A demand response bus look-ahead scheduling method

Abstract

The application discloses a demand response bus forward scheduling method. The method comprises the following steps: based on a rolling horizon framework, a Markov decision process model is established; based on quantile regression, an LSTM model and a Copula function, future demand is predicted; the future demand is incorporated into a general scheduling model, a forward scheduling model based on prediction is established, and an error correction mechanism is designed for forward scheduling and order cancellation respectively; a pruning strategy of decision is designed, and the solution space is compressed to reduce the calculation time; and an approximate dynamic programming algorithm is used to solve the scheduling scheme. The application can not only reduce the operator cost, but also significantly improve the service quality, so that the fine organization and management of demand response bus scheduling are achieved. Meanwhile, the algorithm has good solving characteristics and has strong practical application prospect.

Description

Technical Field

[0001] This invention relates to the research field of demand-response bus dynamic scheduling technology, and in particular to a demand-response bus forward scheduling method. Background Technology

[0002] Demand-responsive public transport (DRT) can dynamically change routes and timetables, providing passengers with more flexible and precise travel services, and has enormous development potential in future public transport systems. Fixed-route public transport systems, with their stable timetables and routes, are often more cost-effective. However, DRT faces significant development obstacles, including high operating costs and service levels limited by factors such as fleet size and personalized passenger needs. On the one hand, operating costs depend on the number of orders responded to and vehicle dispatching schemes, but controlling operating costs can lead to vehicles arriving early or late, and reduce response rates, thus deteriorating service levels. On the other hand, future passenger demand is uncertain for planning purposes; current dispatching schemes may not be suitable for future demand, meaning future demand has potential negative impacts. With the development of personalized travel, operators increasingly need to refine the organization and management of DRT dispatching to achieve cost reduction and efficiency improvement.

[0003] In demand-response bus scheduling, operators divide operating hours into several cycles. Within each cycle, they create a scheduling plan for all passenger travel orders imported into the system, including vehicle routes, departure times, waiting times, and passenger-vehicle allocation. Vehicles depart from different depots, serve passengers according to the routes and schedules provided in the scheduling plan, and ultimately return to the depot.

[0004] In traditional demand-response bus scheduling, operators typically handle both static (advance-booked) and dynamic (real-time submitted) orders, creating scheduling plans and timetables in real time. However, in proactive demand-response bus scheduling, it's crucial not only to process current demand in real time but also to consider the impact of future demand on current scheduling decisions. Furthermore, the system may reject orders due to insufficient capacity, and passengers may cancel orders temporarily due to dissatisfaction with prices, vehicle arrival times, or routes. While deep learning models can be used to predict future demand, these models may contain errors that can significantly impact scheduling plans. Moreover, the sparse and uneven passenger flow encountered by demand-response buses introduces numerous missing values ​​and abnormal spikes in predictions, further exacerbating errors. Therefore, proactive demand-response bus scheduling models must not only create scheduling plans in real time but also consider the impact of future demand to achieve forward-looking scheduling.

[0005] Current research on demand response bus scheduling has the following defects and deficiencies: (1) In actual scenarios, demand response buses should include the process of collecting and processing static and dynamic demands, dynamically inserting orders and optimizing routes, and rejecting demands that exceed capacity. Optimizing routes includes changing existing routes and dispatching new vehicles. Dispatching new vehicles requires planning depot selection, vehicle routes, departure times, and waiting times. Current research lacks one or more of these scenarios. (2) Planning models are mostly expressed in static or pseudo-dynamic forms. The former simply defines passenger demand as reservation-based, that is, the optimal route can be obtained by solving the static demand in a single global solution, which is essentially a category of customized buses. The latter uses simple methods (such as penalty functions or OD matching) to insert real-time dynamic demands into the route based on the initial route in order to approximate dynamic optimization. However, the above methods only try to respond to dynamic demands, but it is difficult to guarantee that the route after inserting new demands can reach the optimal again, that is, it does not achieve dynamic optimization in a strict sense. (3) In terms of solution algorithms, heuristic algorithms are mainly used, and a small number of exact algorithms are used. The demand response bus dynamic optimization problem requires algorithms that can solve the response quickly and optimize with high quality. Precise algorithms are impractical because they violate the concept of fast response, while heuristic algorithms cannot guarantee the quality of the solution. Therefore, there is a lack of fast and high-quality solution algorithms. Summary of the Invention

[0006] The main objective of this invention is to overcome the shortcomings and deficiencies of the prior art and provide a forward-looking scheduling method based on a rolling time-domain planning framework that considers predicted demand. By accurately predicting future demand, this invention solves the problem that in the demand response public transport forward-looking scheduling model, it is necessary not only to formulate a scheduling plan in real time, but also to take into account the impact of future demand to form forward-looking scheduling.

[0007] The objective of this invention is achieved by at least one of the following technical solutions.

[0008] A demand-response public transport forward scheduling method includes the following steps:

[0009] S1. Based on the rolling time-domain framework, establish a Markov decision process model;

[0010] S2. Predicting future demand based on quantile regression, LSTM model and Copula function;

[0011] S3. Incorporate future demand into the general scheduling model, establish a forecast-based forward scheduling model, and design error correction mechanisms for forward scheduling and order cancellation respectively;

[0012] S4. Pruning strategies for design decisions: Compressing the solution space to reduce computation time;

[0013] S5. Solve the scheduling scheme using an approximate dynamic programming algorithm.

