A Method for Constructing and Solving a Diversion Custom Bus Double-Deck Planning Model

Abstract

The present invention discloses a method for constructing and solving a shunt customized bus double-deck planning model. The present invention determines a set of candidate shunt lines for customized buses based on actual data; constructs an upper-layer model with the goal of minimizing the congestion degree of rail transit intervals, constructs a lower-layer model and its solution method according to the shunt lines determined by the decision of the upper-layer model; constructs an ML-OP algorithm to efficiently solve the double-deck model. The present invention can face large urban rail transit networks and quickly find an opening plan for a better combination of shunt lines under limited computing resources, so as to achieve the best effect of alleviating the congestion of rail transit passenger flow. The purpose of the present invention is to relieve the passenger flow pressure during the peak hours of rail transit through customized bus lines and alleviate the congestion problem of the rail transit system.

Description

Technical Field

[0001] The present invention relates to a bus line planning method, and particularly to a customized bus planning method for relieving the passenger flow pressure of rail transit. Background Art

[0002] Due to the separation of employment and residence distribution in large cities, commuting passengers during peak hours become the main body of the passenger flow of the urban rail transit network, and show the characteristics of large flow, concentrated travel paths and time, resulting in the imbalance between travel demand and rail transit supply, and the crowds gathering at train platforms and in carriages, and the congestion problem becomes increasingly prominent. The customized bus for diversion functions during the peak period of rail transit passenger flow travel, and is an effective method to attract passenger flow and relieve rail transit congestion. The customized bus for diversion usually only sets stops in the starting area and the ending area, and does not stop in the middle or has very few stops in the middle, so it has the characteristics of fast, convenient and comfortable, and is a "point-to-point" bus system.

[0003] Currently, the research on the opening of bus lines for sharing the passenger flow pressure of rail transit mainly starts from two perspectives. Some research starts from the perspective of passenger flow distribution identification, and adopts a data-driven method. First, determine the stations that need to be diverted according to certain rules, and then screen out the origin-destination pairs of large passenger flow at the diverted stations, and select the route with the minimum travel cost manually as the proposed diverted bus line. Some research adopts an optimization modeling method from the perspective of passenger flow control, and mainly conducts research in two stages: first, decide at which stations the passenger flow needs to be controlled, and decide the quantity of passenger flow that needs to be controlled; in the next stage, decide how to design the bus line to transport these passengers.

[0004] Both of these two types of methods do not consider the choice behavior of passengers' travel paths in the real scenario, and the assumption of the transfer willingness of rail transit passengers is relatively ideal, and there may be gaps in practical applications. Moreover, the existing research technologies mainly focus on a single rail transit line. However, for the rail transit system in large cities, the causes of congestion in local sections of the network are complex. Considering the access of customized bus lines for diversion at the network level is more practical. In addition, the constructed customized bus line planning model for diversion usually has multiple constraint conditions, involving multi-objective combinatorial optimization, which is an NP-hard problem, and it is difficult to efficiently obtain a globally optimal solution. The complexity of the large urban rail transit network further exacerbates the difficulty of solving the model. Summary of the Invention

[0005] Object of the Invention: To overcome the defects existing in the prior art, the object of the present invention is to provide a method for constructing and solving a two-layer planning model of a customized bus for diversion.

[0006] Technical Solution: The method for constructing and solving a two-layer planning model of a customized bus for diversion according to the present invention includes the following steps:

[0007] S1. Determine the set of candidate diversion routes for customized buses;

[0008] S2. Construct an upper-layer model with the goal of minimizing the congestion level of the rail transit section, which is used to decide on appropriate diversion routes from the set of candidate diversion routes;

[0009] S3. According to the diversion routes decided by the upper-layer model, construct a lower-layer model and its solution method;

[0010] S4. Construct the ML-OP algorithm to solve the bi-level model: Replace the objective function of the upper-layer model with a surrogate objective function, train the surrogate objective function through machine learning, transform the upper-layer model into an integer linear programming problem, and combine initial sample generation, iterative solution, and convergence condition judgment to efficiently solve the bi-level model and obtain a better opening plan for the combination of diverted customized bus lines.

[0011] The specific process of determining the set of candidate diversion routes for customized buses in S1 is as follows: Given the information of the origin-destination pairs of passengers' trips in the rail transit network, extract the set of origin-destination pairs whose path length between stations is greater than a pre-set path length threshold, and the passenger flow volume between stations is greater than a pre-set flow threshold, and the ratio of the fastest travel time between stations in the road network to the fastest travel time in the rail transit network is less than a pre-set time ratio threshold as the set of candidate diversion routes.

