A method for centralized bus dispatching on multiple lines considering travel time fluctuations

Abstract

The invention discloses a method for centralized dispatching of multiple buses considering travel time fluctuations, including S1: collecting operation information, station location information, road condition information and historical driving data information of bus lines, and initializing bus operation parameters in combination with bus operation experience to select time control points; S2: based on the operation information of bus lines, according to station location information and selected time control points, with the goal of minimizing the total cost of the bus pre-dispatching system, establishing a first-stage optimization model for centralized dispatching of multiple buses; S3: establishing a second-stage optimization model for centralized dispatching of multiple buses according to the first-stage optimization model for centralized dispatching of multiple buses; S4: obtaining a dispatching plan according to the second-stage optimization model for centralized dispatching of multiple buses, so as to establish a scene fusion coordination mechanism to obtain a robust dispatching plan for centralized dispatching of multiple buses. This method takes the time cost and operation cost of the bus system as the dual goals, realizes the reduction of operation cost while ensuring service quality, fully considers the interference of travel time fluctuations on dispatching, and realizes the design of centralized dispatching of multiple buses in combination with time control points.

Description

Technical Field

[0001] The present invention belongs to the field of "Internet+" application services, and in particular to the field of conventional bus scheduling technology considering uncertainty, and specifically to a multi-line centralized scheduling method for buses considering travel time fluctuations. Background Art

[0002] With the improvement of people's quality of life, convenient transportation methods have gradually appeared in daily life. The urban public transportation system using "Internet +" application services is an important part of modern urban infrastructure. It is not only related to the daily travel of citizens, but also the key to the sustainable development of the city. It plays a vital role in alleviating urban traffic pressure and improving the travel efficiency of citizens. Among the many public transportation tools, buses have become the backbone of the urban transportation network with their wide coverage and relatively low cost. However, with the growth of urban population and the increasing complexity of transportation needs, traditional bus scheduling methods are facing more and more challenges. Existing bus scheduling technologies often have the following problems:

[0003] 1. Limitations of independent bus dispatching: Most bus dispatching systems use independent dispatching of single lines, lacking consideration for centralized dispatching of multiple lines. This leads to unbalanced resource allocation, potentially resulting in a surplus of vehicles in certain time periods or areas, while a shortage of vehicles in other time periods or areas, increasing bus operating costs.

[0004] 2. Inadequate robustness of scheduling strategies: Existing scheduling methods often adopt a conservative strategy when faced with travel time fluctuations, using the longest historical travel time to formulate plans. This not only increases the time required for buses to complete their shifts but also reduces vehicle turnover, requiring more vehicles to complete operational tasks and significantly increasing operating costs.

[0005] Therefore, how to provide a bus multi-line centralized dispatching method that can ensure service quality and reduce the total cost of the system is a problem that technicians in this field urgently need to solve. Summary of the Invention

[0006] The present invention provides a multi-line centralized dispatching method for buses taking into account travel time fluctuations, so as to overcome the above technical problems.

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

[0008] A method for centralized bus multi-line scheduling considering travel time fluctuations specifically comprises the following steps:

[0009] S1: Collect bus route operation information, station location information, road condition information, and historical bus travel data information, and initialize bus operation parameters based on bus operation experience to select time control points;

[0010] The bus route operation information includes at least the departure intervals, number of departures per bus, and names of stops per bus route; the stop location information includes at least the spatial coordinates of each stop and the distance between each stop; the road condition information includes at least the road congestion conditions at different time periods; the historical travel data includes at least the travel time between stops for each bus trip; bus operation parameters include at least vehicle fuel consumption, idle distance, and idle speed; the time control points include transfer points, passenger preferred travel points, and vacant space stops;

[0011] S2: Based on the bus route operation information, according to the station location information and the selected time control points, with the goal of minimizing the total cost of the bus pre-dispatching system, a first-stage optimization model for bus multi-line centralized scheduling is established;

[0012] S3: Solve the first-stage optimization model of bus multi-line centralized scheduling to obtain the optimal initial departure schedule and vehicle scheduling plan;

[0013] Based on the optimal initial departure schedule, vehicle dispatch plan, and historical bus travel data, a second-stage optimization model for multi-line centralized bus dispatching is established with the goal of minimizing the change cost caused by travel time fluctuations.

[0014] S4: Obtain the scheduling plan based on the second-stage optimization model of bus multi-line centralized scheduling to establish a scenario fusion and coordination mechanism, and then obtain a robust scheduling plan for bus multi-line centralized scheduling.

[0015] Furthermore, the first-stage optimization model for the multi-line centralized bus dispatch established in S2 includes a first-stage optimization objective function and a first objective function constraint;

[0016] The expression of the first stage optimization objective function is:

[0017]

[0018] Where: c1 is the cost coefficient of departure time deviation; c2 is the cost coefficient of the bus arriving earlier than the time window; c3 is the cost coefficient of the bus arriving later than the time window; c4 is the fleet size cost coefficient; c5 is the bus idle cost coefficient; m, n are the shift node numbers; S is the shift node set; i is the route number; j is the route direction number; s is the route shift number; p is the route station number; I is the route set; J is the route direction set; S i,j is the set of shifts in direction j of line i; TPi,j is the set of time control points in the j direction of line i; z i,j,s,p The time when the bus arrives in advance; tf i,j,s,p is a variable with a value of 0 or 1, indicating whether the bus arrives later than the time window; NS i,j is the number of buses in the j direction of line i; k is the bus number; K is the set of available buses; is a variable with a value of 0 or 1, indicating whether bus k runs m or n shifts in sequence; d m,n is the distance between the last stop of schedule node m and the first stop of schedule node n; v is the average empty vehicle speed; C b is the purchase cost of the bus; C d Fuel costs for buses running idle;

