A Timetable Coordination Compilation Method for the Optimization of the Transfer between Intelligent Rail Transit and Bus

Abstract

The present invention relates to the technical field of intelligent rail transit, and discloses a method for collaborative compilation of timetables for optimizing the transfer between intelligent rail and buses. The method includes constructing a dual-mode public transportation network and determining all transfer stations for the transfer between intelligent rail and buses therein; calculating the number of departures of each line within the planned time; estimating the transfer passenger flow between each shift of each line within the planned time range; respectively constructing two single-objective integer programming models; calculating the departure time windows of each bus of each line at the transfer stations, respectively optimizing and solving the first single-objective integer programming model and the second single-objective integer programming model to obtain the optimal departure time of the first bus of each line; calculating the optimal departure time of each bus of each line to obtain the timetables of each line in the dual-mode public transportation network. The present invention realizes the dual optimization of the timetables in terms of the number of successful passenger transfers and the total transfer waiting time by constructing two single-objective integer programming models.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent rail transit, and particularly relates to a method for collaborative compilation of timetables for optimizing the transfer between intelligent rail and buses. Background Art

[0002] With the rapid growth of urban population and the rapid increase in the number of private cars, many large cities are facing serious traffic congestion, traffic safety accidents, and traffic exhaust emissions problems. The sustainable development of urban transportation systems faces severe challenges. Especially during the morning and evening rush hours on weekdays, the road congestion is serious, resulting in an extension of commuting time and a decline in travel efficiency. At the same time, environmental problems such as vehicle exhaust emissions and air pollution are also becoming increasingly serious, threatening the health of urban residents and the environmental quality.

[0003] Public transportation, as a low-cost and high-efficiency transportation mode, has become the key to solving these problems. Compared with private cars, public transportation has a greater transportation capacity, can effectively relieve urban traffic pressure, improve environmental quality, and promote the sustainable development of urban transportation systems.

[0004] The intelligent rail express system, also known as intelligent rail (English: Autonomous Rail Rapid Transit, ART), is a new type of medium and low-capacity rail transit system with unique advantages. Compared with traditional rail transit systems, intelligent rail has the characteristics of low investment cost, short construction period, and flexible operation. It is a powerful supplement to urban public transportation. The rapid development and popularization of intelligent rail have achieved certain achievements at home and abroad, and more and more cities have begun to introduce and operate intelligent rail lines.

[0005] However, at present, the vast majority of intelligent rail lines still adopt the mode of single-line independent operation, which has led to a series of problems. First, the transfer experience of passengers is poor because they usually need to adopt the method of "getting off at the station first and then entering the station" to achieve transfer, which increases the pressure on transfer stations and also reduces the convenience of travel. Second, the capacity resources of intelligent rail cannot be fully shared, and the equipment utilization rate is not high, which leads to an increase in operating costs and a decrease in efficiency. In addition, there are competitions and disharmonies between intelligent rail lines and conventional bus lines, resulting in waste of resources and inconvenience for passengers to travel. Summary of the Invention

[0006] In view of the above deficiencies in the prior art, the present invention provides a method for collaborative compilation of timetables for optimizing the transfer between intelligent rail and buses.

[0007] In order to achieve the above object of the invention, the technical solution adopted by the present invention is:

[0008] A method for collaborative compilation of timetables for optimizing the transfer between intelligent rail and buses, comprising the following steps:

[0009] Construct a dual-mode public transportation network based on the intelligent rail lines and bus lines, and determine all the transfer stations where the intelligent rail and bus transfer;

[0010] According to the planned time and the operation time of the intelligent rail and bus, determine the departure intervals of each intelligent rail and bus line within the planned time, and calculate the number of departures of each line within the planned time;

[0011] Estimate the transfer passenger flow between each shift of each line within the planned time range according to the historical passenger flow data of mutual transfer between lines;

[0012] Construct a first single-objective integer programming model with the departure time of the first bus of each line as the decision variable and the maximization of the number of successful transfer passengers as the optimization goal, and introduce parameters to characterize the transfer waiting time based on the optimization results of the first single-objective integer programming model, and construct a second single-objective integer programming model with the minimization of the total transfer waiting time as the optimization goal;

[0013] According to the departure intervals, departure schedules and travel times to each transfer station of each line, calculate the departure time windows of each bus of each line at the transfer station, and optimize and solve the first single-objective integer programming model and the second single-objective integer programming model respectively to obtain the optimal departure time of the first bus of each line;

[0014] Calculate the optimal departure time of each bus of each line according to the optimal departure time of the first bus of each line and the departure intervals and the number of departures of each line, and obtain the timetables of each line of the dual-mode public transportation network.