[0012] The specific process of constructing an upper-layer model with the goal of minimizing the congestion level of the rail transit section in S2 to decide on appropriate diversion routes from the set of candidate diversion routes is as follows:

[0013] S21. Construct the objective function with the goal of minimizing the congestion level of the rail transit section as:

[0014] ;

[0015] ;

[0016] where ω e = x e / C e represents the load factor of the passenger flow in the rail transit section e ; x e is the passenger flow volume in the rail transit section e ; C e is the restricted flow volume in the rail transit section e within a given time period; L eFor the length of the rail transit section e ; is a continuous function of the full load rate of passenger flow in the section, is the full load rate threshold for the carriage to start getting crowded, which is preset, is a preset adjustment parameter greater than 0;

[0017] S22. Set constraint conditions to limit the number of selected diversion customized bus lines not to exceed a preset number threshold P :

[0018] ;

[0019] Among them, is a decision variable of the upper - layer model, which is a discrete 0 - 1 variable, indicating whether a certain candidate diversion line is selected. If it is 1, it is selected; if it is 0, it is not selected; represents the set of candidate diversion lines; P is the preset number threshold.

[0020] As a preferred technical solution, in S3, according to the diversion lines determined by the upper - layer model, a lower - layer model and its solution method are constructed; the lower - layer model is used to reasonably load all passenger origin - destination pairs (O - D pairs) in the rail transit network onto the sections connecting the origin and destination. It is a multi - path passenger flow equilibrium distribution model and is solved by the MSA method. The specific process is as follows:

[0021] S31. Based on the Space - L method in complex network theory, construct a rail transit network: Define a directed network where, represents the set of rail transit stations; represents the rail transit section, including the rail transit operation section between adjacent stations on the rail transit line and the transfer walking section between different lines;

[0022] Set the impedance of the rail transit operation section :

[0023] ;

[0024] ;

[0025] ;

[0026] Among them, represents the actual running time of the operation section ; ω e =x e / C e , representing the passenger load factor of the rail transit section e , x e is the rail transit section e passenger flow volume, C e is the rail transit section e the restricted flow volume within a given time period; represents the load factor when passengers all have seats; μ and γ are preset adjustment parameters;

[0027] Set the impedance of the transfer walking section : :

[0028] ;

[0029] Among them, is the walking transfer time of the section e ; is a preset adjustment parameter, indicating that the transfer perception time is greater than the actual transfer time required;

[0030] S32. Based on the upper-layer model decision, the diversion line is constructed on the basis of the rail transit network to build a fusion network of rail and diversion customized buses: The starting and ending points of the diversion customized buses are at the rail transit stations. For each selected diversion customized bus line, an additional diversion customized bus section is added between the corresponding nodes of the original rail transit network to obtain the fusion network , among which, represents the set of rail transit stations; represents the set of sections of the fusion network of rail and diversion customized buses, represents the rail transit section; represents the diversion customized bus section;

[0031] Set the impedance of the diversion customized bus section : :

[0032] ;

[0033] Among them, represents the travel time of this diversion customized bus section in the road network;

[0034] S33. Initialization: Let the number of iterations n= 1; Set the flow of each section in the integrated network of rail transit and customized feeder buses to 0. Use the Dial algorithm to search for the path with the minimum impedance between each passenger's origin-destination (O-D) pair in the integrated network of rail transit and customized feeder buses, and use the all-or-nothing assignment method to perform passenger flow loading to obtain the section flow in the first iteration. ;

[0035] S34. Update path impedance: Update the impedance of the rail transit operation section according to the current section flow .

[0036] S35. Load passenger flow: According to the current section impedance, use the Dial algorithm to search for the path with the minimum impedance between each passenger's O-D pair in the integrated network of rail transit and customized feeder buses, and use the all-or-nothing assignment method to perform passenger flow loading to obtain the auxiliary section flow ;

[0037] S36. Update the section flow in the n +1-th iteration: :

[0038] ;

[0039] S36. Check for convergence: The convergence condition is:

[0040] ;

[0041] where is a preset sufficiently small positive number; if the convergence condition is not satisfied, then set , and continue with step S34; if the convergence condition is satisfied, stop the algorithm to obtain the passenger flow of each section in the integrated network of rail transit and customized feeder buses.

[0042] As a preferred technical solution, in S4, the ML-OP algorithm is constructed to solve the bilevel model: Replace the objective function of the upper-level model with a surrogate objective function, train the surrogate objective function through machine learning, transform the upper-level model into an integer linear programming problem, and combine initial sample generation, iterative solution, and convergence condition judgment to efficiently solve the bilevel model and obtain a better opening plan for the combination of customized feeder bus lines; the specific process is as follows:

[0043] S41. Generate initial samples: For a set of decision variables of the upper-level model, generate | Bc | + 2 sets of initial decision variable sets:

[0044] ;

[0045] where is the kThe decision variables of the upper-layer model of the group are discrete 0-1 variables, indicating whether a certain candidate diversion line is selected. If it is 1, it is selected; if it is 0, it is not selected. Indicates the set of candidate diversion lines;