[0014] Further, in step S1, within the rolling time-domain framework, a delayed batch matching method is used to allocate orders for one cycle to the fleet. The principle is to divide the operating time range into a set of cycles P = {p | p = 1, 2, ..., |P|} with a duration of T. Then, ride orders for any cycle are imported into the system with a delay until the end of the cycle, at which point the imported orders are matched to vehicles. The matching result can be either acceptance or rejection, and this result is buffered for a pre-set buffer time t after the cycle ends. B The passenger will then be notified; orders matched in each cycle will be executed in the next cycle. Based on the execution status, they can be divided into served orders and matched but unserved orders; since they have been matched by the system and the passenger has been notified, matched but unserved orders cannot be rejected. They will be reassigned to a vehicle in the next cycle. The reassigned vehicle can be either the same vehicle or a different vehicle.

[0015] The rolling time-domain framework includes an order phase, a planning phase, an operation phase, and a forecasting phase. The phase sequence is as follows: first, the order and forecasting phases import orders into the system; then, the planning phase plans routes for the imported orders; finally, the operation phase executes the planned routes. The scheduling plan for the current period is correlated with the execution status of the previous period. Dynamic orders are no longer imported at the beginning of period |P|. Therefore, all phases except the operation phase terminate at the end of period |P|-1. Only vehicles v in the operation phase will execute the planned routes of period |P|-1 in period |P|. The dynamic orders imported in period p+1 will affect the route planning of vehicle v in period p. Incomplete execution; in each subsequent cycle, the operator must consider not only the newly imported dynamic orders for passengers from boarding station i to alighting station j in cycle p. We also need to consider matched but unserved passengers from boarding station i to alighting station j up to cycle p. Since the planning phase always lags behind the order phase by one cycle, a buffer period t of negligible length is set at the end of each cycle. B To plan dynamic orders; the planned routes will be executed immediately during the operational phase after the buffer period.

[0016] Furthermore, the DRT scheduling problem is modeled as a Markov Decision Process (MDP), as follows:

[0017] Define state variables:

[0018]

[0019] In formula (1), Represents the state variables of stage k in period p; This indicates the state of the boarding station for order r in stage k of period p. If the passenger has already boarded, then... otherwise, This indicates the state of the drop-off station for order r in stage k of period p. If the passenger has already arrived, then... otherwise, This indicates the position of vehicle v in phase k of period p; This represents the remaining mileage traveled by vehicle v during phase k of period p. This represents the remaining passenger capacity of vehicle v in phase k of period p. This represents the cumulative travel time of vehicle v during phase k of period p; This represents the time beyond the cycle of vehicle v in period p. If the vehicle's travel time exceeds one cycle time T, then... otherwise, This represents the travel route of vehicle v during period p;

[0020] |K p The specific values ​​for each period are as follows:

[0021]

[0022] Due to the planned route The execution time may exceed one cycle time T; the execution time may only cover part of the stations in the planned route, meaning the vehicle cannot complete the planned route of cycle p within the next cycle p+1, causing confusion in the state variable information; to solve this problem, a supercycle time for vehicle v in stage k of cycle p is introduced. If the vehicle's travel time exceeds one cycle time T, then otherwise,

[0023] Define decision variables:

[0024]

[0025] In formula (3), if vehicle v located in parking lot m is used in phase k of period p, then otherwise, If order r is assigned to vehicle v in cycle p stage k, then otherwise, If vehicle v travels from station i to station j during period p, then otherwise, This represents the waiting time of vehicle v at station j during phase p of the cycle;

[0026] The scenario is as follows:

[0027] Scenario 1:

[0028] This scenario indicates that the waiting time for vehicle v in the parking lot is... Since the vehicle is waiting in the parking lot, the station j that the vehicle is currently heading to is still the parking lot m to which vehicle v belongs. v ;

[0029] If the vehicle is at the earliest departure time ET declared in order r r Before arriving at its boarding station, the vehicle needs to be at boarding station i r If waiting, the vehicle will be made to wait in the parking lot. The waiting time will be calculated as follows:

[0030]

[0031] In formula (4), d ij This represents the shortest distance from station i to station j; Indicates the vehicle's speed. This represents the cumulative travel time of vehicle v during phase k of period p;

[0032] Scenario 2:

[0033] This scenario indicates that vehicle v departing from station i travels to station j and can wait at station j; vehicle v en route to station j may have the following states:

[0034] 1) The vehicle was empty before it reached the boarding station;

[0035] 2) There were passengers on the vehicle before it reached the boarding station;

[0036] 3) The vehicle proceeds to the drop-off station;

[0037] Since there is no specified time window for disembarking at the station, the third scenario will not be discussed; assuming there are still passengers on the train before heading to the boarding station, if the train is at its earliest boarding time ET... r Upon arrival at the boarding station, the vehicle must wait for a period of time; however, waiting at the boarding station is unpleasant for the passengers; more importantly, under the rolling time-domain planning framework of DRT scheduling, when vehicle v is in period p stage k at station j, the waiting time... If the cycle time T is long enough, it may be exceeded, rendering the decision for that cycle invalid; therefore, when there are passengers on board, boarding stations requiring waiting should be avoided; to this end, the following constraint is introduced:

[0038] Before making a scheduling decision, the state variables in The travel route of vehicle v during period p has been recorded; if This includes the alighting station corresponding to the boarding station it serves. If there are no passengers on the train, then the train can go to any boarding station, and the waiting time of train v at station j is within phase p of the cycle. Calculated by formula (4); otherwise, if there are passengers on board, the vehicle is only allowed to go to the boarding point that can be reached within the time window; if the vehicle arrives at the boarding station ahead of time with passengers on board, it means that its planned route is wrong.

[0039] Scenario 3:

[0040] This scenario indicates that vehicle v, which has left the parking lot, is returning to its assigned parking lot m. v .