[0015] Preferably, calculate the number of departures of each line within the planned time, specifically:

[0016]

[0017] where n l is the number of departures of line l within the planned time T, h l is the departure interval of line l, is the ceiling function.

[0018] Preferably, estimate the transfer passenger flow between each shift of each line within the planned time range, specifically:

[0019]

[0020] where u piqjs is the number of passengers transferring from the i-th bus of line p to the j-th bus of line q at the transfer station s; v pqs is the total passenger flow from line p to line q within the planned time T at the transfer station s; n pis the departure frequency of line p within the planning time T.

[0021] Preferably, a first single-objective integer programming model is constructed with the departure time of the first bus of each line as the decision variable and the maximization of the number of successful transfer passengers as the optimization objective. Specifically:

[0022]

[0023]

[0024] c piqjs ∈{0, 1}

[0025] where max is the maximum value function; F1 is the first objective function; c piqjs is a 0-1 variable indicating whether the difference between the departure time of the j-th bus of the transferred line q at the transfer station s and the arrival time of the i-th bus of the line p from which the transfer passengers come at the transfer station s is within the time window; u piqjs is the number of passengers transferring from the i-th bus of line p to the j-th bus of line q at the transfer station s; L is the set of lines in the dual-mode public transport network; I p is the set of departure schedules of line p; J q is the set of departure schedules of line q; S t is the set of transfer stations for the intelligent rail and bus transfer; x pi is the departure time of the i-th bus of line p; x qj is the departure time of the j-th bus of line q; t ps is the travel time of line p from the starting point to the transfer station s; t qs is the travel time of line q from the starting point to the transfer station s; M is a set positive integer; W is the upper limit of the transfer waiting time; h p is the headway of line p; h q is the headway of line q; is the departure time of the n p -th bus of line p; is the departure time of the n q -th bus of line q; T is the planning time; x p1 is the departure time of the first bus of line p; x q1 is the departure time of the first bus of line q.

[0026] Preferably, based on the optimization result of the first single-objective integer programming model, parameters are introduced to characterize the transfer waiting time, and a second single-objective integer programming model is constructed with the minimization of the total transfer waiting time as the optimization objective. Specifically:

[0027]

[0028]

[0029] c piqjs ∈ {0, 1}

[0030] where min is the minimum value function; F2 is the second objective function; c piqjs is a 0-1 variable indicating whether the difference between the departure time of the j-th bus of line q to be transferred at the transfer station s and the arrival time of the i-th bus of line p from which the transfer passenger comes at the transfer station s is within the time window; u piqjs is the number of passengers transferring from the i-th bus of line p to the j-th bus of line q at the transfer station s; r piqjs is the transfer waiting time of the passengers of the i-th bus of line p transferring to the j-th bus of line q at the transfer station; L is the set of lines in the dual-mode public transport network; I p is the set of departure schedules of line p; J q is the set of departure schedules of line q; S t is the set of transfer stations for the transfer between the APM and buses; B is to maximize the number of successfully transferred passengers; x pi is the departure time of the i-th bus of line p; x qj is the departure time of the j-th bus of line q; t ps is the travel time of line p from the starting point to the transfer station s; t qs is the travel time of line q from the starting point to the transfer station s; M is a set positive integer; W is the upper limit of the transfer waiting time; h p is the headway of line p; h q is the headway of line q; is the departure time of the n p -th bus of line p; is the departure time of the n q -th bus of line q; T is the planning time; x p1 is the departure time of the first bus of line p; x q1 is the departure time of the first bus of line q.

[0031] Preferably, according to the headways, departure schedules of each line, and travel times to each transfer station, calculate the departure time windows of each bus of each line at the transfer station, including the following steps:

[0032] Select any transfer station s and lines p and q with transfers at this transfer station;

[0033] According to the headway h p of line p and the travel time t ps of line p to the transfer station s, determine the time window {[tps ,t ps +h p ,[t ps +h p ,t ps +2h p ,…,[t ps +(i - 1)h p ,t ps +ih p ,…,[t ps +(n p - 1)h p ,t ps +n p h p}, where i is the shuttle bus number;

[0034] According to the departure interval h of line q q and the travel time t from line q to the transfer station s qs , determine the time window {[t qs ,t qs +h q ,[t qs +h q ,t qs +2h q ,…,[t qs +(j - 1)h q ,t qs +jh q ,…,[t qs +(n q - 1)h q ,t qs +n q h q} for each shuttle bus of line p to the transfer station s, where j is the shuttle bus number.