[0046] This initial decision variable set contains Bc | decision variable combinations with only 1 variable being 1, and two combinations of all 0s and all 1s;

[0047] For the initial decision variables of each group of upper-layer models, construct and solve the lower-layer model to obtain the passenger flow data of each section in the integrated network of rail transit and diversion customized buses, and substitute this data into the upper-layer model to calculate the objective function of the upper-layer model Z , obtaining an initial sample set containing Bc | + 2 decision variable combinations and objective function pairs:

[0048] ;

[0049] Let the iteration number i = 0; Let the set of samples generated by iteration be , the total sample set ;

[0050] S42. Train machine learning: Based on the current n group ( ) sample set of decision variable combinations and objective function pairs, train a multiple linear regression model to obtain a surrogate objective function about the variable , that is, an approximation function of the objective function Z:

[0051] ;

[0052] Among them, represents the estimated value of the bias term in the regression model; represents the estimated value of the regression coefficient about , and actually represents the weight of the diversion line b in the objective function. The smaller it is, the more likely the diversion line b is to be selected;

[0053] S43. Establish and solve the surrogate upper-layer model: By using the linear surrogate upper-layer objective function , the upper-layer model will be transformed into an integer linear programming model; add constraint conditions to this integer linear programming model to obtain a new solution in the iteration and limit the generation of solutions different from those in the existing samples; the surrogate upper-layer model is established as:

[0054] ;

[0055] ;

[0056] Among them, m represents the number of samples generated by iteration, ; and respectively represent the number of times the decision variable takes 1 and the number of times the decision variable takes 0 in the k th sample; Use a classical algorithm or solver for solving integer linear programming problems, such as the branch and bound method, the cutting plane method, the CPLEX solver, the Gurobi solver, or the GLPK solver, to solve this surrogate upper-level model and obtain a new solution different from the solutions in the existing samples , and obtain the shunt line combination ;

[0057] S44. Solve the lower-level model and update the sample set: Input the shunt line combination obtained by solving the surrogate upper-level model into the lower-level model, solve the lower-level model, obtain the passenger flow data of each section in the integrated network of rail transit and shunt customized buses, and extract the passenger flow belonging to the rail transit section , among which, represents the rail transit section in the integrated network of rail transit and shunt customized buses; Calculate the actual upper-level objective function , and obtain a new set of decision variable vectors and objective function combinations ; Update the sample data set as:

[0058] ;

[0059] ;

[0060] S45. Determine whether the termination condition is reached: Set the termination condition of the iteration as that the iteration number i reaches the pre-set maximum iteration number i max , then end the iteration and return the solution corresponding to the minimum objective function D in the sample set , that is: , namely:

[0061] ;

[0062] That is, obtain a relatively optimal opening plan for the shunt customized bus line combination;

[0063] If i < i max , then let i = i + 1, return to step S42, and continue the iteration.

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] 1. The present invention establishes a shunt customized bus two-layer planning model. Taking the multi-path passenger flow equilibrium distribution model in the integrated network of rail transit and shunt customized buses as the lower-layer model, the upper-layer model minimizes the objective function of the congestion degree of a rail transit section. This enables the present invention to actually consider the choice behavior of passengers' travel paths, making the decision-making shunt bus line combination opening plan more reasonable. The model of the present invention involves three main bodies: rail transit, passengers, and customized buses, enabling relevant interests to be considered in the shunt line planning method: the operation pressure of rail transit is alleviated; the riding comfort of passengers is improved; the customized buses meet the flow conditions for opening.

[0066] 2. The present invention customizes the design of the ML-OP method to solve the NP-hard two-layer planning model: replaces the objective function of the upper-layer model with a surrogate objective function, trains the surrogate objective function through machine learning, transforms the upper-layer model into an integer linear programming problem, and combines initial sample generation, iterative solution, and convergence condition judgment to finally obtain a better shunt customized bus line combination opening plan. Compared with traditional methods, such as genetic algorithms, the ML-OP method designed by the present invention can obtain a better solution, making the solution efficiency of the model higher, and there are no random factors, and it can stably output the model results. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a schematic diagram of the steps for constructing and solving the shunt customized bus two-layer planning model in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0068] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be further described below.

[0069] The method for constructing and solving the shunt customized bus two-layer planning model in this embodiment specifically includes the following steps:

[0070] S1. Determine the set of candidate shunt lines for customized buses;

[0071] S2. Construct an upper-layer model with the goal of minimizing the congestion degree of the rail transit section, and use it to decide on appropriate shunt lines from the set of candidate shunt lines;

[0072] S3. According to the shunt lines decided by the upper-layer model, construct a lower-layer model and its solution method;

[0073] S4. Construct the ML-OP algorithm to solve the bilevel model: Replace the objective function of the upper-level model with a surrogate objective function, train the surrogate objective function through machine learning, transform the upper-level model into an integer linear programming problem, and combine initial sample generation, iterative solution, and convergence condition judgment to efficiently solve the bilevel model and obtain a better customized bus line combination opening plan for flow diversion.

