , the change in hidden layer weight Δw ij , the hidden layer threshold change Δθ j ; Where E is the total error function of all P training sample data, that is Substitute it into the above formula to get the adjustment formula: Step 2.5: Update the weights and thresholds of each layer and calculate the total error function E P , if E P If the convergence accuracy standard or the number of iterations is reached, the training ends. Otherwise, the learning rate is adjusted according to the adaptive learning rate and the next round of learning continues until the requirements are met. The adaptive learning rate adjustment formula is: Among them, λ1 and λ2 are the adjustment factors of the adaptive learning rate.

4. The method for optimizing a timetable and speed curve considering passenger flow according to claim 1, characterized in that: The basic line data of the rail train obtained in step 3 mainly includes line slope and curve data, and train electrical data, mainly including contact network unit impedance, track unit impedance, traction substation location, traction substation characteristic parameters, station location, power supply division, and operating parameters, such as the number of online trains, and the departure station and departure time of each train.

5. The method for optimizing a timetable and speed curve considering passenger flow according to claim 1, characterized in that: Based on the single-section operation conditions described in step 4, a dynamic model is built according to the train line data and electrical data. Taking the punctuality rate, passenger comfort, running time and traction energy consumption in the actual train operation process as the optimization objectives, a speed curve optimization model based on the parallel simulated annealing algorithm is established to obtain the energy-saving running speed curve of each station with different running time. The specific steps are as follows: Step 4.1, initialization, set the control algorithm control parameters, initialize M X0 populations, where X0 is the optimization command of the speed curve, X i0 ={mod e,s1,s2,s3,s4,s5,s6} i=0,1,…M Since the original simulated annealing algorithm has low search efficiency and is incomplete for speed curves with a wide range of speed commands, it is easy to fall into local optimality. Therefore, in order to improve the efficiency of the algorithm, the improved parallel simulated annealing algorithm is used for search and solution. The specific steps are as follows: First, during the initialization process, M initial solution populations are randomly generated, the corresponding objective function values ​​are calculated, and the smallest objective function value is selected as the optimal initial solution; then, a candidate solution is generated for each initial solution using the state generation function, and the inner loop Metropolis algorithm is executed in sequence until the inner loop ends, forming M populations under the new temperature state; individuals in the new state population that are better than the previous state population are retained, and then the cooling operation is repeated until the algorithm stops, and an optimal solution is selected from the last remaining population as the final global optimal solution; Because multiple populations execute their inner loops independently, they operate in parallel. The Metropolis algorithm executes multiple populations simultaneously. Although this increases the computational effort compared to single-solution serial optimization, the solution coverage generated by multiple populations is higher, allowing for early exits from local optima and inner loop iterations, thereby improving the overall efficiency of the algorithm. This paper uses the maximum acceleration traction-first coasting-second traction-second coasting-first braking-third coasting-second braking mode for speed curve optimization. The middle mixed mode includes the other two coasting modes and the cruise mode. A total of 7 commands are used to optimize the train energy saving and time saving, namely operation mode mode, first coasting starting point s1, first coasting ending point s2, second coasting starting point s3, second coasting ending point s4, third coasting starting point s5, and third coasting ending point s6. Step 4.2: Based on the initialized parameter command, use the dynamic train speed reverse derivation formula to calculate the speed curve and power curve under each initial command parameter and the corresponding train operation energy consumption data. The train is regarded as a single-point model to simplify the problem. The train's motion conforms to Newton's laws of kinematics. The forces acting on the train are divided into five categories: vertical downward gravity G; upward support force F of the track on the train; 支 ;Train traction force F t , train braking force B b and the total train running resistance W o , but the force of gravity G in the direction of the track is offset by the support force, and the formula is as follows: Where K1, K2, and A are constants; m, n, p, q, d, e, f, a, b, and c are polynomial coefficients; v1 and v2 are the speed transition points between the constant torque region and the constant power region of the train's traction and braking characteristics, respectively; i is the slope during the train's travel, which is equivalent to the slope resistance per unit mass; r is the curve radius; L s is the tunnel length; M c is the net weight of the train, M p is the average net weight of a single person, n is the passenger capacity of the train, γ is the rotation