[0035] Preferably, optimize and solve the first single - objective integer programming model and the second single - objective integer programming model to obtain the optimal first - departure time of each line, including the following steps:

[0036] For passengers transferring from line p to line q, judge whether it satisfies t ps +(i - 1)h p >t qs +jh q , where i and j are shuttle bus numbers; if so, delete the auxiliary variables representing feasible transfers and the parameters and related constraints of transfer waiting time; otherwise, do not process;

[0037] For passengers transferring from line q to line p, judge whether it satisfies t qs +(j - 1)hq >t ps +ih p ; If so, delete the auxiliary variables representing feasible transfers, the parameters of transfer waiting time, and the related constraints; otherwise, do nothing;

[0038] Solve the optimized first single-objective integer programming model and the second single-objective integer programming model respectively to obtain the optimal first departure time of each line.

[0039] Preferably, calculate the optimal departure time of each bus of each line according to the optimal first departure time of each line, the headway of each line, and the number of departures. Specifically:

[0040] x pi =x p1 +(i - 1)h p , i≥2

[0041] x qj =x q1 +(j - 1)h q , j≥2

[0042] where, x pi is the optimal departure time of the i-th bus of line p; x qj is the optimal departure time of the j-th bus of line q; x p1 is the optimal first departure time of line p; x q1 is the optimal first departure time of line q; h p is the headway of line p; h q is the headway of line q.

[0043] The present invention has the following beneficial effects:

[0044] 1. The present invention proposes a new method for collaborative compilation of timetables for tram-train and bus transfer optimization, which comprehensively considers the optimization model of the number of successful passenger transfers and transfer waiting time. Through computer optimization software, the optimized compilation of the timetable is realized, providing the timetable for tram-train and bus collaborative transfer for operation dispatchers.

[0045] 2. The present invention proposes two single-objective optimization models based on maximizing the number of successful transfer passengers and minimizing the total transfer waiting time based on maximizing the number of successful transfer passengers. By introducing the constraints and auxiliary variables of feasible transfers, two single-objective integer programming models are established, realizing the dual optimization of the timetable in terms of the number of successful passenger transfers and the total transfer waiting time.

[0046] 3. The present invention efficiently solves the problem of compiling an optimized transfer schedule for a large-scale intelligent rail transit and bus collaborative network by reducing the number of constraint conditions. By analyzing the headway, departure frequency of routes, and transfer situations at transfer stations, redundant constraints are eliminated, enabling detailed scheduling of the schedule and ensuring smooth transfers and convenient travel. Brief Description of the Drawings

[0047] Figure 1 It is a schematic flowchart of a method for collaborative compilation of a schedule for optimizing the transfer between intelligent rail transit and buses. Detailed Embodiments

[0048] The following describes the detailed embodiments of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the detailed embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions created using the concept of the present invention are within the scope of protection.

[0049] As Figure 1 shown, an embodiment of the present invention provides a method for collaborative compilation of a schedule for optimizing the transfer between intelligent rail transit and buses, including the following steps S1 to S6:

[0050] S1. Construct a dual-mode public transportation network based on the intelligent rail transit lines and bus lines, and determine all transfer stations where intelligent rail transit and buses transfer.

[0051] In an alternative embodiment of the present invention, this embodiment determines the optimized lines through step S1. Select a dual-mode public transportation network composed of the intelligent rail transit and bus lines to be optimized, and determine all stations where intelligent rail transit and buses transfer. The obtained dual-mode bus network is represented as G = {L, S t}, where L is the set of bus lines included in the network (including buses and intelligent rail transit), and S t is the set of stations where intelligent rail transit and buses transfer.

[0052] S2. Determine the headway of each intelligent rail transit and bus line within the planning time according to the planning time and the operation time of intelligent rail transit and buses, and calculate the departure quantity of each line within the planning time.

[0053] In an alternative embodiment of the present invention, this embodiment determines the planning time through step S2, that is, which time period's operation needs to be optimized for the schedule. According to the operation information of intelligent rail transit and buses, determine the headway time of each intelligent rail transit and bus line within the planning time, and further calculate the departure quantity of each line within the planning time.