[0074] In this method, the specific process of step S1 to determine the set of candidate flow-diversion bus lines is as follows: Given the information of the origin-destination pairs of passengers' trips in the rail transit network, extract the set of origin-destination pairs whose path length between stations is greater than a pre-set path length threshold, and the passenger flow volume between stations is greater than a pre-set flow threshold, and the ratio of the fastest travel time between stations in the road network to the fastest travel time in the rail transit network is less than a pre-set time ratio threshold as the set of candidate flow-diversion lines.

[0075] In this embodiment, the network and passenger flow conditions of the Shanghai rail transit network during a certain peak period on a certain day are selected as the background of the embodiment for research. Specifically, the selected research period is from 8:00 to 9:00 on November 4, 2022 (Friday). The origin-destination pairs (O-D pairs) of the whole network during this period are obtained, with a quantity of 95,419 and a total flow of 908,281 person-times. Set the path length threshold to 10 km, and extract the origin-destination pairs with a path length greater than 10 km between stations, obtaining 79,255 origin-destination pairs; set the flow threshold to 300 person-times, and continue to extract the origin-destination pairs with a passenger flow volume greater than 300 person-times between stations, obtaining 2,061 origin-destination pairs; set the time ratio threshold to 1.15, and continue to extract the origin-destination pairs whose ratio of the fastest travel time between stations in the road network to the fastest travel time in the rail transit network is less than 1.15, obtaining 64 origin-destination pairs, that is, 64 candidate flow-diversion lines are finally obtained.

[0076] In this embodiment, all 64 candidate flow-diversion lines serve the suburbs and the urban fringe. On the one hand, this is determined by the passenger flow characteristics during the weekday morning rush hour (from the suburbs to the urban area), and on the other hand, it is also because the road congestion in the urban area is more serious. The routes adopted by the candidate flow-diversion bus lines generally involve highways or urban expressways, such as the Beijing-Shanghai Expressway, Shanghai Ring Expressway, North-South Elevated Road, Shanghai-Chongqing Expressway, Shanghai-Kunming Expressway, Shanghai-Jinshan Expressway, Shanghai-Fengxian Expressway, and Shenjiahu Expressway, etc. In this way, the driving speed of the customized bus can be guaranteed to a certain extent, providing a competitive travel time for the customized bus.

[0077] In this method, the specific process of step S2 to construct the upper-level model with the goal of minimizing the congestion degree of rail transit intervals for making decisions on appropriate flow-diversion lines from the set of candidate flow-diversion lines is as follows:

[0078] S21. Construct the objective function with the goal of minimizing the congestion level of the rail transit section as follows:

[0079] ;

[0080] ;

[0081] Among them, ω e = x e / C e , representing the passenger load factor of the rail transit section e ; x e is the passenger flow of the rail transit section e ; C e is the restricted flow of the rail transit section e within a given time period; L e is the length of the rail transit section e ; is a continuous function of the passenger load factor of the section, is the preset full load rate threshold at which the carriage starts to get crowded, is a preset adjustment parameter greater than 0;

[0082] S22. Set the constraint condition to limit the number of selected diverted customized bus lines not to exceed a preset number threshold P :

[0083] ;

[0084] Among them, is the decision variable of the upper-level model, a discrete 0-1 variable, indicating whether a certain candidate diverted line is selected. If it is 1, it is selected; if it is 0, it is not selected; represents the set of candidate diverted lines; P is the preset number threshold.

[0085] In this embodiment, the full load rate threshold parameter at which the carriage starts to get crowded is taken as 0.5, and the adjustment parameter is taken as 1. The number threshold P of the diverted customized bus lines is taken as 5% (i.e., the value is 3), 10% (i.e., the value is 6), 15% (i.e., the value is 10), 20% (i.e., the value is 13), 25% (i.e., the value is 16), 30% (i.e., the value is 19), 35% (i.e., the value is 22), 40% (i.e., the value is 26), 45% (i.e., the value is 29), or 50% (i.e., the value is 32) of the number of candidate diverted lines.