[0041] Furthermore, define the constraints:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] Among them, constraint (5) requires that each parking lot has a maximum number of available vehicles; constraint (6) requires that each vehicle can be used at most once per cycle; constraint (7) ensures that all submitted orders are imported into the system; constraint (8) ensures that all orders are processed at the beginning of cycle |P|; and constraint (9) ensures that all imported orders should be processed in the final stage. From the boarding station to the corresponding alighting station; constraint (10) states that from period 1 to period |P|-1, order r can be decided at most twice; due to the route decision at each stage It contains only one boarding or alighting station for order r, and each order can only be served by one vehicle, therefore there are two stations associated with order r in each cycle. The decision; due to and This forms a tuple, so There are at most two decisions; constraint (11) states that there is no decision within the period |P|; constraints (12) and (13) ensure that the assigned orders do not exceed the vehicle's remaining driving distance and remaining capacity, respectively; constraint (14) requires that the vehicle's lateness does not exceed a threshold. Constraint (15) defines the duration constraint of the supercycle time; constraints (16)-(19) describe the properties of the decision variables. If vehicle v located in parking lot m is used in stage k of cycle p, then otherwise, If vehicle v travels from station i to station j during period p, then otherwise,

[0058] Define the state transition equation:

[0059] (3) Stage state transition equation

[0060]

[0061] Stage state transition equation It describes the changes in various attributes of the state variables under different decision variables, with the aim of planning the route for each cycle;

[0062] The state variables of k in periodic phase p The transition function for each attribute depends on the context of the decision variables, as follows:

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] In formulas (21) and (22), once a vehicle is dispatched to the boarding or alighting station, and The following are updated respectively; Formula (23) specifies the position of vehicle v; In Formula (24), for scenario 1, the remaining travel distance of vehicle v remains unchanged; for scenario 2, the remaining travel distance of vehicle v is reduced by the shortest distance between station i and station j; for scenario 3, the remaining travel distance is updated to the maximum travel distance when the vehicle returns to the depot; In Formula (25), for scenario 1, the remaining capacity of vehicle v remains unchanged; for scenario 2, the remaining capacity of vehicle v is reduced by the number of passengers in order r; for scenario 3, the capacity is updated to the maximum passenger capacity when the vehicle returns to the depot; In Formula (26), for scenario 1, the cumulative travel time of vehicle v is increased by the waiting time in the depot; for scenario 2, the cumulative travel time of vehicle v is increased by the travel time between station i and station j; for scenario 3, the cumulative travel time is increased by the travel time, waiting time, and service time;

[0070] (4) Periodic state transition equation

[0071] Although the stage state transition equation Using the state variables of period p in phase k Plan the route for each cycle, but due to the vehicle v's planned route in cycle p... It has not been executed yet, so the state variable is not yet executed. The value of v will not change, and the vehicle v will travel along the path in period p+1. The planned route for period p is executed only within the time T of period p+1. Only after this can it be determined; therefore, a periodic state transition equation is required.

[0072] External information G from period p to period p+1 p According to the planned route The initial state variables for the next period are obtained from the period time T. It can be achieved through periodic state transition equations Iterative calculations are performed; based on this principle, the external information G between each cycle... p It can be obtained in the following way;

[0073] The actual available driving time of vehicle v in period p is External information Gp From available driving time The length of the route within the specified range;

[0074] Specifically, the first step is to determine the available driving time. When the vehicle runs out of gas, it will reach a certain station, and the routes will be formed by connecting the stations it passed through with that station. State variables for the next period It is possible to calculate the driving route It is obtained from the changes that occur.

[0075] Furthermore, define the objective function:

[0076] The cost of DRT dispatching includes fixed transportation costs, variable transportation costs, and time penalty costs. Fixed transportation costs are related to the number of vehicles used, and are calculated using the following formula:

[0077]

[0078] In the above expression, α f This represents the fixed transportation cost per vehicle. Variable transportation costs depend on the distance traveled; since a new route is generated at each stage k, the variable transportation cost can be calculated as follows:

[0079]

[0080] The penalty cost for violating the time window includes arriving early and late; the lateness penalty system α l Early arrival penalty coefficient α e Satisfy α l >β e If the vehicle's arrival time falls within the specified time window, the penalty cost is zero; otherwise, the penalty cost depends on the length of the violation period. The early and late arrival times of order r can be calculated as follows: and The penalty cost for violating the time window in each stage is calculated as follows:

[0081]

[0082] The value function of the DRT model is related to the newly generated cost of each stage k; the cost of stage k in period p is equal to the cost of the previous stage. In addition to the variable transportation costs incurred during this stage and penalty costs As shown below:

[0083]

[0084] Because fixed transportation costs occur in the final stage of the cycle. The final stage cost should be calculated by adding the fixed transportation cost CF, as follows:

[0085]

[0086] To formulate the DRT problem as a SADP model, the following optimal state-value function is proposed based on the Bellman equation:

[0087]

[0088] in, The execution path strategy for stage k of period p. The optimal state value function;

[0089] Under look-ahead scheduling, the predicted random order matrix probability value of occurrence It needs to be included in the objective function; to ensure the iterative stability of the SADP algorithm, let This indicates that the path strategy is executed in phase k of period p. The optimal state value function and the objective function are modified as follows:

[0090]

[0091] Passenger-vehicle assignment is crucial for route planning;

[0092] An order rejection mechanism is proposed, with the following rules:

[0093] If orders cannot be fully matched, The planning process is then terminated; for orders r that cannot be matched, the boarding station i... r and disembarkation station J r If a station is identified as a potential rejection station, it is removed one by one, and the solution is repeated until the remaining orders can be matched.

[0094] Furthermore, in step S2, the prediction of future demand based on quantile regression, LSTM model, and Copula function is as follows:

[0095] Interval estimation is achieved by predicting the future demand of each OD pair in the conditional quantile equation at different quantile levels, thereby constructing an empirical distribution.