[0054]

[0055] where n l is the number of departures of line l within the planning time T, and h l is the headway of line l, and [] is the ceiling function.

[0056] S3. Estimate the transfer passenger flow between each class of each line within the planning time range according to the historical passenger flow data of transfers between lines;

[0057] In an alternative embodiment of the present invention, the specific transfer passenger flow is determined in step S3. Specifically, first, according to the historical passenger flow data of transfers between lines, the total transfer passenger flow between lines within the planning time range is estimated; then, according to the number of departures of each line within the planning time calculated in step S2, the detailed transfer passenger flow between each class of each line can be calculated, and this passenger flow is considered to be evenly distributed.

[0058] In this embodiment, it is set that the number of passengers transferring from line p to line q at the transfer station s is evenly distributed with the number of departures of line p, that is, the number of transfers of each bus for the same transfer action is the same. To estimate the transfer passenger flow between each class of each line within the planning time range, specifically:

[0059]

[0060] where u piqjs is the number of passengers transferring from the i-th bus of line p to the j-th bus of line q at the transfer station s; where line p and line q belong to different transportation modes, that is, one comes from the intelligent rail and the other comes from the conventional bus, I p ={1, 2,..., n p}, J q ={1, 2,..., n q}, representing the set of departure schedules of each line. Here, the value of j cannot be directly determined, that is, it cannot be determined which specific bus of line q the i-th bus of line p transfers to, and the result can only be obtained after model optimization; v pqs is the total passenger flow from line p to line q within the planning time T at the transfer station s; n p is the number of departures of line p within the planning time T.

[0061] S4. Construct a first single-objective integer programming model with the departure time of the first bus of each line as the decision variable and the maximization of the number of successfully transferred passengers as the optimization objective, and introduce parameters to characterize the transfer waiting time based on the optimization result of the first single-objective integer programming model, and construct a second single-objective integer programming model with the minimization of the total transfer waiting time as the optimization objective;

[0062] In an alternative embodiment of the present invention, two integer programming models for optimizing timetables are established through step S4, and the established models are as follows:

[0063] In the first model, by introducing the departure time of the first bus of each line as a decision variable and using a 0-1 auxiliary variable to represent whether a feasible transfer exists, the objective function is to maximize the number of passengers with successful transfers. The objective function and constraints included in the first model are as follows:

[0064]

[0065] The constraints are as follows:

[0066]

[0067] These two constraints indicate that when the difference between the departure time of the j-th bus of the transferred line q at the transfer station s and the departure time of the i-th bus of the line p from which the transfer passengers come at the transfer station s is within the time window [0, W], it is regarded as a feasible transfer.

[0068]

[0069] This constraint indicates that the passengers of each bus will only transfer to a certain bus of another line.

[0070]

[0071] These two constraints indicate that the headway of each line is uniform.

[0072]

[0073] These two constraints are the departure time constraints for the last bus.

[0074]

[0075] These two constraints indicate the value range of the decision variables.

[0076] c piqjs ∈ {0, 1}

[0077] This constraint indicates the value range of the auxiliary variable.

[0078] Among them, max is the maximum value function; F1 is the first objective function; c piqjs is a 0-1 variable representing whether the difference between the departure time of the j-th bus of the transferred line q at the transfer station s and the arrival time of the i-th bus of the line p from which the transfer passengers come at the transfer station s is within the time window [0, W]. If it is within the time window, it is regarded as a feasible transfer, and the value is 1 at this time; otherwise, the value is 0; upiqjs The number of passengers transferring from the \(i\)-th bus of line \(p\) to the \(j\)-th bus of line \(q\) at transfer station \(s\); \(L\) is the set of lines in the dual-mode public transport network; \(I\) p is the set of departure schedules of line \(p\); \(J\) q is the set of departure schedules of line \(q\); \(S\) t is the set of transfer stations for the transfer between the APM and buses; \(x\) pi is the departure time of the \(i\)-th bus of line \(p\); \(x\) qj is the departure time of the \(j\)-th bus of line \(q\); \(t\) ps is the travel time of line \(p\) from the starting point to transfer station \(s\); \(t\) qs is the travel time of line \(q\) from the starting point to transfer station \(s\); \(M\) is a set positive integer; \(W\) is the upper limit of the transfer waiting time, which depends on whether the transferred vehicle is the first bus of the corresponding line. If it is the first bus, the value is \(t\) qs , otherwise the value is \(h\) q - 1; \(h\) p is the headway of line \(p\); \(h\) q is the headway of line \(q\); is the departure time of the \(n\) p -th bus of line \(p\); is the departure time of the \(n\) q -th bus of line \(q\); \(T\) is the planning time; \(x\) p1 is the departure time of the first bus of line \(p\); \(x\) q1 is the departure time of the first bus of line \(q\).