[0086] In this method, in step S3, according to the diversion line decided by the upper-layer model, a lower-layer model and its solution method are constructed. The lower-layer model is used to reasonably load all passenger origin-destination pairs (O-D pairs) in the rail transit network onto the intervals connecting the origin and destination. It is a multi-path passenger flow equilibrium distribution model and is solved by the MSA method. The specific process is as follows:

[0087] S31. Based on the Space-L method in complex network theory, construct the rail transit network: Define a directed network , where represents the set of rail transit stations; represents the rail transit interval, including the rail transit operation interval between adjacent stations on the rail transit line and the transfer walking interval between different lines;

[0088] Set the impedance of the rail transit operation interval :

[0089] ;

[0090] ;

[0091] ;

[0092] Among them, represents the actual running time of the operation interval ; ω e =x e / C e , represents the passenger flow full load rate of the rail transit interval e ; x e is the passenger flow volume of the rail transit interval e ; C e is the restricted flow volume of the rail transit interval e within a given time period; represents the full load rate when passengers all have seats; μ and γ are preset adjustment parameters;

[0093] Set the impedance of the transfer walking interval :

[0094] ;

[0095] Among them, is the interval eThe walking transfer time; is a preset adjustment parameter, indicating that the transfer perception time is greater than the actual transfer time required;

[0096] S32. Based on the diversion lines determined by the upper-layer model, on the basis of the rail transit network, construct a combined network of rail and diversion customized buses: The starting and ending points of the diversion customized buses are at the rail transit stations. For each selected diversion customized bus line, add a diversion customized bus section between the corresponding nodes in the original rail transit network to obtain the combined network , where represents the set of rail transit stations; represents the set of sections of the combined network of rail and diversion customized buses, represents the rail transit section; represents the diversion customized bus section;

[0097] Set the impedance of the diversion customized bus section as :

[0098] ;

[0099] Among them, represents the travel time of this diversion customized bus section in the road network;

[0100] S33. Initialization: Let the iteration number n = 1; Let the flow of each section in the combined network of rail and diversion customized buses be 0, use the Dial algorithm to search for the path with the minimum impedance between each passenger travel O-D pair in the combined network of rail and diversion customized buses, and use the all-or-nothing assignment method to perform passenger flow loading to obtain the section flow of the first iteration ;

[0101] S34. Update the path impedance: According to the current section flow , update the impedance of the rail transit operation section;

[0102] S35. Load the passenger flow: According to the current section impedance, use the Dial algorithm to search for the path with the minimum impedance between each passenger travel O-D pair in the combined network of rail and diversion customized buses, and use the all-or-nothing assignment method to perform passenger flow loading to obtain the auxiliary section flow ;

[0103] S36. Update the section flow of the n +1-th iteration :

[0104] ;

[0105] S36. Check for convergence: The convergence condition is:

[0106] ;

[0107] where is a preset sufficiently small positive number; if the convergence condition is not satisfied, then let , and continue with step S34; if the convergence condition is satisfied, then stop the algorithm to obtain the passenger flow of each section in the integrated network of the orbit and the diversion customized bus.

[0108] In this embodiment, the adjustment parameter μ is taken as 0.11, γ is taken as 0.11, is taken as 1.31.

[0109] In this method, step S4 constructs an ML-OP algorithm to solve the bilevel model: replace the objective function of the upper-level model with a surrogate objective function, train the surrogate objective function through machine learning, transform the upper-level model into an integer linear programming problem, and combine initial sample generation, iterative solution, and convergence condition judgment to efficiently solve the bilevel model and obtain a better opening plan for the diversion customized bus line combination; the specific process is as follows:

[0110] S41. Generate initial samples: For a set of decision variables of the upper-level model, generate | Bc | + 2 sets of initial decision variable sets:

[0111] ;

[0112] where is the decision variable of the k th group of the upper-level model, which is a discrete 0-1 variable indicating whether a certain candidate diversion line is selected. If it is 1, it is selected; if it is 0, it is not selected; represents the set of candidate diversion lines;

[0113] This initial decision variable set contains | Bc | decision variable combinations with only 1 variable being 1, and two combinations of all 0s and all 1s;

[0114] For each set of initial decision variables of the upper-level model, construct and solve the lower-level model to obtain the passenger flow data of each section in the integrated network of the orbit and the diversion customized bus, and substitute this data into the upper-level model to calculate the objective function Z of the upper-level model, obtaining an initial sample set containing | Bc | + 2 decision variable combinations and objective function pairs:

[0115] ;

[0116] Let the number of iterations i = 0; Let the set of samples generated by the iteration , the total sample set ;

[0117] S42. Train the machine learning: Based on the current n group ( ) decision variable combination and the sample set of the objective function pairs, train a multiple linear regression model to obtain a surrogate objective function about the variable , that is, an approximation function of the objective function Z:

[0118] ;

[0119] Among them, represents the estimated value of the bias term in the regression model; represents the estimated value of the regression coefficient about , and actually represents the weight of the shunt line b in the objective function. The smaller is, the more likely the shunt line b will be selected;

[0120] S43. Establish and solve the surrogate upper-level model: By using the linear surrogate upper-level objective function , the upper-level model will be transformed into an integer linear programming model; add constraint conditions to this integer linear programming model to obtain a new solution in the iteration and limit the generation of solutions different from those in the existing samples; the surrogate upper-level model is established as:

[0121] ;

[0122] ;