[0019] The first objective function constraints include the import constraint of the first and last station information of the schedule node, the departure time constraint of the first bus on the line, the departure time constraint of the subsequent schedules on the line, the estimated arrival time constraint before the departure time offset, the departure time offset constraint, the time constraint of reaching the intermediate time control point, the import constraint of the schedule node time information, the path constraint of the schedule node being visited by the bus, the time constraint of the schedule node being visited by the bus, and the empty distance constraint;

[0020] Import constraints for the first and last stop information of a shift node:

[0021]

[0022] Where: sp m is the first stop of the trip node m; ep m is the last stop of the trip node m; FP i，j，s The first stop of the j-to-s train on line i; LP i,j，s The last stop for the j-to-s train on line i; NST i*NJ+j is the cumulative number of flights; is the distance between the last station of schedule node m and the first station of schedule node n;

[0023] Departure time constraints for the first bus on the route:

[0024]

[0025] Where: t i，j，s，p is the estimated time for the bus from line i to station p before the departure time shift; tls i，j is the departure time of the previous train of the first departure in the j direction of line i during the scheduling operation period; h i，j，s The expected departure interval between the j-direction s trip on line i and its previous trip;

[0026] Departure time constraints for subsequent services on this route:

[0027]

[0028] Where: t i，j，s-1，p The estimated time for the previous bus of the j-bound s-bound bus on line i to arrive at station p before the departure time shift;

[0029] Estimated arrival time constraint before departure time offset:

[0030]

[0031] Where: t i，j，s，0 is the estimated departure time of the first stop of the j-to-s trip on line i before the departure time offset; τ i，j，s，q The estimated travel time of the j-direction s trip on line i from station q-1 to station q;

[0032] Departure time offset constraint:

[0033]

[0034] Where: pt i，j，s，p ρ is the estimated time for the bus from line i to bus number s to arrive at station p after the departure time is offset; m is the departure offset of the shift node m, and its value is in [-ρ m_max , ρ m_max ]inside; m_max is the maximum departure time offset;

[0035] Time constraints for reaching the intermediate time control point:

[0036] z i，j，s,p =max(ar i,j，s，p -pt i，j，s,p ,0) (12)

[0037]

[0038]

[0039] Where: ar i，j，s，p is the upper limit of the time window of the time control point p of the j-to-s shift of line i; de i，j，s，p is the lower bound of the time window of the time control point p on the j-to-s shift of line i; w I，j，s，p，1 , w I，j，s，p，2 It is an auxiliary variable for linearizing the bus arrival constraint, and its value is 0 or 1. M is an infinite constant.

[0040] Constraints for importing shift node time information:

[0041]

[0042] In the formula: pt_en m The completion time of the shift node m after the departure time is offset; pt_st m is the departure time of the node m after the departure time shift; NP i，j is the number of stations in the j direction of line i;

[0043] Path constraints for bus nodes to be visited:

[0044]

[0045] Where: E is the virtual departure station; F is the virtual receiving station; S∪F represents the set of schedule nodes and virtual receiving station nodes; S∪E represents the set of schedule nodes and virtual departure station nodes; Indicates whether bus k executes schedule n, l in sequence; l represents a node in the set of schedule nodes and virtual departure station nodes; Indicates whether bus k returns to the virtual departure station after completing trip m; Indicates whether bus k departs from the virtual terminal to execute trip m; Indicates whether bus k departs from the virtual departure station to the virtual arrival station;

[0046] The time constraint for a bus to visit a node is:

[0047]

[0048] Empty distance constraint:

[0049]

[0050] Where: d max is the maximum allowed dispatch distance.

[0051] Furthermore, the second-stage optimization model for the multi-line centralized bus dispatch established in S3 includes a second-stage optimization objective function and a second objective function constraint;

[0052] The expression of the second stage optimization objective function is:

[0053]

[0054]

[0055] Where: Pr u is the probability of the preset bus operation scenario u∈U; U is the set of bus operation scenarios; For resource functions; The time when the bus arrives in advance in scenario u; is a variable with a value of 0 or 1, indicating whether the bus arrives later than the time window in scenario u; C pas is the time window deviation cost of the first stage; is a variable with a value of 0 or 1, indicating whether bus k executes the m and n shifts in sequence under scenario u; is a variable with a value of 0 or 1, indicating whether bus k executes the m and n shifts in sequence under scenario u;

[0056] The second objective function constraint includes at least a travel time adjustment constraint, a bus actual arrival time constraint, and other constraints;

[0057] The travel time adjustment constraint:

[0058]

[0059] Where: A is the travel adjustment time of the j-direction s trip from the first station to the station p on line i under scenario u; i，j，a，b，c The j-upward stations a, b, and c of line i are adjacent time control points; α i，j，s，b，c is the time controllability parameter of the section between stations b and c for the j-direction s-shift of line i; is the deviation of the estimated travel time of the j-direction s trip from station d-1 to station d on line i under scenario u;

[0060] Actual bus arrival time constraints:

[0061]

[0062] Where: The estimated time for the bus from route i to route s to arrive at station p after the departure time shift in scenario u;

[0063] The other constraints are

[0064]

[0065]

[0066]

[0067] Where: A variable with a value of 0 or 1, indicating whether bus k executes the m and l shifts in sequence in scenario u; A variable with a value of 0 or 1, indicating whether bus k executes the m and l shifts in sequence in scenario u; A variable with a value of 0 or 1, indicating whether bus k returns to the virtual departure station after completing trip m in scenario u; A variable with a value of 0 or 1, indicating whether bus k returns to the virtual departure station after completing trip m in scenario u; A variable with a value of 0 or 1, indicating whether bus k departs from the virtual bus terminal to perform trip m in scenario u; A variable with a value of 0 or 1, indicating whether bus k departs from the virtual bus terminal to perform trip m in scenario u; A variable with a value of 0 or 1, indicating whether bus k departs from the virtual departure station to the virtual arrival station in scenario u; A variable with a value of 0 or 1, indicating whether bus k departs from the virtual departure station to the virtual arrival station in scenario u; It is an auxiliary variable for linearizing the bus early arrival constraint in scenario u, and its value is 0 or 1; is the completion time of shift node m after the departure time shift in scenario u; It is the departure time of shift node n after the departure time offset in scenario u.