[0079] The second model is based on the first model to optimize the maximization of the number of successful transfer passengers, and introduces the transfer waiting time parameter on the basis of the first model. The objective function is to minimize the total transfer waiting time. The objective function and constraints included in the second model are as follows:

[0080]

[0081] The constraints are as follows:

[0082]

[0083] This constraint means that the model is constrained by the optimization result of the first model (maximizing the number of successful transfer passengers).

[0084]

[0085] This constraint represents the calculation method of the transfer waiting time. Only when the transfer is feasible will the corresponding transfer waiting time be calculated.

[0086] In addition, the second model also includes all the constraints of the first model, as follows:

[0087]

[0088]

[0089] c piqjs ∈{0,1}

[0090] where min is the minimum value function; F2 is the second objective function; c piqjs is a 0-1 variable representing whether the difference between the departure time of the j-th bus of line q to be transferred at the transfer station s and the arrival time of the i-th bus of line p from which the transfer passenger comes at the transfer station s is within the time window [0, W]; u piqjs is the number of passengers transferring from the i-th bus of line p to the j-th bus of line q at the transfer station s; r piqjs is the transfer waiting time of the passengers of the i-th bus of line p transferring to the j-th bus of line q at the transfer station. Only when the corresponding transfer is feasible, that is, when c piqjs = 1, the constraint condition for calculating the transfer waiting time takes effect and the corresponding transfer waiting time will be calculated; L is the set of lines in the dual-mode public transport network; I p is the set of departure schedules of line p; J q is the set of departure schedules of line q; S t is the set of transfer stations for the transfer between the intelligent rail and the bus; B is to maximize the number of successfully transferred passengers, which is the optimization result of the first single-objective integer programming model; x pi is the departure time of the i-th bus of line p; x qj is the departure time of the j-th bus of line q; t ps is the travel time of line p from the starting point to the transfer station s; t qs is the travel time of line q from the starting point to the transfer station s; M is a set positive integer; W is the upper limit of the transfer waiting time; h p is the headway of line p; h q is the headway of line q; is the departure time of the n p -th bus of line p; is the departure time of the n q -th bus of line q; T is the planning time; x p1 is the departure time of the first bus of line p; x q1 is the departure time of the first bus of line q.

[0091] S5. Calculate the departure time windows of each bus on each line at the transfer stations according to the headway, departure frequency of each line, and the travel time to each transfer station, and optimize and solve the first single-objective integer programming model and the second single-objective integer programming model respectively to obtain the optimal first departure time of each line.

[0092] In an alternative embodiment of the present invention, this embodiment determines the situations where transfers cannot occur through step S5, that is, removes redundant constraint conditions, so that the model is applicable to large-scale timetable optimization problems. Specifically, it includes: First, according to the headway, departure frequency of each line, and the transfer situations at each transfer station, deduce the departure time windows (earliest arrival time and latest departure time, since it is assumed that the vehicle stay time is 0, the departure time is the same as the arrival time) of each bus on each line at the transfer stations. From this, the detailed situations where transfers cannot occur can be determined, and the corresponding relevant constraint conditions can be further excluded, thereby greatly reducing the number of constraint conditions in the model. Through an optimization software, large-scale problems can be efficiently solved.

[0093] This embodiment calculates the departure time windows of each bus on each line at the transfer stations according to the headway, departure frequency of each line, and the travel time to each transfer station, including the following steps:

[0094] Select any transfer station s and the lines p and q that have transfers at this transfer station;

[0095] According to the headway h of line p p and the travel time t from line p to transfer station s ps , determine the time window {[t ps , t ps + h p , [t ps + h p , t ps + 2h p , …, [t ps + (i - 1)h p , t ps + ih p , …, [t ps + (n p - 1)h p , t ps + n p h p} composed of the earliest arrival time and the latest departure time of each bus of line p at transfer station s, that is, the first bus is: [t ps , t ps + h p , the second bus is: [t ps + h p , t ps+2h p , … The i-th bus is: [t ps +(i - 1)h p , t ps +ih p . … The last bus is [t ps +(n p -1)h p , t ps +n p h p ;

[0096] According to the departure interval h of line q q and the travel time t from line q to the transfer station s qs , determine the time window {[t qs , t qs +h q , [t qs +h q , t qs +2h q , …, [t qs +(j - 1)h q , t qs +jh q , …, [t qs +(n q -1)h q , t qs +n q h q} for each bus of line p to reach the transfer station s, that is, the first bus is: [t qs , t qs +h q , the second bus is: [t qs +h q , t qs +2h q , … The j-th bus is: [t qs +(j - 1)h q , t qs +jh q , … The last bus is [t qs +(n q -1)h q , t qs +n q h q .