[0123] Among them, m represents the number of samples generated by the iteration, ; and respectively represent the number of times the decision variable takes 1 and the number of times the decision variable takes 0 in the k th sample; use a classical algorithm or solver for solving integer linear programming problems, such as the branch and bound method, the cutting plane method, the CPLEX solver, the Gurobi solver, or the GLPK solver, to solve this surrogate upper-level model to obtain a new solution different from the solutions in the existing samples, and obtain the shunt line combination ;

[0124] ​S44, solve the lower model and update the sample set: input the diversion route combination obtained by solving the proxy upper model into the lower model, solve the lower model, obtain the passenger flow data of each section in the rail and diversion customized bus integration network, and extract the passenger flow of the rail transit section. ,in, Represents the rail transit interval in the rail and diversion customized bus integration network; calculates the actual upper-level objective function , and obtain a new set of decision variable vectors and objective function combinations ; Update the sample data set to:

[0125] ;

[0126] ;

[0127] S45, determine whether the termination condition is reached: set the termination condition of the iteration to the number of iterations i Reaching the pre-set maximum number of iterations i max , the iteration ends and the sample set is returned D The minimum objective function The corresponding solution ,Right now:

[0128] ;

[0129] That is to obtain a better combination plan for opening diversion customized bus routes;

[0130] if i < i max , then let i = i + 1. Return to step S42 and continue iterating.

[0131] In this embodiment, the maximum number of iterations i max Take 1000 times.

[0132] In this embodiment, when the number threshold of the diversion customized bus routes is P When 15% of the number of candidate diversion routes is taken, that is, when the value is 10, Table 1 shows the calculated optimal route combination, and Table 2 shows the effect of diversion routes in alleviating some congested sections.

[0133] Table 1 Basic situation of the optimal line combination when the number threshold is 10

[0134] Starting point End point Rail transit time (min) Road time (min) Passing traffic flow Number of passengers Huinan Zhangjiang Hi-Tech 57.4 60.2 769 350 Huaqiao Caoyang Road 65.1 64.0 2135 741 Huinan Yingchun Road 58.3 66.7 1037 508 Zhaofeng Road Caoyang Road 58.1 51.0 1350 658 Anting Caoyang Road 56.2 48.0 1227 609 Huaqiao Shanghai West Station 58.8 64.6 2435 582 Huinan Century Park 55.4 60.5 1764 933 Huinan Sanlin 51.5 57.9 1007 501 Shuyuan Longyang Road 69.0 51.9 686 516 Lingang Avenue Longyang Road 80.2 69.9 532 355

[0135] Table 2 The effect of diversion lines on alleviating some congested sections when the number threshold is 10

[0136] Interval starting point Interval end point Previous traffic flow Previous load factor Traffic flow after diversion Load factor after diversion Decrease value of load factor Shanghai Automobile City Changji East Road 8616 0.579 6026 0.405 0.174 Anting Shanghai Automobile City 8308 0.558 5718 0.384 0.174 Changji East Road Shanghai Circuit 10070 0.677 7480 0.503 0.174 Zhou Pudong Luoshan Road 22768 0.857 19605 0.738 0.119 Hesha Hangcheng Zhou Pudong 21012 0.791 17849 0.672 0.119 Wild Animal Park Xinchang 13684 0.515 10521 0.396 0.119 Xinchang Hangtou East 16859 0.634 13696 0.515 0.119 Hangtou East Hesha Hangcheng 17154 0.646 13991 0.527 0.119 Luoshan Road Huaxia Middle Road 19495 0.734 16855 0.634 0.100 Huaxia Middle Road Longyang Road 15956 0.600 13438 0.506 0.094 Chenxiang Highway Nanxiang 28677 0.707 26087 0.643 0.064 Malu Chenxiang Highway 26171 0.645 23581 0.581 0.064 Jiading New City Malu 22254 0.548 19664 0.485 0.063 Wuwei Road Qilianshan Road 37410 0.670 34820 0.624 0.046 Taopu New Village Wuwei Road 37416 0.671 34826 0.624 0.047 Liyuan Shanghai West Station 37473 0.672 34883 0.625 0.047 Qilianshan Road Liyuan 36815 0.660 34225 0.613 0.047 Nanxiang Taopu New Village 32628 0.585 30038 0.538 0.047 Shanghai West Station Zhenru 38323 0.687 36357 0.652 0.035 Zhenru Fengqiao Road 36931 0.662 35113 0.629 0.033 Sanlin East Sanlin 16094 0.541 15580 0.524 0.017 Longyang Road Yingchun Road 21164 0.569 20686 0.556 0.013

[0137] It can be found that the number of passengers in the optimal diversion route combination when the quantity threshold is 10 is in the range of 300 to 900 people, and the maximum reduction effect on the section load factor reaches 17.4%. Therefore, from the perspective of the quality and convenience of the services provided by the customized bus, the diversion routes are highly attractive to passengers, and there is market potential for opening the diversion customized bus routes.