[0068] Furthermore, the scene fusion and coordination mechanism established in S4 is as follows:

[0069] S41: Solve the second phase optimization model of bus multi-line centralized scheduling to obtain the scheduling plan to obtain the vehicle path of the scenario With the deterministic path π y The path similarity matrix of the similarity between

[0070]

[0071] Where: is the path similarity matrix; is the scenario vehicle path, specifically the vehicle scheduling plan obtained by solving the second-stage optimization model of bus multi-line centralized scheduling; π y It is a deterministic path, specifically the initial vehicle scheduling plan obtained by solving the first stage optimization model of bus multi-line centralized scheduling;

[0072] S42: Based on the path similarity matrix The scene vehicle path Assigned to the deterministic path π with the greatest similarity y ;

[0073] S43: Based on path similarity matrix According to step S42, a membership matrix is ​​constructed, and its expression is:

[0074] MDM(m,π y )=∑ u∈U Pr u ·∑ k∈KΨ(m,u,k,y) (39)

[0075] Where: MDM(m,π y ) is the membership matrix; (m, π y ) is obtained by assigning shift node m to π ymax Scenario Vehicle Path The score obtained by adding the probabilities of y The mapping function of y is the bus number;

[0076] S44: obtaining a sequence of shift nodes in a robust path according to the membership matrix, so as to obtain a robust dispatching plan for bus multi-line concentration according to the sequence of shift nodes in the robust path;

[0077] And the expression for obtaining the order of shift nodes in the robust path is

[0078]

[0079] Where PM(y,m) is the position matrix that sorts the nodes on the robust vehicle path.

[0080] Beneficial effects: The present invention provides a method for centralized multi-line bus dispatching that takes travel time fluctuations into account. Compared with the existing technology, it has the following advantages:

[0081] 1. The first phase of bus multi-line centralized dispatch optimization optimized departure times. By determining departure time offsets, this increased space for cross-line bus operations, effectively utilized resources, reduced fleet size, and lowered vehicle costs, forming a new optimization mechanism for multi-line centralized bus dispatch.

[0082] 2. In the second stage, the impact of travel time uncertainty on the original scheduling plan is considered. On the premise of completing all shift tasks, time control points are introduced to control the bus travel time, forming a robust timetable and vehicle scheduling plan, namely the vehicle robust scheduling plan, and establishing a new scheduling method that can improve the punctuality rate of buses and ensure service quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0084] Figure 1This is a flow chart of the multi-line centralized scheduling method for buses taking into account travel time fluctuations of the present invention. DETAILED DESCRIPTION

[0085] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0086] This embodiment provides a bus multi-line centralized scheduling method considering travel time fluctuations. Figure 1 As shown, the specific steps include:

[0087] S1: Collect bus route operation information, station location information, road condition information, and historical bus travel data information, and initialize bus operation parameters based on bus operation experience to select time control points;

[0088] The bus route operation information includes at least the departure intervals, number of departures per bus, and names of stops per bus route; the stop location information includes at least the spatial coordinates of each stop and the distance between each stop; the road condition information includes at least the road congestion conditions at different time periods; the historical driving data includes at least the travel time between stops for each bus trip; bus operation parameters include at least vehicle fuel consumption, idle distance, and idle speed; the time control points include transfer points, passenger preferred travel points, and vacant space stops (such as bus bay stops);

[0089] S2: Based on the operation information of bus routes, according to the location information of bus stops and the selected time control points, the first stage optimization model (MP) of bus multi-line centralized scheduling is established with the goal of minimizing the total cost of the bus pre-scheduling system;

[0090] Specifically, the established first-stage optimization model for multi-line centralized bus dispatching includes a first-stage optimization objective function and a first objective function constraint;

[0091] The expression of the first stage optimization objective function is:

[0092]

[0093] Where: c1 is the departure time deviation cost coefficient; c2 is the cost coefficient of the bus arriving earlier than the time window; c3 is the cost coefficient of the bus arriving later than the time window; c4 is the fleet size cost coefficient; c5 is the bus idle cost coefficient; m, n are the shift node numbers; S is the shift node set; i is the route number; j is the route direction number; s is the route shift number; p is the route station number; I is the route set; J is the route direction set; S i，j is the set of shifts in direction j of line i; TP i，j is the set of time control points in the j direction of line i; z i，j，s，p The time when the bus arrives in advance; tf i，j，s，p is a variable with a value of 0 or 1, indicating whether the bus arrives later than the time window; NS i，j is the number of buses in the j direction of line i; k is the bus number; K is the set of available buses; is a variable with a value of 0 or 1, indicating whether bus k runs m or n shifts in sequence; d m，n is the distance between the last stop of schedule node m and the first stop of schedule node n; v is the average empty vehicle speed; C b is the purchase cost of the bus; C d Fuel costs for buses running idle;

[0094] The first stage optimization objective function includes five items. The first item is the departure time offset cost, i.e. c1∑ m∈S jρ m The second and third items together constitute the deviation time cost of the time window, that is, The fourth is the bus fleet size cost, i.e. The fifth item is the cost of the bus running idle, that is

[0095] The first objective function constraints include the import constraint of the first and last station information of the schedule node, the departure time constraint of the first bus on the line, the departure time constraint of the subsequent schedules on the line, the estimated arrival time constraint before the departure time offset, the departure time offset constraint, the time constraint of reaching the intermediate time control point, the import constraint of the schedule node time information, the path constraint of the schedule node being visited by the bus, the time constraint of the schedule node being visited by the bus, and the empty distance constraint;

[0096] Import constraints for the first and last stop information of a shift node:

[0097]

[0098] Where: sp m is the first stop of the trip node m; ep m is the last stop of the trip node m; FP i，j，s The first stop of the j-to-s train on line i; LPi,j，s The last stop for the J-to-S train on Line I; NST i*NJ+j is the cumulative number of flights; is the distance between the last station of schedule node m and the first station of schedule node n;

[0099] Departure time constraints for the first bus on the route:

[0100]

[0101] Where: t i，j，s，p is the estimated time for the bus from line i to station p before the departure time shift; tls i，j is the departure time of the previous train of the first departure in the j direction of line i during the scheduling operation period; h i，j，s The expected departure interval between the j-direction s trip on line i and its previous trip;

[0102] Departure time constraints for subsequent services on this route:

[0103]

[0104] Where: t i，j，s-1，p The estimated time for the previous bus of the j-bound s-bound bus on line i to arrive at station p before the departure time shift;

[0105] Estimated arrival time constraint before departure time offset:

[0106]

[0107] Where: t i，j，s，0 is the estimated departure time of the first stop of the j-to-s trip on line i before the departure time offset; τ i，j，s，q The estimated travel time of the j-direction s trip on line I from station q-1 to station q;

[0108] Departure time offset constraint:

[0109]

[0110] Where: pt i，j，s，p ρ is the estimated time for the bus from line i to bus number s to arrive at station p after the departure time is offset; m is the departure offset of the shift node m, and its value is in [-ρ m_max , ρ m_max ]inside; m_max is the maximum departure time offset; constraint (8) ensures the estimated arrival time of the bus after the departure time offset, constraint (9) is the absolute value of the departure time deviation, and constraints (10)-(11) are the linear expressions of formula (9);

[0111] Time constraints for reaching the intermediate time control point:

[0112] z i，j，s,p =max(ar i，j，s，p -pt i，j，s,p ,0)(12)

[0113]

[0114] Where: ar i，j，s，p is the upper limit of the time window of the time control point p of the j-to-s shift of line i; de i，j，s，p is the lower bound of the time window of the time control point p on the j-to-s shift of line i; w i,j，s，p,1 , w i,j，s，p，2 is the auxiliary variable for linearizing the bus's early arrival constraint, with a value of 0 or 1, and M is an infinite constant; the early arrival time of the bus can be obtained by constraint (12), constraints (13)-(16) are the linearized expressions of constraint (12), and constraints (17)-(18) are used to determine whether the bus arrives later than the time window;

[0115] Constraints for importing shift node time information:

[0116]

[0117] In the formula: pt_en m The completion time of the shift node m after the departure time is offset; pt_st m is the departure time of the node m after the departure time shift; NP i，j is the number of stations in the j direction of line i;

[0118] Path constraints for bus nodes to be visited:

[0119]

[0120] Where: E is the virtual departure station; F is the virtual receiving station; S∪F represents the set of schedule nodes and virtual receiving station nodes; S∪E represents the set of schedule nodes and virtual departure station nodes; Indicates whether bus k executes schedule n, l in sequence; l represents a node in the set of schedule nodes and virtual departure station nodes; Indicates whether bus k returns to the virtual departure station after completing trip m; Indicates whether bus k departs from the virtual terminal to execute trip m; Indicates whether bus k departs from the virtual departure station and goes to the virtual terminal station; constraints (21)-(22) ensure that all schedule nodes are visited once, constraint (23) ensures that the schedule node flow is conserved, constraint (24) ensures that no loop is formed, constraint (25) ensures that the vehicle will not return to the virtual departure station after completing the schedule, constraint (26) ensures that the vehicle will not depart from the virtual terminal station, and constraint (27) ensures that the vehicle will not go directly from the virtual departure station to the virtual terminal station;

[0121] The time constraint for a bus to visit a node is:

[0122]

[0123] Constraint (28) ensures that when schedule nodes m and n are visited sequentially by bus k, the departure time of node n is not less than the sum of the completion time of schedule node m and the idle time between stations;

[0124] Empty distance constraint:

[0125]

[0126] Where: d max is the maximum allowed dispatch distance; constraint (29) ensures that when bus k visits schedule nodes m and n in sequence, the idle distance between stations is not greater than the maximum idle distance;

[0127] In this embodiment, the model (MP) is decomposed into the initial timetable optimization model MP1 and the initial vehicle cross-line scheduling model MP2. The objective function of MP1 is the first three terms of formula (1), and the constraints are (8)-(18). The objective function of MP2 is the last two terms of formula (1), and the constraints are (19)-(29). MP1 and MP2 are solved separately, and the departure time offset constraint pt is used. i，j，s，p Connect the initial timetable optimization model MP1 and the initial vehicle cross-line scheduling model MP2. m Get the optimal value. m Under the given value, MP_Obj1 is the optimal value of MP1, and MP_Obj2 is the optimal value of MP2. For MP1, since ρ m In the model, it is equivalent to a known variable, and its current optimal value MP_Obj1 can be calculated by formulas (5)-(18); for MP2, in a single scenario, is a known variable, and its current optimal value MP_Obj2 can be calculated by formulas (2)-(4) and (19)-(29). The current ρ is obtained by summing MP_Obj1 and MP_Obj2. m The solution of MP_Obj is MP_Obj. By comparing with the optimal value of the current first stage model, if MPObj <MP_Obj_Best, then update the current optimal value MP_Obj_Best = MP Obj , by iteratively updating the current optimal value MP_Obj_Best, the optimal solution of MP is obtained; when the stop search condition is met (the set number of iterations is reached or the difference is small enough), the search for ρ is stopped. m The search is completed to solve the first stage model and obtain the optimal initial departure schedule and initial vehicle scheduling plan;

[0128] S3: Solve the first-stage optimization model of bus multi-line centralized scheduling to obtain the optimal initial departure schedule and vehicle scheduling plan;