[0097] In this embodiment, the first single-object integer programming model and the second single-object integer programming model are respectively optimized and solved to obtain the departure time of the first bus of each line, including the following steps:

[0098] Judge whether it meets the condition t for a passenger to transfer from line p to line q ps +(i - 1)h p >t qs +jh q where i and j are the shuttle numbers; if so, delete the corresponding variables and constraints, that is, the earliest arrival time of the i-th shuttle on line p is later than the latest departure time of the j-th shuttle on line q, then it is impossible for a passenger to transfer from the i-th shuttle on line p to the j-th shuttle on line q, corresponding to the auxiliary variable c representing feasible transfer in the first integer programming model piqjs Delete, and delete the variable c piqjs The relevant constraints for judging whether the transfer is feasible are also deleted, corresponding to the auxiliary variable c representing feasible transfer in the second integer programming model piqjs and the parameter r representing the transfer waiting time piqjs Delete, and delete the variable c piqjs The relevant constraints for judging whether the transfer is feasible and the constraints for calculating the transfer waiting time r piqjs are deleted; otherwise, no processing is done;

[0099] Judge whether it meets the condition t for a passenger to transfer from line q to line p qs +(j - 1)h q >t ps +ih p ; if so, delete the corresponding variables and constraints, that is, the earliest arrival time of the j-th shuttle on line q is later than the latest departure time of the i-th shuttle on line p. Then it is impossible for a passenger to transfer from the j-th shuttle on line q to the i-th shuttle on line p, corresponding to the auxiliary variable c representing feasible transfer in the first integer programming model qjpis Delete, and delete the variable c qjpis The relevant constraints for judging whether the transfer is feasible are also deleted, corresponding to the auxiliary variable c representing feasible transfer in the second integer programming model qjpis and the parameter r representing the transfer waiting time qjpis Delete, and delete the variable c qjpis The relevant constraints for judging whether the transfer is feasible and the constraints for calculating the transfer waiting time r qjpis are deleted; otherwise, no processing is done;

[0100] Solve the optimized first single-objective integer programming model and the second single-objective integer programming model respectively to obtain the first departure times of each line; specifically, solve the first single-objective integer programming model and the second single-objective integer programming model after deleting the variables and constraint conditions corresponding to impossible transfer situations; first, calculate the first single-objective integer programming model to obtain the maximum number of successful transfers and the corresponding first departure times; then, substitute the maximum number of successful transfers into the second single-objective integer programming model to obtain the minimum total transfer waiting time based on the maximum number of successful transfers and the corresponding first departure times.

[0101] In this embodiment, the model is preprocessed to reduce the number of constraint conditions, thereby accelerating the solving speed and achieving the rapid solution of the two mathematical models.

[0102] In this embodiment, the process of reducing redundant constraints is preprocessed in advance by Excel to find out the situations where transfers are impossible, and the models of maximizing the number of successful transfers and minimizing the total transfer waiting time are efficiently solved using the commercial optimization solver Gurobi.

[0103] S6. Calculate the optimal departure times of each bus on each line according to the optimal first departure times of each line, the headway, and the number of departures of each line, and obtain the timetables of each line in the dual-mode public transportation network.

[0104] In an alternative embodiment of the present invention, in this embodiment, according to the optimization result in step S6, the optimal departure time of each shift of each line is calculated, that is, the complete timetables of each line in the entire network. Specifically, it includes: first, through the optimization software, solve the two preprocessed models respectively, and the obtained optimal solutions are the optimal first departure times of each line; then, through the headway and the number of departures of each line, the complete timetables of each line in the network can be determined.