[0138] In this embodiment, to comparatively analyze the superiority of the present ML-OP method, a traditional model solving method, i.e., the genetic algorithm, is also selected as the comparative method. Table 3 shows the information on the number of times of solving the lower-level model required by the ML-OP method and the genetic algorithm when obtaining the optimal solution, and the solving of the lower-level model is exactly the key factor restricting the model solving speed. Among them, the settings of the genetic algorithm are 20 individuals in each generation population, with a maximum of 100 generations of evolution, and an enhanced elite retention strategy is adopted.

[0139] Table 3 Analysis of the time efficiency of the ML-OP method and the genetic algorithm for obtaining the optimal solution

[0140]

[0141] It can be found that in most cases, the number of times of solving the lower-level model required by ML-OP is far less than that required by the genetic algorithm, and it has better solution quality, that is, the obtained optimal solution is smaller.

[0142] The time required for the equipment adopted in this embodiment to solve the lower-level model once and calculate the objective function is about 20 seconds. Calculated based on the average difference of 1000 times in the number of times of solving the lower-level model required by the ML-OP method and the genetic algorithm, the ML-OP method saves about 5.6 hours compared with the genetic algorithm, showing an obvious computational advantage. Moreover, compared with the genetic algorithm, the solving process of the ML-OP method has no random factors and can stably output the results.

[0143] The above are only the preferred embodiments of the present invention and do not impose any limitation on the present invention. Any person skilled in the art within the technical field, without departing from the technical solution of the present invention, makes any form of equivalent replacement or modification and other changes to the technical solution and technical content disclosed by the present invention, all of which fall within the content of the technical solution of the present invention and still belong to the protection scope of the present invention.

Claims

1. A method for constructing and solving a two-layer planning model for diversion and customized public transportation, characterized in that: The following steps are involved: S1. Determine a set of candidate customized bus diversion routes; S2. Build an upper-level model with the goal of minimizing the congestion level of rail transit sections, and use it to decide on the appropriate diversion route from the set of candidate diversion routes; S3, constructing a lower-level model and its solution method according to the diversion route determined by the upper-level model; S4, build ML-OP algorithm to solve the two-layer model, The process of step S1 is as follows: given the information of the passenger travel start station-end station pairs in the rail transit network, a set of station pairs whose path length between the station pairs is greater than a preset path length threshold, whose travel passenger flow between the station pairs is greater than a preset flow threshold, and whose fastest travel time in the road network divided by the fastest travel time in the rail transit network is less than a preset time ratio threshold is extracted as a set of candidate diversion routes; The process of step S2 is: S21. The objective function is constructed with the goal of minimizing the congestion level of rail transit sections as follows: ； ； in, ω e = x e / C e , indicating the rail transit section e Passenger load factor; x e For rail transit section e passenger flow; C e For rail transit section e Limit traffic during a given period; L e For rail transit section e Length; is a continuous function of the interval passenger flow load factor, is the pre-set full load threshold at which the carriage begins to become crowded. is a preset adjustment parameter greater than 0; S22. Set constraints to limit the number of selected diversion customized bus routes to not exceed a preset number threshold. P : ； in, represents the set of candidate diversion routes, It is one of the candidate diversion routes; It is the decision variable of the upper model, which is a discrete 0-1 variable and represents a candidate diversion route. Whether it is selected, 1 means selected, 0 means not selected; P is a preset number threshold.