[0129] And according to the optimal initial departure schedule (specifically according to the core parameters of the optimal initial departure schedule: time window deviation cost ), vehicle dispatch plan (specifically based on the core parameters of the vehicle dispatch plan: the decision variables in the path constraints (21)-(27) of the bus nodes visited by the bus) ) and historical bus travel data information, with the goal of minimizing the change cost caused by travel time fluctuations, a second-stage optimization model (SP) for bus multi-line centralized scheduling is established;

[0130] Specifically, the established second-stage optimization model for multi-line centralized bus dispatching includes a second-stage optimization objective function and a second objective function constraint;

[0131] The expression of the second stage optimization objective function is:

[0132]

[0133]

[0134] Where: Pr u is the probability of the preset bus operation scenario u∈U; U is the set of bus operation scenarios; For resource functions; The time when the bus arrives in advance in scenario u; is a variable with a value of 0 or 1, indicating whether the bus arrives later than the time window in scenario u; C pas is the time window deviation cost of the first stage; is a variable with a value of 0 or 1, indicating whether bus k executes the m and n shifts in sequence under scenario u. If bus k is not assigned to bus k in the first stage optimization model, it takes 1 if it executes the shifts, and 0 otherwise. is a variable with a value of 0 or 1, indicating whether bus k executes the m and n shifts in sequence under scenario u, where it is assigned to bus k in the first stage optimization model. If it does not execute, it takes 1, otherwise it takes 0;

[0135] The second objective function constraint includes at least a travel time adjustment constraint, a bus actual arrival time constraint, and other constraints;

[0136] The travel time adjustment constraint:

[0137]

[0138] Where: A is the travel adjustment time of the j-direction s trip from the first station to the station p on line i under scenario u; I，j，a，b，c The a, b, and c stations on the j-up side of line i are adjacent time control points, i.e., A i，j，a，b，c =1;α i，j，s，b，c is the controllability parameter of the section time between stations b and c of the j-direction s-shift on line i, which is affected by factors such as road traffic conditions and the driver's working status; is the deviation from the expected travel time of the j-direction s trip of line i from station d-1 to station d under scenario u; in the process of scenario modeling, constraints (32)-(33) express the adjusted travel time in the subsequent trip;

[0139] Actual bus arrival time constraints:

[0140]

[0141] Where: is the estimated time for the bus from route i to route s to arrive at station p after the departure time shift in scenario u; constraint (34) expresses the actual arrival time of the bus affected by travel time fluctuation after the departure time shift;

[0142] The other constraints are

[0143]

[0144] Where: A variable with a value of 0 or 1, indicating whether bus k executes shifts m and l in sequence under scenario u. If bus k is not assigned to it in the first stage optimization model, it takes 1 if it executes shifts, and 0 otherwise. A variable with a value of 0 or 1, indicating whether bus k executes the m and l shifts in sequence under scenario u, where it is assigned to bus k in the first stage optimization model. If it does not execute, it takes 1, otherwise it takes 0; A variable with a value of 0 or 1, indicating whether bus k returns to the virtual departure station after completing trip m in scenario u. If bus k is not assigned to bus k in the first-stage optimization model, it takes 1 if it completes trip m and 0 otherwise. A variable with a value of 0 or 1, indicating whether bus k returns to the virtual departure station after completing trip m in scenario u, where it is assigned to bus k in the first stage optimization model. If it does not execute, it takes 1, otherwise it takes 0; A variable with a value of 0 or 1, indicating whether bus k departs from the virtual bus terminal to execute trip m in scenario u. If bus k is not assigned to the virtual bus terminal in the first stage optimization model, it takes 1 if it executes trip m, otherwise it takes 0; A variable with a value of 0 or 1, indicating whether bus k departs from the virtual bus terminal to execute trip m in scenario u, where it is assigned to bus k in the first stage. If it does not execute, it takes 1, otherwise it takes 0; A variable with a value of 0 or 1, indicating whether bus k departs from the virtual departure station to the virtual arrival station in scenario u. If bus k is not assigned to the virtual departure station in the first stage optimization model, it takes 1 if it is assigned to the virtual departure station, otherwise it takes 0; A variable with a value of 0 or 1, indicating whether bus k departs from the virtual departure station to the virtual arrival station in scenario u, where it is assigned to bus k in the first stage optimization model. If it is not executed, it takes 1, otherwise it takes 0; It is an auxiliary variable for linearizing the bus early arrival constraint in scenario u, and its value is 0 or 1; is the completion time of shift node m after the departure time shift in scenario u; is the departure time of shift node n after the departure time shift in scenario u;

[0145] In this embodiment, the second-stage problem model is decomposed into several sub-problems based on different travel time scenarios. Among them, a single sub-problem is defined as SP, the objective function of SP is formula (31), and the constraints are (32)-(37). SP is decomposed into SP1 and SP2, and SP1 is the actual schedule model affected by time fluctuations. Its objective function is the first three terms of formula (31), that is, And the constraints satisfied are Equation (32)-Equation (35); SP2 is a bus scheduling model, and its objective function is the last two terms of Equation (31), that is, And the constraints satisfied are equations (36) and (37);

[0146] S4: Obtain a scheduling plan based on the second-stage optimization model of bus multi-line centralized scheduling to establish a scenario fusion and coordination mechanism, and then obtain a robust scheduling plan for bus multi-line centralized scheduling;

[0147] The established scene fusion and coordination mechanism is specifically as follows:

[0148] S41: Path similarity matrix: Solve the second phase optimization model of bus multi-line centralized scheduling to obtain the scheduling plan to obtain the vehicle path of the scenario With the deterministic path π y The path similarity matrix of the similarity between

[0149]