[0096]

[0097] Here, ζ represents the equation coefficients when the quantile level equals τ; when the optimal ζ is obtained using linear programming, the conditional τ quantile equation can be derived. For different quantiles τ, formula (34) can be solved separately for each τ, from which different quantile levels can be obtained.

[0098] In order to predict future demand Historical data from period 1 to period p As a training dataset; due to the need to predict future demands at different quantile levels, let τ represents the quantile level l The OD demand is given by τ, and the quantile level set is given by τ. l ={5%,25%,50%,75%,95%}; Therefore, the loss function of the LSTM model is modified to the optimization equation of quantile regression in formula (35), as follows:

[0099]

[0100] In this way, quantile samples of future demand for each OD pair can be obtained. need The distribution follows the quantile sample performance, i.e. It can be represented as the following empirical distribution:

[0101]

[0102] Therefore, by analyzing empirical distributions By sampling from the middle, we can obtain random predicted values ​​for each OD pair. Specifically as follows:

[0103]

[0104] By repeating the random sampling process, multiple predicted samples can be obtained for each OD pair; therefore, by sampling all OD pairs, a random OD matrix with period p is obtained. Its dimension is |S| 2 The details are as follows:

[0105]

[0106] The marginal distributions of different OD pairs may be correlated, and the joint distribution can capture this correlation;

[0107] Therefore, a copula is used to merge the marginal distributions into a joint demand distribution, as follows:

[0108] make Each OD pair represents a different requirement. The cumulative distribution function (CDFs); based on the multivariate CDF composed of independent variables, random vectors It can be represented as follows:

[0109]

[0110] For each OD pair, it can be obtained from the empirical distribution. Random demand is obtained by sampling from the middle.

[0111] Give the marginal distribution of each OD pair Right now The CDF, and according to Sklar's Copula theory, random vectors The multivariate cumulative distribution function can be defined as the marginal distribution of each vector. And a Copula function, as follows:

[0112]

[0113] Applying Gaussian Copulas, specifically as follows:

[0114]

[0115] Among them, C G Denotes Gaussian Copula, Φ σ This represents the joint CDF of a multivariate normal distribution with a covariance matrix of σ and a mean of 0.

[0116] Using C G From To obtain future demand samples from the joint distribution; in doing so, First, let's start with C. G Extract from the middle, and then convert the samples to Finally, Φ is mapped to the selected samples through the inverse mapping of edge CDFs, as shown below:

[0117]

[0118] Finally, the joint distribution function Φ was obtained. σ ,Will Substitute into Φ σ Then we obtain the joint occurrence probability.

[0119] Furthermore, in step S3, future demand is incorporated into the general scheduling model to establish a prediction-based forward scheduling model. Error correction mechanisms are designed for forward scheduling and order cancellation, as follows:

[0120] Unlike ordinary scheduling, look-ahead scheduling not only considers and Also consider the projected future demand for the upcoming period p+1; under this scheduling mode, the future demand for the next period... It is predicted in advance in cycle p, and is consistent with and Optimize together; therefore, training to predict future demand should be performed periodically on a rolling basis; in period p, to predict future demand in period p+1, the training dataset should include the demand from previous and current periods, i.e.

[0121] Furthermore, in step S3, a correction mechanism is proposed to mitigate the negative effects of prediction errors;

[0122] Because the vehicle executes the planned path of look-ahead scheduling at the end of period p. The route cannot be adjusted within the next cycle time T; therefore, it can only be adjusted when vehicle v arrives at station i. r Only then can the remaining passenger capacity be checked. Can it accommodate the number of actual passengers?

[0123] Therefore, prediction errors can be divided into two types: predicted values ​​are greater than actual values. And less than the actual value

[0124] For the former, the remaining passenger capacity can accommodate the number of passengers, so it is only necessary to adjust the original remaining passenger capacity. Update to the correct value

[0125] For the latter, route planning is ineffective;

[0126] To avoid wasting already traveled distance and time, only accept requests that can be separated. One passenger, and the extra Passengers can be added as new dynamic orders at the end of period p+1. Import and plan together; in contrast, for inseparable orders, if the remaining passenger capacity is insufficient, the order must be rejected.

[0127] For order cancellations, forecasting errors can be categorized into two types:

[0128] The projected future demand was not cancelled, but it was actually cancelled;

[0129] The predicted future demand was cancelled, but it was not actually cancelled;

[0130] For the former, the incorrect state variable can be updated directly; for the latter, the vehicle has three states: 'not yet arrived at the pick-up point', 'just arrived at the pick-up point', and 'has already passed the pick-up point'; the prediction error for the first two states can be updated directly; while for the state 'has already passed the pick-up point', another vehicle needs to be dispatched to provide service at the end of period p+1.

[0131] Furthermore, in step S4, the pruning strategy for the design decision compresses the solution space to reduce computation time, specifically including:

[0132] Pruning is performed based on the remaining distance to the lower bound of the vehicle, as detailed below:

[0133] Since vehicle v must transport all passengers to their corresponding drop-off points, if it is possible to travel along arc (i,j)∈A to the new boarding point j=i... r Previously, it was very meaningful to determine whether the vehicle's remaining range could meet the mileage requirements of the subsequent route;

[0134] Theorem 1: Vehicle v travels to boarding point j=i during period p at stage k. r At that time, its remaining range always has a lower bound.

[0135] Theorem 2: Compared to the standard dynamic programming algorithm, after pruning, the state space saved in all stages of period p reaches [value missing].