2. The method for constructing and solving the diversion customized bus double-layer programming model according to claim 1 is characterized in that: The method of S3; the lower model is used to reasonably load all passenger travel starting station-terminal station pairs in the rail transit network to the intervals connecting the starting and ending points. It is a multi-path passenger flow equilibrium allocation model, which is solved by the MSA method. The specific process is: S31. Building a rail transit network based on the Space-L method in complex network theory: Defining a directed network ,in, Represents a set of rail transit stations; Indicates rail transit intervals, including rail transit driving intervals between adjacent stations of rail transit lines, and transfer walking intervals between different lines; Set up rail transit driving range Impedance : ； ； ； in, Indicates driving range The actual running time; ω e =x e / C e , indicating the rail transit section e The passenger load factor, x e For rail transit section e of passenger flow, C e For rail transit section e Limit traffic during a given period; It indicates the load factor when all passengers have seats; μ and γ is a preset adjustment parameter; Set up transfer walking zones Impedance : ； in, Is the interval e Walking transfer time; It is a pre-set adjustment parameter, which indicates that the perceived transfer time is greater than the actual transfer time. S32. Based on the diversion routes decided by the upper model, a rail and diversion customized bus fusion network is constructed on the basis of the rail transit network: the starting and ending points of the diversion customized bus are at the rail transit stations. For each selected diversion customized bus route, a diversion customized bus section is added between the corresponding nodes of the original rail transit network to obtain a fusion network. ,in, Represents a set of rail transit stations; represents the interval set of the rail and diversion customized bus fusion network, Indicates the rail transit section; Indicates the diversion customized bus section; Set up customized bus sections Impedance : ； in, Indicates the travel time of the diversion customized bus section in the road network; S33, Initialization: Let the number of iterations n =1; Set the flow rate of each section in the rail and diversion customized bus fusion network to 0, use the Dial algorithm to search for the path with the minimum impedance between each passenger travel OD pair in the rail and diversion customized bus fusion network, use the all-or-nothing allocation method to perform passenger flow loading, and obtain the interval flow rate of the first iteration ; S34, Update path impedance: according to the current interval flow , update the impedance of rail transit driving section; S35, passenger flow loading: according to the current interval impedance, use the Dial algorithm to search for the path with the minimum impedance between each passenger travel OD pair in the rail and diversion customized bus fusion network, and use the all-or-nothing allocation method to perform passenger flow loading to obtain the auxiliary interval flow ; S36, Update n +1 interval flow : ； S36, check convergence: The convergence conditions are: ； in, is a preset sufficiently small positive number; if the convergence condition is not met, let , proceed to step S34; if the convergence condition is met, stop the algorithm and obtain the passenger flow of each section in the rail and diversion customized bus fusion network.

3. The method for constructing and solving the diversion customized bus double-layer programming model according to claim 2 is characterized in that: The construction method of step S4 is as follows: the objective function of the upper model is replaced by a proxy objective function, the proxy objective function is trained by machine learning, the upper model is converted into an integer linear programming problem, and the double-layer model is efficiently solved by combining initial sample generation, iterative solution and convergence condition judgment to obtain a better combination opening plan for diversion customized bus routes. The specific process is as follows: S41. Generate initial samples: a set of decision variables for the upper model , generating a file containing | Bc |+2 sets of initial decision variables: ； in, It is k The decision variable of the upper model of the group is a discrete 0-1 variable, indicating whether a candidate diversion route is selected. If it is 1, it is selected, and if it is 0, it is not selected; represents the set of candidate diversion routes, It is one of the candidate diversion routes; This initial set of decision variables contains | Bc | a decision variable combination with only one variable being 1, and two combinations of all 0s and all 1s; For each set of initial decision variables of the upper model, the lower model is constructed and solved to obtain the passenger flow data of each section in the rail and diversion customized bus integration network, and the data is substituted into the upper model to calculate the objective function of the upper model. Z , got the inclusion | Bc |+The initial sample set of 2 decision variable combinations and objective function pairs: ； Let the number of iterations i =0; let the set of samples generated by iteration , the total sample set ; S42. Training machine learning: Based on the current n Group( ) A sample set of decision variable combinations and objective function pairs is used to train a multivariate linear regression model to obtain a variable The proxy objective function , which is the approximate function of the objective function Z: ； in, represents the set of candidate diversion routes, It is one of the candidate diversion routes; Is a discrete 0-1 variable, representing a candidate diversion route Whether it is selected, 1 means selected, 0 means not selected; Represents the estimated value of the bias term in the regression model; Indicates about The estimated regression coefficient of actually represents the diversion route b The weights in the objective function are The smaller the value, the more shunt the circuit. b The more likely you are to be selected; S43. Establish and solve the proxy upper layer model: by using a linear proxy upper layer objective function , so that the upper model will be transformed into an integer linear programming model; constraints are added to the integer linear programming model to obtain new solutions in iterations and limit the generation of solutions different from those in existing samples; the proxy upper model is established as: ； ； in, m represents the number of samples generated by the iteration, ; and Respectively represent k The number of times the decision variable takes 1 and the number of times the decision variable takes 0 in the samples; the meanings of other variables are the same as before; use the classical algorithm or solver for solving integer linear programming problems to solve the proxy upper model and obtain a new solution that is different from the solution in the existing samples , and obtain the shunt line combination ; S44, solve the lower model and update the sample set: input the diversion route combination obtained by solving the proxy upper model into the lower model, solve the lower model, obtain the passenger flow data of each section in the rail and diversion customized bus integration network, and extract the passenger flow of the rail transit section. ,in, Represents the rail transit interval in the rail and diversion customized bus integration network; calculates the actual upper-level objective function , and obtain a new set of decision variable vectors and objective function combinations ; Update the sample data set to: ； ； S45, determine whether the termination condition is reached: set the termination condition of the iteration to the number of iterations i Reaching the pre-set maximum number of iterations i max , the iteration ends and the sample set is returned D The minimum objective function The corresponding solution ,Right now: ； Get a better combination plan for opening diversion customized bus routes; if i i=i+ max , then let ​ 1. Return to step S42 and continue iterating.

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