[0105] In this embodiment, calculate the optimal departure times of each bus on each line according to the optimal first departure times of each line, the headway, and the number of departures of each line, specifically:

[0106] x pi =x p1 +(i - 1)h p , i≥2

[0107] x qj =x q1 +(j - 1)h q , j≥2

[0108] Among them, x pi is the optimal departure time of the i-th bus on line p; x qjis the optimal departure time of the j-th bus on line q; x p1 is the optimal departure time of the first bus on line p; x q1 is the optimal departure time of the first bus on line q; h p is the headway of line p; h q is the headway of line q.

[0109] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, and the combination of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in one process Figure 1 one process or multiple processes and / or blocks Figure 1 or multiple blocks.

[0110] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that implement the functions specified in one process Figure 1 one process or multiple processes and / or blocks Figure 1 or multiple blocks.

[0111] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one process Figure 1 one process or multiple processes and / or blocks Figure 1 or multiple blocks.

[0112] Specific embodiments are applied in the present invention to elaborate on the principles and implementation manners of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, based on the idea of the present invention, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to the present invention.

[0113] Those of ordinary skill in the art will realize that the embodiments described herein are provided to assist the reader in understanding the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations without departing from the essence of the present invention based on the technical revelations disclosed in the present invention, and these deformations and combinations are still within the scope of protection of the present invention.

Claims

1. A method for collaborative compilation of timetables for the optimization of the transfer between intelligent rail transit and buses, characterized in that, It includes the following steps: Construct a dual-mode public transportation network based on the intelligent rail line and bus line, and determine all transfer stations where the intelligent rail and bus transfer; According to the planned time and the operation time of the intelligent rail and bus, determine the departure intervals of each intelligent rail and bus line within the planned time, and calculate the number of departures of each line within the planned time; Estimate the transfer passenger flow between each shift of each line within the planned time range according to the historical passenger flow data of mutual transfer between lines; Construct a first single-objective integer programming model with the departure time of the first bus of each line as the decision variable and the maximization of the number of successfully transferred passengers as the optimization objective, and introduce parameters to characterize the transfer waiting time based on the optimization result of the first single-objective integer programming model, and construct a second single-objective integer programming model with the minimization of the total transfer waiting time as the optimization objective; Calculate the departure time window of each bus of each line at the transfer station according to the departure interval, departure frequency of each line and the driving time to each transfer station; Optimize and solve the first single-objective integer programming model and the second single-objective integer programming model respectively to obtain the optimal departure time of the first bus of each line, including the following steps: Determine whether it satisfies t for a passenger to transfer from line p to line q ps +(i - 1)h p >t qs +jh q , t ps is the travel time from line p to transfer station s, h p is the departure interval of line p, t qs is the travel time from line q to transfer station s, h q is the departure interval of line q, i and j are the shuttle numbers; if so, delete the auxiliary variables representing feasible transfers, the parameters of transfer waiting time, and the relevant constraints; otherwise, do nothing; Determine whether it meets the condition t for a passenger to transfer from line q to line p qs +(j - 1)h q >t ps +ih p ; if so, delete the auxiliary variables representing feasible transfers, the parameters of transfer waiting times, and the relevant constraints; otherwise, do nothing Solve the optimized first single-objective integer programming model and the second single-objective integer programming model respectively to obtain the optimal departure time of the first bus of each line; Calculate the optimal departure time of each bus of each line according to the optimal departure time of the first bus of each line and the departure interval and number of departures of each line to obtain the timetable of each line of the dual-mode public transportation network.

2. A timetable collaborative compilation method for optimizing the transfer between intelligent rail transit and buses according to claim 1, characterized in that, Calculate the number of departures of each line within the planned time, specifically: Among them, n l is the number of departures of line l within the planning time T, h l is the headway of line l, and is the ceiling function.

3. A collaborative schedule compilation method for the optimization of the transfer between intelligent rail transit and buses according to claim 1, characterized in that, Estimate the transfer passenger flow between each shift of each line within the planned time range, specifically: where, u piqjs is the number of passengers transferring from the i-th bus of line p to the j-th bus of line q at the transfer station s; v pqs is the total passenger flow from line p to line q within the planned time T at the transfer station s; n p is the number of departures of line p within the planned time T.