[0136] Waiting time optimization, as detailed below:

[0137] When a vehicle is in the parking lot, it can wait, thus optimizing departure time and preventing significant time penalties when traveling to the first pick-up point. This is because the pick-up point i needs to be served after waiting... r The decision has already been made, and the subsequent path from this pick-up point is not observable; only the vehicle's arrival time at the pick-up point will be optimized; waiting time... The optimal value is calculated as shown in equation (43):

[0138]

[0139] The optimal penalty cost is calculated by (44). Specifically as follows:

[0140]

[0141] Return to the parking lot for pruning, as detailed below:

[0142] When the vehicle has visited the drop-off point and there are no other passengers on board, the vehicle will face two decisions:

[0143] (e) Proceed to another boarding point;

[0144] (f) Return to your parking lot m v ;

[0145] The pruning strategy is as follows: When When, make a decision such as path (f); when At that time, make a decision such as path (e).

[0146] Furthermore, in step S5, the scheduling scheme is solved using an approximate dynamic programming algorithm, as follows:

[0147] In the In the next iteration, the operator used the first The value function after the next iteration Make a decision

[0148]

[0149] The estimated value of the state after the decision is approximated by the temporal difference update method. The next iteration makes converges to

[0150]

[0151] When λ = 0 in TD(λ), there is a special case, as shown in formula (48):

[0152]

[0153] Due to the unbiased sample estimation at the end stage Value function involving the initial stage of the next cycle However, the state It is often not The state after the decision-making process, the incomplete execution of the planned path, and direct iteration will cause... A significant deviation has occurred, therefore a value function rolling strategy is required;

[0154] Assume the first The planning path for the next iteration, period p. Actual execution by the vehicle Therefore, after calculation using the periodic state transition equation, the initial state of period p+1 is essentially equal to Right now To ensure the stability of the update of the initial and final state value functions of adjacent periods, the first period will be... State after the next iteration The estimated value rolled over to As in formula (49):

[0155]

[0156] No. The final state after the next iteration. Although unbiased sample estimation involves But the initial state of the next cycle The value function is inherited from the state of that period. Therefore, its calculation should include... Make a decision Value:

[0157]

[0158] Similarly, The value function can be approximated using the TD(λ) and TD(0) methods in formula (51).

[0159]

[0160] In the initial stage of period p, n period p+1 stochastic OD matrices given by the prediction model are imported, followed by sample decisions made under n stochastic demands. Specifically as follows:

[0161]

[0162] When the sample state Run to This will generate n sample planning paths; to evaluate the impact of stochastic demand on each sample planning path, the TD(λ) and TD(0) methods are used to approximate the value of each sample path:

[0163]

[0164] Due to the random OD matrix probability of occurrence There are differences in the value function of n samples. Search for the minimum expected value function in the middle, and use it and the corresponding stochastic demand as the value function and the optimal stochastic demand for period p+1, respectively, under the forward-looking strategy:

[0165]

[0166] The present invention has the following advantages and effects compared with the prior art:

[0167] This invention establishes a Markov decision process model within a rolling time-domain framework; predicts future demand based on quantile regression, LSTM models, and Copula functions; incorporates future demand into a general scheduling model to establish a prediction-based look-ahead scheduling model, and designs error correction mechanisms for look-ahead scheduling and order cancellations respectively; designs a decision-making pruning strategy to compress the solution space and reduce computation time; and utilizes an approximate dynamic programming algorithm to solve the scheduling scheme. This achieves refined organization and management of demand-response public transport scheduling, realizing cost reduction and efficiency improvement in services. Attached Figure Description

[0168] Figure 1 This is a flowchart of a demand-response bus forward scheduling method according to an embodiment of the present invention;

[0169] Figure 2 This is a scheduling flowchart in an embodiment of the present invention;

[0170] Figure 3 This is a schematic diagram of the rolling time-domain scheduling framework in an embodiment of the present invention;

[0171] Figure 4 This is a schematic diagram of the supercycle time in an embodiment of the present invention;

[0172] Figure 5 This is a schematic diagram of decision variables in an embodiment of the present invention;

[0173] Figure 6 This is a schematic diagram of the value function rolling and look-ahead strategy in an embodiment of the present invention;

[0174] Figure 7 This is a map showing the distribution of bus stops and parking lots for the "PinBus" project in this embodiment of the invention;

[0175] Figure 8 This is a schematic diagram of the EAUC calculation results in the "PinBus" project in this embodiment of the invention;

[0176] Figure 9 This is a schematic diagram of the EAPM calculation results in the "PinBus" project in this embodiment of the invention;

[0177] Figure 10 This is a schematic diagram of the MUR calculation results in the "PinBus" project in this embodiment of the invention;

[0178] Figure 11 This is a schematic diagram of the calculation results of RR in the "PinBus" project in this embodiment of the invention;

[0179] Figure 12 This is a schematic diagram of the calculation results of LR in the "PinBus" project in this embodiment of the invention;

[0180] Figure 13This is a schematic diagram of the ALT calculation results in the "PinBus" project in this embodiment of the invention. Detailed Implementation

[0181] The present invention will now be described in further detail with reference to embodiments and accompanying drawings, but the implementation of the present invention is not limited thereto. First, for the convenience of describing the mathematical model later, Table 1 lists the symbolic variables involved in the present invention.

[0182] Table 1 Symbolic Variables

[0183]

[0184]

[0185]

[0186] A demand-response bus forward scheduling method, such as Figure 1 and Figure 2 As shown, it includes the following steps:

[0187] S1. Based on the rolling time-domain framework, establish a Markov decision process model;

[0188] like Figure 3 As shown, the rolling time-domain framework includes an order phase, a planning phase, an operation phase, and a forecasting phase. The phase sequence is as follows: first, the order and forecasting phases import orders into the system; then, the planning phase plans routes for the imported orders; and finally, the operation phase executes the planned routes. The scheduling plan for the current period is correlated with the execution status of the previous period. Dynamic orders are no longer imported at the beginning of period |P|; only vehicles v in the operation phase execute the planned routes in period |P|. The dynamic orders imported in period p+1 will affect the route planning of vehicle v in period p. Incomplete execution; in each subsequent cycle, the operator must consider not only the newly imported dynamic orders for passengers from boarding station i to alighting station j in cycle p. We also need to consider matched but unserved passengers from boarding station i to alighting station j up to cycle p. Since the planning phase always lags behind the order phase by one cycle, a buffer period t of negligible length is set at the end of each cycle. B To plan dynamic orders; the planned routes will be executed immediately during the operational phase after the buffer period.