[0150] Where: is the path similarity matrix; is the scenario vehicle path, specifically the vehicle scheduling plan obtained by solving the second-stage optimization model of bus multi-line centralized scheduling; π y is a deterministic path, specifically the initial vehicle scheduling plan obtained by solving the first phase optimization model of bus multi-line centralized scheduling; for each scenario u∈U, a similarity matrix SM is defined to represent the scenario vehicle path With the deterministic path π y The similarity between them is calculated using formula (38);

[0151] S42: Assign scenario vehicle paths: Based on the path similarity matrix The scene vehicle path Assigned to the deterministic path π with the greatest similarity y ;

[0152] S43: Membership Matrix: Based on Path Similarity Matrix According to step S42, a membership matrix is ​​constructed, and its expression is:

[0153]

[0154] Where: MDM(m,π y ) is the membership matrix; (m, π y ) is obtained by assigning shift node m to π y Scenario Vehicle Path The score obtained by adding the probabilities of y The mapping function of y is the bus number; by using formula (39) to calculate the membership matrix, the items in the matrix (m, π y ) is a score obtained by assigning shift node m to π y Scenario Vehicle Path The probability of adding is calculated; if and Assigned to πy , the mapping function Ψ(m, u, k, y) is 1; according to the similarity matrix and the membership matrix, each shift node m is assigned to the robust path;

[0155] S44: Determine the order of the shift nodes in the robust path: obtain the order of the shift nodes in the robust path according to the membership matrix, so as to obtain a robust scheduling plan for the bus multi-line concentration according to the order of the shift nodes in the robust path;

[0156] And the expression for obtaining the order of shift nodes in the robust path is

[0157]

[0158] Where: PM(y, m) is the position matrix for sorting the nodes on the robust vehicle path. The position matrix PM is calculated using formula (40), and PM(y, m) is sorted by size to complete the sorting of the nodes on the robust vehicle path. Indicates the shift node m in the scene vehicle path Position in

[0159] The goal of the scene fusion coordination mechanism in this embodiment is to obtain the access order of nodes in the path, that is, to merge the bus paths in different scenarios into one path through the path similarity matrix. For example, the deterministic paths are π1, π2 (π1 is bus 1: node 1, node 3, node 2, node 5; π2 is bus 2: node 7, node 8, node 4, node 6), and the scene path is ( That is, bus 1 is in scene 1: node 1, node 2, node 5; That is, bus 1 is in scene 2: node 1, node 2, node 4; That is, bus 1 is in scene 3: node 1, node 3, node 2), ( That is, bus 2 is in scene 1: node 7, node 3, node 8, node 4, node 6; That is, bus 2 is in scene 2: node 7, node 3, node 8, node 5, node 6; That is, bus 2 is in scene 3: node 7, node 8, node 4, node 5, node 6);

[0160] By calculating the similarity matrix (for example: and π1 pass through nodes 1, 2, and 5, so the corresponding matrix positions The value of is 3, No similarity with π2 is 0, 3>0, so is assigned to π1, which means is assigned to the deterministic path with the greatest similarity, i.e., π1);

[0161] By the same token is assigned to π1, is assigned to π2, so now π1 corresponds to 3 scene paths ( 1, 2, 5, 1, 2, 4, 1, 3, 2), and π2 in the same way ( 7, 3, 8, 4, 6, 7, 3, 8, 5, 6, 7, 8, 4, 5, 6). So MDM(1, π1) = 1 / 3*1+1 / 3*1+1 / 3*1=1 (1 / 3 is the probability of the scene, 1 is because node 1 is in Zhongqie Assigned to π1, that is, Ψ(1, 1, 1, 1) = 1), MDM(1, π2) = 1 / 3*0+1 / 3*0+1 / 3*0 = 0, MDM(3, π1) = 1 / 3, MDM(3, π2) = 2 / 3, MDM(6, π1) = 0, MDM(6, π2) = 1, and then according to the membership matrix, we can get the robust path 1: node 1, node 2 (MDM(1, π1) > MDM(1, π2), so node 1 is given to robust path 1), robust path 2: node 3, node 4, node 5, node 6, node 7, node 8 (one path corresponds to one bus), and finally according to PM(y, m), determine the order of visiting the shift nodes in the path.

[0162] In this embodiment, the MP1 model described in S2 and the SP1 model described in S3, i.e., the timetable model, can both be calculated to obtain the results; specifically, the departure intervals, number of departures per shift, and information on the stations passed by each line are input into the timetable model. For MP1, by adjusting the departure offset variable ρ within the limited range of the maximum departure offset, the departure offset variable ρ is calculated. m The objective function value can be calculated by performing a large-scale search based on the values ​​of . For SP1, in scenario u, the travel time offset is a known variable. By inputting the controllable time parameters of the road section and the location information of the time control points, the variable cost caused by travel time fluctuations can be calculated. Specifically, the final model solution results in a timetable that includes the estimated arrival time and departure time of each trip at all time control stations.

[0163] The vehicle scheduling model involved in the multi-line centralized scheduling method for buses considering travel time fluctuations disclosed in this embodiment is solved using a branch-cutting pricing algorithm, as follows:

[0164] Based on the solution of the timetable model in the first and second stage optimization models of bus multi-line centralized scheduling, combined with the bus stop location and historical travel data, the results are input into the vehicle scheduling model in the first and second stage optimization models of bus multi-line centralized scheduling;

[0165] 1) Using the DW decomposition algorithm, the original problem (MP2 / SP2) is split into a master problem and subproblems. The decision variables in the master problem are relaxed to continuous variables in the range [0, 1]. The relaxed master problem is then solved to obtain an initial solution, and a constrained master problem is constructed. The master problem consists of a series of bus schedule chains. Partial schedule chains must be selected while satisfying constraints. Each schedule chain is assigned to a bus, ultimately forming a vehicle scheduling plan. The subproblem is finding a feasible schedule chain.