4. A collaborative schedule compilation method for optimizing the transfer between intelligent rail transit and buses according to claim 1, characterized in that Construct a first single-objective integer programming model with the departure time of the first bus of each line as the decision variable and the maximization of the number of successfully transferred passengers as the optimization objective, specifically: s.t. C piqjs ∈{0,1} where max is the maximum value function; F1 is the first objective function; c piqjs is a 0-1 variable indicating whether the difference between the departure time of the j-th bus of line q to be transferred at transfer station s and the arrival time of the i-th bus of line p from which the transfer passenger comes at transfer station s is within the time window; u piqjs is the number of passengers transferring from the i-th bus of line p to the j-th bus of line q at transfer station s; L is the set of lines in the dual-mode public transport network; I p is the set of departure schedules of line p; J q is the set of departure schedules of line q; S t is the set of transfer stations for the transfer between the APM and buses; x pi is the departure time of the i-th bus of line p; x qj is the departure time of the j-th bus of line q; t ps is the travel time of line p from the starting point to transfer station s; t qs is the travel time of line q from the starting point to transfer station s; M is a set positive integer; W is the upper limit of the transfer waiting time; h p is the headway of line p; h q is the headway of line q; is the departure time of the n p -th bus of line p; is the departure time of the n q -th bus of line q; T is the planning time; x p1 is the departure time of the first bus of line p; x q1 is the departure time of the first bus of line q.

5. A collaborative schedule compilation method for the optimization of the transfer between intelligent rail transit and buses according to claim 1, characterized in that Based on the optimization result of the first single-objective integer programming model, introduce parameters to characterize the transfer waiting time, and construct a second single-objective integer programming model with the minimization of the total transfer waiting time as the optimization objective, specifically: s.t. c piqjs ∈{0,1} where min is the minimum value function; F2 is the second objective function; c piqjs is a 0-1 variable indicating whether the difference between the departure time of the j-th bus of line q to be transferred at transfer station s and the arrival time of the i-th bus of line p from which the transfer passengers come at transfer station s is within the time window; u piqjs is the number of passengers transferring from the i-th bus of line p to the j-th bus of line q at transfer station s; r piqjs is the transfer waiting time of the passengers of the i-th bus of line p transferring to the j-th bus of line q at the transfer station; L is the set of lines in the dual-mode public transport network; I p is the set of departure schedules of line p; J q is the set of departure schedules of line q; S t is the set of transfer stations for the transfer between the APM and buses; B is to maximize the number of successful transfer passengers; x pi is the departure time of the i-th bus of line p; x qj is the departure time of the j-th bus of line q; t ps is the travel time of line p from the starting point to transfer station s; t qs is the travel time of line q from the starting point to transfer station s; M is a set positive integer; W is the upper limit of the transfer waiting time; h p is the headway of line p; h q is the headway of line q; is the departure time of the n p -th bus of line p; is the departure time of the n q -th bus of line q; T is the planning time; x p1 is the departure time of the first bus of line p; x q1 is the departure time of the first bus of line q.

6. The collaborative schedule compilation method for the optimization of the tram-train and bus transfer according to claim 1, wherein Calculate the departure time window of each bus of each line at the transfer station according to the departure interval, departure frequency of each line and the driving time to each transfer station, including the following steps: Select any transfer station s and lines p and q that have transfers at this transfer station; According to the departure interval h of line p p and the travel time t from line p to the transfer station s ps , determine the time window {[t ps ,t ps +h p ,[t ps +h p ,t ps +2h p ,…,[t ps +(i-1)h p ,t ps +ih p ,…,[t ps +(n p -1)h p ,t ps +n p h p} formed by the earliest arrival time and the latest departure time of each bus of line p at the transfer station s, where i is the bus number; According to the departure interval \(h\) of line \(q\) q and the travel time \(t\) of line \(q\) to the transfer station \(s\) qs , determine the time window \(\{[t qs ,t qs + h q ,[t qs + h q ,t qs + 2h q ,…,[t qs +(j - 1)h q ,t qs + jh q ,…,[t qs +(n q - 1)h q ,t qs + n q h q}\) composed of the earliest arrival time and the latest departure time for each bus of line \(p\) at the transfer station \(s\), where \(j\) is the bus sequence number.

7. A collaborative timetable compilation method for the optimization of the tram-train and bus transfer, as claimed in claim 1, wherein Calculate the optimal departure time of each bus of each line according to the optimal departure time of the first bus of each line and the departure interval and number of departures of each line, specifically: x pi = x p1 + (i - 1)h p , i ≥ 2 x qj = x q1 + (j - 1)h q , j ≥ 2 where x pi is the optimal departure time of the i-th bus on route p; x qj is the optimal departure time of the j-th bus on route q; x p1 is the optimal first departure time of route p; x q1 is the optimal first departure time of route q; h p is the headway of route p; h q is the headway of route q.

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