[0189] Furthermore, the DRT scheduling problem is modeled as a Markov Decision Process (MDP), as follows:

[0190] Define state variables:

[0191]

[0192] |K p The specific values ​​for each period are as follows:

[0193]

[0194] like Figure 4 As shown, the planned route for the first cycle is However, the execution time of the second cycle only occurs between stations 2 and 3. This means that before the vehicle reaches station 3, the system will import a new order and regenerate the route. A reasonable improvement would be to have the vehicle continue to station 3 on the previously planned route, thus extending the first cycle's travel route from... Change to The extra time spent traveling to station 3 was recorded as over-cycle time.

[0195] Define decision variables:

[0196]

[0197] like Figure 5 As shown, the decision-making scenario is constructed as follows:

[0198] Scenario 1:

[0199] Scenario 2:

[0200] Scenario 3:

[0201] If the vehicle is at the earliest departure time ET declared in order r r Before arriving at its boarding station, the vehicle needs to be at boarding station i r If waiting is the only option, a reasonable approach is to have the vehicle wait in the parking lot. The waiting time can be calculated as follows:

[0202]

[0203] Furthermore, define the objective function:

[0204] The cost of DRT dispatching includes fixed transportation costs, variable transportation costs, and time penalty costs. Fixed transportation costs are related to the number of vehicles used, and are calculated using the following formula:

[0205]

[0206] In the above expression, β f This represents the fixed transportation cost per vehicle.

[0207] The variable transportation cost for each stage k can be calculated as follows:

[0208]

[0209] The time penalty cost for each stage k can be calculated as follows:

[0210]

[0211] The value function of the DRT model is related to the newly generated cost of each stage k; the cost of stage k in period p is equal to the cost of the previous stage. In addition to the variable transportation costs incurred during this stage and penalty costs As shown below:

[0212]

[0213] Because fixed transportation costs occur in the final stage of the cycle. The final stage cost should be calculated by adding the fixed transportation cost CF, as follows:

[0214]

[0215] To formulate the DRT problem as a SADP model, the following optimal state-value function is proposed based on the Bellman equation:

[0216]

[0217] in, The execution path strategy for stage k of period p. The optimal state value function;

[0218] Under look-ahead scheduling, the predicted random order matrix probability value of occurrence It needs to be included in the objective function; let This indicates that the path strategy is executed in phase k of period p. The optimal state value function and the objective function are modified as follows:

[0219]

[0220] An order rejection mechanism is proposed, with the following rules:

[0221] If orders cannot be fully matched, The planning process is then terminated; for orders r that cannot be matched, the boarding station i... r and disembarkation station J r If a station is identified as a potential rejection station, it is removed one by one, and the solution is repeated until the remaining orders can be matched.

[0222] S2. Predicting future demand based on quantile regression, LSTM model, and Copula function, as detailed below:

[0223] By predicting the future demand of each OD pair in the conditional quantile equation at different quantile levels, an empirical distribution is constructed to achieve interval estimation. The optimized model of quantile regression is modified to formula (35), as follows:

[0224]

[0225] This patent uses an LSTM model to predict future demand. Its loss function has been modified as follows:

[0226]

[0227] In this way, quantile samples of future demand for each OD pair can be obtained. need The distribution follows the quantile sample performance, i.e. It can be represented as the following empirical distribution:

[0228]

[0229] By analyzing empirical distributions By sampling from the middle, we can obtain random predicted values ​​for each OD pair. Specifically as follows:

[0230]

[0231] By repeating the random sampling process, multiple predicted samples can be obtained for each OD pair; therefore, by sampling all OD pairs, a random OD matrix with period p is obtained. Its dimension is |S| 2 The details are as follows:

[0232]

[0233] A copula is used to merge the marginal distributions of different demand sources into a joint demand distribution, as follows:

[0234]

[0235] Applying Gaussian Copulas, specifically as follows:

[0236]

[0237] Φ is mapped to the selected sample through the inverse mapping of edge CDFs, as shown below:

[0238]

[0239] Finally, the joint distribution function Φ was obtained. σ ,Will Substitute into Φ σ Then we obtain the joint occurrence probability.

[0240] S3. Incorporate future demand into the general scheduling model, establish a forecast-based forward scheduling model, and design error correction mechanisms for forward scheduling and order cancellation, as follows:

[0241] Simultaneous optimization of forward scheduling And the projected future demand for the upcoming cycle p+1; such as Figure 3 As shown, future demand in the next cycle It is predicted in advance in period p, and is consistent with and Optimize together. Meanwhile, the prediction error will be corrected when importing dynamic orders in the next cycle; for example, in cycle 2, first, based on the dynamic orders... Remove the correction time period [t0-T,t0] The prediction error, and obtain matched but unserved orders. Meanwhile, future demand in the forecast period [t0, t0+T] After that, and In the time interval [t0, t0+t] B Plan together within the time period [t0+t], and then schedule vehicles within that time period. B Execute in ,t0+T];

[0242] Furthermore, in step S3, a correction mechanism is proposed to mitigate the negative effects of prediction errors;

[0243] Because the vehicle executes the planned path of look-ahead scheduling at the end of period p. The route cannot be adjusted within the next cycle time T; therefore, it can only be adjusted when vehicle v arrives at station i. r Only then can the remaining passenger capacity be checked. Can it accommodate the number of actual passengers?