[0166] 2) Solve the restricted master problem to obtain the value of the dual variable, and give this value to the subproblem that adds the valid inequality;

[0167] 3) Decide whether to add columns to the restricted main problem based on the solutions to the subproblems until no more columns are needed;

[0168] 4) Based on the value of the decision variable, decide whether to branch or solve other nodes until there are no nodes in the queue and the solution ends to obtain the vehicle scheduling plan.

[0169] In this embodiment, all bus routes depart from the same station, and the time control points are selected as the first and last stations of each bus trip and busy transfer stations. Only the estimated arrival time of the time control points excluding the first and last stations is given in the form of a time window; the final bus scheduling plan path only includes the first and last stations of the executed bus trip.

[0170] The method provided in this embodiment can effectively handle NP-hard problems. While fine-tuning departure times and ensuring on-time bus arrival times, it takes minimizing the total system cost as the design goal, considers the impact of key factors such as the maximum allowable dispatching distance and idle speed on scheduling, and adjusts the multi-line centralized bus scheduling plan and timetable based on historical travel time data to adapt to the complex and changing travel environment, completing the design of a multi-line centralized bus scheduling method that takes travel time fluctuations into account.

[0171] In summary, the multi-line centralized bus dispatching method considering travel time fluctuations provided by the present invention has the following advantages over the prior art:

[0172] 1. The first phase of bus multi-line centralized dispatch optimization optimized departure times. By determining departure time offsets, this increased space for cross-line bus operations, effectively utilized resources, reduced fleet size, and lowered vehicle costs, forming a new optimization mechanism for multi-line centralized bus dispatch.

[0173] 2. In the second stage, the impact of travel time uncertainty on the original scheduling plan was considered. On the premise of completing all shift tasks, time control points were introduced to control the bus travel time, forming a robust timetable and vehicle scheduling plan, and establishing a new scheduling method that can improve bus punctuality and ensure service quality.

[0174] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for centralized dispatching of buses on multiple lines taking into account travel time fluctuations, characterized in that: The specific steps include: S1: Collect the operation information, station location information, road condition information and historical driving data of the bus routes, and initialize the bus operation parameters based on the bus operation experience to select the time control point; The operation information of the bus routes at least includes the departure intervals, the number of departures per bus and the names of the stations passed by each bus route; the station location information at least includes the spatial coordinates of each station and the distance between each station; the road condition information at least includes the congestion of roads at different time periods; the historical driving data information at least includes the driving time between each bus station; the bus operation parameters at least include the vehicle fuel consumption, idle driving distance and idle driving speed; the time control points include transfer points, passenger preferred travel points and free space stations; S2: Based on the operation information of bus routes, according to the station location information and the selected time control points, the first stage optimization model of bus multi-line centralized scheduling is established with the goal of minimizing the total cost of the bus pre-scheduling system; S3: Solve the first phase optimization model of bus multi-line centralized scheduling to obtain the optimal initial departure schedule and vehicle scheduling plan; Based on the optimal initial departure schedule, vehicle dispatch plan and historical bus travel data, the second-stage optimization model of multi-line centralized dispatching of buses is established with the goal of minimizing the change cost caused by travel time fluctuations. S4: Obtain the scheduling plan based on the second-stage optimization model of multi-line centralized bus scheduling to establish a scenario fusion and coordination mechanism, and then obtain a robust scheduling plan for multi-line centralized buses.

2. A method for centralized bus multi-line dispatching considering travel time fluctuations according to claim 1, characterized in that: The first stage optimization model of the bus multi-line centralized dispatch established in S2 includes a first stage optimization objective function and a first objective function constraint; The expression of the first stage optimization objective function is: Where: c1 is the departure time deviation cost coefficient; c2 is the cost coefficient for the bus arriving earlier than the time window; c3 is the cost coefficient for the bus arriving later than the time window; c4 is the fleet size cost coefficient; c5 is the bus idle cost coefficient; m, n are the shift node numbers; S is the shift node set; i is the route number; j is the route direction number; s is the route shift number; p is the route station number; I is the route set; J is the route direction set; S i,j is the set of shifts in the j direction of line i; TP i,j is the set of time control points in the j direction of line i; z i,j,s,p Allow time for buses to arrive in advance; tf i,j,s,p is a variable with a value of 0 or 1, indicating whether the bus arrives later than the time window; NS i,j is the number of buses in the j direction of line i; k is the bus number; K is the set of available buses; is a variable with a value of 0 or 1, indicating whether bus k runs m or n shifts in sequence; d m,n is the distance between the last stop of schedule node m and the first stop of schedule node n; v is the average empty vehicle speed; C b The cost of purchasing buses; C d Fuel costs for buses running idle; The first objective function constraint includes the import constraint of the first and last station information of the schedule node, the departure time constraint of the first bus of the line, the departure time constraint of the subsequent buses of the line, the estimated arrival time constraint before the departure time offset, the departure time offset constraint, the time constraint of reaching the intermediate time control point, the import constraint of the schedule node time information, the path constraint of the schedule node being visited by the bus, the time constraint of the schedule node being visited by the bus, and the empty driving distance constraint; Import constraints of the first and last stop information of the shift node: Where: sp m is the first stop of the trip node m; ep m is the last stop of the shift node m; FP i,j,s The first stop of the j-bound s-bound train on line i; LP i,j,s The last stop of the j-to-s train on line i; NST i*NJ+j is the cumulative number of flights; is the distance between the last station of schedule node m and the first station of schedule node n; Departure time constraints for the first bus on the route: Where: t i,j,s,p The estimated time for the bus of route i to arrive at station p before the departure time shifts; tls i,j h is the departure time of the previous train of the first departure of line i in the j direction during the scheduling operation period; i,j,s is the estimated departure interval between the j-direction s train of line i and its previous train; Departure time constraints for subsequent services on the route: Where: t i,j,s-1,p The estimated time for the previous bus of the j-bound s-bound bus on line i to arrive at station p before the departure time shift; Estimated arrival time constraint before departure time offset: Where: t i,j,s,0 is the estimated departure time of the first stop of the j-to-s trip on line i before the departure time shift; τ i,j,s,q is the estimated travel time of the j-direction s-trip on line i from station q-1 to station q; Departure time offset constraint: Where: pt i,j,s,p is the estimated time for the bus of route i to arrive at station p after the departure time is offset; m is the departure offset of the shift node m, and its value is in [-ρ m_max ,ρ m_max ]Inside; m_max is the maximum departure time offset; Time constraints for reaching intermediate time control points: Where: ar i,j,s,p is the upper limit of the time window of the time control point p of the j-to-s shift of the i-line; i,j,s,p is the lower limit of the time window of the time control point p of the j-to-s shift of line i; w i,j,s,p,1 ,w i,j,s,p,2 It is an auxiliary variable for linearizing the bus early arrival constraint, with a value of 0 or 1, and M is an infinite constant; Constraints for importing shift node time information: In the formula: pt_en m is the completion time of the shift node m after the departure time is offset; pt_st m is the departure time of the node m after the departure time shift; NP i,j is the number of stations in the j direction of line i; The path constraints for the bus nodes to be visited are: Where: E is the virtual departure station; F is the virtual receiving station; S∪F represents the set of schedule nodes and virtual receiving station nodes; S∪E represents the set of schedule nodes and virtual departure station nodes; Indicates whether bus k executes the schedule n, l in sequence; l represents a node in the set of schedule nodes and virtual departure station nodes; Indicates whether bus k returns to the virtual departure station after completing trip m; Indicates whether bus k departs from the virtual terminal to execute trip m; Indicates whether bus k departs from the virtual departure station to the virtual arrival station; The time constraint for a bus to visit a node is: Empty distance constraint: Where: d max is the maximum allowed dispatch distance.