mass coefficient, M eq The mass converted for the train; According to the above formula, the following formula can be derived: When the train is in traction state, the traction force formula F t (v) and the running resistance formula W o Substituting (v,i,r) into the above formula, we get the differential equation for displacement x and time t, as follows: Get the running distance and running time of the traction phase: Where v1, v2, v3 are equations The three roots of Similarly, the running distance and running time of the coasting phase are: The running distance and running time of the braking phase are: Combining the above formula, we can get the total running time and running distance: According to the speed data provided by the subway company, there is a speed point every 0.1s. Therefore, when calculating the power and energy consumption of the train, we calculate point by point with Δt = 0.1, and we have: In step 4.3, based on the above steps, the interval speed, power, displacement, time, and energy consumption values ​​under the initial parameter command are obtained. Then, the following metrics are added to judge the optimization effect: Fixed-point parking index constraint function: Punctuality index constraint function: Passenger comfort function: Energy-saving constraint index function: Finally, the fitness function F expression is obtained: Step 4.4: Calculate the objective function value of each initial population according to the dynamic model and formula and save the optimal solution P for each population. best And the global optimal solution g best Since the parallel simulated annealing algorithm increases the number of populations, the solution coverage rate generated in multiple populations is larger, but the amount of calculation is increased. In order to jump out of the local optimum and the inner and outer loop iterations in advance, the inner and outer loop iterations are improved; The specific implementation is as follows: at the beginning of each temperature T, a local solution counter num and the number of times it has not been improved are set and initialized to 0. If the target value calculated by the next new solution is improved compared to the previous solution value, num is reset to 0, otherwise num is increased by 1, that is, num = num + 1; when num > L, the Metropolis algorithm for the current temperature T is exited; Step 4.5, outer loop setting: While(T>T e &&NUM<N), judge whether the current annealing temperature is greater than the set termination temperature, and whether the number of times the outer loop global solution is maintained is less than the set value. If not satisfied, jump out of the outer loop and terminate the algorithm; Step 4.6, start traversing M populations for (i=1; i<=M;i++) and before traversal, set the local solution counter num and the number of times the inner loop has not been improved K, set the inner loop termination condition While(l<L&&num<K), and judge whether the number of inner loop iterations has reached the set number and whether the number of times it has not been improved is less than the set value K; Step 4.7: Generate a candidate solution X′ from the results within the current solution domain and calculate the fitness function value F according to the above dynamic formula. In order to accept the optimized solution, set the state acceptance function min[1, exp(-ΔC / t]). It is generally given in the form of probability. The design principle of state acceptance probability is that when the temperature is fixed, the acceptance probability of the solution set that makes the objective function value decrease is greater than the acceptance probability of the solution set that makes the objective function value increase; when the temperature decreases, the acceptance probability of the solution set that makes the objective function value increase should be reduced; and when the temperature approaches zero, only solutions with decreasing objective function values ​​are accepted. The value generated by min[1, exp(-ΔC / t]) is used to determine whether to accept the new value. Step 4.8, calculate the increment ΔF = F(X′) - F(X). If ΔF > 0, reset num = 0; otherwise, reset num = num + 1. Determine whether the current number of executions or the number of times the solution has not been improved meets the inner loop conditions. Step 4.9: Determine whether each population has a historical optimal solution and update the local optimal solution P best and the global optimal solution g best , if the global solution has not been updated NUM = NUM ​​+ 1; otherwise NUM = 0; Step 4.10: Perform the cooling operation to determine whether the current temperature is equal to or lower than the termination temperature, or if the global value has not been updated NUM times > N, then exit the current loop. In step 4.11, find the optimal solution for each population in the M memory arrays, and then find the optimal solution for all populations, which is the global optimal solution. Input the output command into the dynamic calculation model to generate the optimized speed curve, power curve, and corresponding energy consumption value. Step 4.2, output the results, the algorithm ends, and the optimal speed curve optimization result in the single-interval offline case is obtained.

6. The method for optimizing a timetable and speed curve considering passenger flow according to claim 1, characterized in that: The optimized result is outputted in step 6, i.e., the section energy-saving speed curve and the optimal train schedule for the entire line.

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