[0244] Therefore, prediction errors can be divided into two types: predicted values ​​are greater than actual values. And less than the actual value

[0245] For the former, the remaining passenger capacity can accommodate the number of passengers, so it is only necessary to adjust the original remaining passenger capacity. Update to the correct value

[0246] For the latter, route planning is ineffective;

[0247] To avoid wasting already traveled distance and time, only accept requests that can be separated. One passenger, and the extra Passengers can be added as new dynamic orders at the end of period p+1. Import and plan together; in contrast, for inseparable orders, if the remaining passenger capacity is insufficient, the order must be rejected.

[0248] For order cancellations, forecasting errors can be categorized into two types:

[0249] The projected future demand was not cancelled, but it was actually cancelled;

[0250] The predicted future demand was cancelled, but it was not actually cancelled;

[0251] For the former, the incorrect state variable can be updated directly; for the latter, the vehicle has three states: 'not yet arrived at the pick-up point', 'just arrived at the pick-up point', and 'has already passed the pick-up point'; the prediction error for the first two states can be updated directly; while for the state 'has already passed the pick-up point', another vehicle needs to be dispatched to provide service at the end of period p+1.

[0252] S4. Pruning strategies for design decisions, compressing the solution space to reduce computation time, specifically including:

[0253] Pruning is performed based on the remaining distance to the lower bound of the vehicle, as detailed below:

[0254] The lower limit of the remaining driving range is uniformly represented by formula (20).

[0255]

[0256] By using the lower bound of the vehicle's remaining travel distance for pruning, decisions with remaining travel distances less than the lower bound can be eliminated. Since these decisions are less than the lower bound, they cannot be the decisions made on the optimal path, thus ensuring that the optimal solution will not be pruned.

[0257] Waiting time optimization, as detailed below:

[0258] When vehicles are located in the parking lot, their arrival time at the boarding station can be optimized. Waiting time The optimal value is calculated as shown in equation (21):

[0259]

[0260] The optimal penalty cost is calculated by (22). Specifically as follows:

[0261]

[0262] Return to the parking lot for pruning, as detailed below:

[0263] when When, make a decision such as path (f); when At that time, make a decision such as path (e).

[0264] S5. Solve the scheduling scheme using an approximate dynamic programming algorithm, as follows:

[0265] In the In the next iteration, the operator used the first The value function after the next iteration Make a decision

[0266]

[0267] The estimated value of the state after the decision is approximated by the temporal difference update method. The next iteration makes converges to

[0268]

[0269] When λ = 0 in TD(λ), there is a special case, as shown in formula (25):

[0270]

[0271] To ensure the stability of the update of the initial and final state value functions of adjacent periods, the first period will be... State after the next iteration The estimated value rolled over to As in formula (26):

[0272]

[0273] No. The final state after the next iteration. Although unbiased sample estimation involves But the initial state of the next cycle The value function is inherited from the state of that period. Therefore, its calculation should include... Make a decision Value:

[0274]

[0275] Similarly, The value function can be approximated using the TD(λ) and TD(0) methods in formula (28).

[0276]

[0277] All steps of the value function rolling strategy are summarized in Table 2.

[0278] Table 2. Pseudocode for the value function rolling strategy

[0279]

[0280]

[0281] In the initial stage of period p, n period p+1 stochastic OD matrices given by the prediction model are imported, followed by sample decisions made under n stochastic demands. Specifically as follows:

[0282]

[0283] When the sample state Run to This will generate n sample planning paths; to evaluate the impact of stochastic demand on each sample planning path, the TD(λ) and TD(0) methods are used to approximate the value of each sample path:

[0284]

[0285] Due to the random OD matrix probability of occurrence There are differences in the value function of n samples. Search for the minimum expected value function in the middle, and use it and the corresponding stochastic demand as the value function and the optimal stochastic demand for period p+1, respectively, under the forward-looking strategy:

[0286]

[0287] Example 1:

[0288] In this embodiment, a real-demand-response bus project, namely the "shared bus" project in Guangzhou University Town, is used. Guangzhou Public Transport Company has already established 68 boarding stations and 100 alighting stations for the "shared bus" project in this area. The spatial distribution of bus stops and depots is as follows: Figure 7 As shown.

[0289] Figures 8 to 13The actual operation of the "Shared Bus" project was compared between regular operation and forward-looking operation across six indicators. It was found that both regular and forward-looking operations outperformed the actual operation in all six indicators, except for a few days when the actual operation slightly outperformed the regular operation in terms of delay rate and average delay time. Compared to the actual operation, the average increases of forward-looking operation over 7 days are as follows: number of vehicles decreased by 11.43%, average cost per effective passenger decreased by 38.35%, average mileage per effective passenger decreased by 23.76%, mileage utilization increased by 20.05%, response rate increased by 13.30%, delay rate decreased by 14.46%, and average delay time decreased by 1.81 minutes. Then, compared to the "LSTM+Quantile" model, the total increases of the "LSTM+Quantile+Copula" model over 7 days are as follows: Effective Passenger Average Cost (EAUC) increased by 3.73%, Effective Passenger Average Mileage (EAPM) decreased by 11.31%, Mileage Utilization Rate (MUR) increased by 6.26%, Response Rate (RR) increased by 14.09%, Delay Rate (LR) increased by 0.13%, and Average Delay Time (ALT) increased by 0.02 minutes. Although Copula theory worsened the delay rate and average delay time, thus worsening the Effective Passenger Average Cost, this negative impact is almost negligible. However, the performance improvement in Effective Passenger Average Mileage, Mileage Utilization Rate, and Response Rate due to Copula's capture of spatial correlation is significant. This demonstrates that strengthening the exploration of spatial features in predictive models can improve the service efficiency of forward-looking operations with only a small increase in system costs. In addition, compared to the "LSTM" model, the total increases of the "quantile + LSTM" model over 7 days are as follows: average cost per effective passenger decreased by 4.19%, average mileage per effective passenger decreased by 17.91%, mileage utilization increased by 17.41%, response rate increased by 7.67%, delay rate decreased by 0.40%, and average delay time decreased by 0.06 minutes. Since quantile interval estimation can overcome the prediction uncertainty of sparse passenger flow and reduce prediction bias caused by default values ​​and abnormal peaks, replacing the point estimation of the "LSTM" model with interval estimation can effectively address the challenges of sparse order data.