3. A method for centralized bus multi-line dispatching considering travel time fluctuations according to claim 2, characterized in that: The second-stage optimization model of the bus multi-line centralized dispatch established in S3 includes a second-stage optimization objective function and a second objective function constraint; The expression of the second stage optimization objective function is: Where: Pr u is the probability of the preset bus operation scenario u∈U; U is the set of bus operation scenarios; is the resource function; is the time when the bus arrives in advance in scenario u; is a variable with a value of 0 or 1, indicating whether the bus arrives later than the time window in scenario u; C pas is the time window deviation cost of the first stage; is a variable with a value of 0 or 1, indicating whether bus k executes m and n shifts in sequence in scenario u; is a variable with a value of 0 or 1, indicating whether bus k executes m and n shifts in sequence in scenario u; The second objective function constraint includes at least a travel time adjustment constraint, a bus actual arrival time constraint, and other constraints; The travel time adjustment constraint: Where: is the travel adjustment time of the j-direction s-trip of line i from the first stop to the stop p under scenario u; i,j,a,b,c The a, b, and c stations on the j-upward direction of line i are adjacent time control points; α i,j,s,b,c is the time controllability parameter of the section between stations b and c of the j-direction s-shift of line i; is the deviation of the estimated travel time of the j-direction s-trip from station d-1 to station d on line i under scenario u; The actual bus arrival time constraints: Where: is the estimated time for the bus of route i to arrive at station p after the departure time shift in scenario u; The other constraints are Where: A variable with a value of 0 or 1, indicating whether bus k executes the m and l shifts in sequence in scenario u; A variable with a value of 0 or 1, indicating whether bus k executes the m and l shifts in sequence in scenario u; A variable with a value of 0 or 1, indicating whether bus k returns to the virtual departure station after completing trip m in scenario u; A variable with a value of 0 or 1, indicating whether bus k returns to the virtual departure station after completing trip m in scenario u; A variable with a value of 0 or 1, indicating whether bus k departs from the virtual terminal to perform trip m in scenario u; A variable with a value of 0 or 1, indicating whether bus k departs from the virtual terminal to perform trip m in scenario u; A variable with a value of 0 or 1, indicating whether bus k departs from the virtual departure station to the virtual arrival station in scenario u; A variable with a value of 0 or 1, indicating whether bus k departs from the virtual departure station to the virtual arrival station in scenario u; It is an auxiliary variable for linearizing the bus early arrival constraint in scenario u, and its value is 0 or 1; is the completion time of shift node m after the departure time shift in scenario u; It is the departure time of shift node n after the departure time shift in scenario u.

4. A method for centralized bus multi-line dispatching considering travel time fluctuations according to claim 2, characterized in that: The scene fusion coordination mechanism established in S4 is as follows: S41: Solve the second phase optimization model of bus multi-line centralized scheduling to obtain the scheduling plan to obtain the vehicle path of the scenario With the deterministic path π y The path similarity matrix of the similarity between Where: is the path similarity matrix; is the scenario vehicle path, specifically the vehicle scheduling plan obtained by solving the second-stage optimization model of bus multi-line centralized scheduling; π y It is a deterministic path, specifically, the initial vehicle dispatch plan obtained by solving the first stage optimization model of bus multi-line centralized dispatch; S42: Based on the path similarity matrix The scene vehicle path Assign to the deterministic path π with the greatest similarity y ; S43: Based on the path similarity matrix According to step S42, a membership matrix is ​​constructed, and its expression is: MDM(m,π y )=∑ u∈U Pr u ·∑ k∈K Ψ(m,u,k,y) (39) Where: MDM(m,π y ) is the membership matrix; (m,π y ) is to assign shift node m to π y Scenario Vehicle Path The score obtained by adding the probabilities of y The mapping function of y is the bus number; S44: obtaining the order of the shift nodes in the robust path according to the membership matrix, so as to obtain a robust dispatching plan for the bus multi-line concentration according to the order of the shift nodes in the robust path; And the expression for obtaining the order of shift nodes in the robust path is: Where: Indicates the shift node m in the scene vehicle path PM(y,m) is the position matrix for sorting the nodes on the robust vehicle path.

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