[0290] The results show that the look-ahead scheduling method and solution algorithm proposed in this invention have good characteristics and can be extended to practical applications.

[0291] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A demand-response public transport forward scheduling method, characterized in that, Includes the following steps: S1. Based on the rolling time-domain framework, a Markov decision process model is established. The demand-response bus (DRT) scheduling problem is a variant of the pickup and delivery vehicle routing problem with time windows, and also considers multiple depots, departure time optimization, waiting time optimization, dynamic orders, passenger-vehicle matching, and order rejection mechanisms. The DRT scheduling problem is modeled as a Markov decision process (MDP), as follows: Define state variables: In formula (1), Indicates period stage State variables; Indicates order The boarding station in the cycle stage If passengers have already boarded, then... ,otherwise, ; Indicates order The stop at the cycle stage If the passenger has arrived, then ,otherwise, ; Indicates vehicle In the cycle stage Location; Indicates vehicle In the cycle stage The remaining driving range; Indicates vehicle In the cycle stage The remaining passenger capacity; Indicates vehicle In the cycle stage The cumulative driving time; Indicates vehicle In the cycle The over-cycle time, if the vehicle's travel time exceeds one cycle time. ,but ,otherwise, ; Indicates vehicle In the cycle The driving route; Next, we derive the cycle. Total Stage The value; for stage The system will process the order. Assigned to vehicles and generate external information Through the stage state transition equation Obtain the state variables for the next stage; in each cycle, route planning is performed on all imported orders, if the order... In the cycle If imported, then ,otherwise, In the first cycle, since the imported orders have not yet been served by vehicles, the final stage number is... The number of stations equal to the number of static orders; in the second cycle to the... cycle, It is an induced variable, and its specific value for each period is equal to the number of unserved sites with all imported orders, as detailed below: Introduce a vehicle In the cycle stage supercycle time , If the vehicle's travel time exceeds one cycle time ,but ,otherwise, ; Define decision variables: in, For planning period set, This is the set of stages for dynamic programming in each cycle. ,in ; For order collection, Gather at the parking lot, For parking lots and bus stops, For vehicle assembly; In formula (3), if it is located in a parking lot vehicles In the cycle stage If used, then ,otherwise, If the order In the cycle stage Assigned to vehicles ,but ,otherwise, If the vehicle In the cycle stage From the station Head to Station ,but ,otherwise, ; Indicates vehicle In the cycle stage At the station Waiting time; The scenario is as follows: Scenario 1: This scenario indicates that the vehicles in the parking lot The waiting time is Since the vehicle is waiting in the parking lot, the station the vehicle is currently heading to... Still a vehicle The parking lot ; If the vehicle is on the order The earliest time to enter the city as stated The vehicle needs to arrive at its boarding station before it can board. If waiting is the only option, a reasonable approach is to have the vehicle wait in the parking lot. The waiting time can be calculated as follows: In formula (4), Station Arrival The shortest distance; Indicates the vehicle's speed. Indicates vehicle In the cycle stage The cumulative driving time; Scenario 2: This scenario indicates that the vehicle is leaving the site. From the station Arrive at the station It can be found on the station Waiting; heading to the station Vehicles on the way The following states exist: 1) The vehicle was empty before it reached the boarding station; 2) There were passengers on the vehicle before it reached the boarding station; 3) The vehicle proceeds to the drop-off station; Since there is no specified time window for disembarking at the station, the third scenario will not be discussed; assuming there are still passengers on the train before heading to the boarding station, if the train is at its earliest boarding time... Previously, upon arrival at the boarding station, the vehicle had to wait for a period of time; therefore, the following restrictions are introduced: Before making a scheduling decision, the state variables in The vehicle has been recorded. In the cycle The driving route; if This includes the alighting station corresponding to the boarding station it serves. That is, if there are no passengers on the train, then the vehicle can go to any boarding station, and the vehicle... In the cycle stage At the station Waiting time Calculated by formula (4); otherwise, if there are passengers on board, the vehicle is only allowed to go to the boarding point that can be reached within the time window; if the vehicle arrives at the boarding station ahead of time with passengers on board, it means that its planned route is wrong. Scenario 3: This scenario indicates a vehicle leaving the site. Return to your assigned parking lot ; S2. Predicting future demand based on quantile regression, LSTM model, and Copula function; the specific details of predicting future demand based on quantile regression, LSTM model, and Copula function are as follows: Interval estimation is achieved by predicting the future demand of each OD pair in the conditional quantile equation at different quantile levels, thereby constructing an empirical distribution. By finding a functional relationship This makes expected demand and actual demand equal. The difference between them is the smallest, that is: The optimized model for quantile regression is given by formula (35), as follows: Among them, It is the dependent variable The conditional expectation equation; This indicates that when the quantile level is equal to The equation coefficients at that time; when the optimal solution is obtained using linear programming. When conditions are obtained Quantile equations For different quantiles For each Solve formula (35) separately to obtain the results for different quantile levels. ; In order to predict future demand , from period 1 to period Historical data As a training dataset; due to the need to predict future demands at different quantile levels, let Indicates quantile level The OD demand under the following conditions, and the quantile level set is Therefore, the loss function of the LSTM model is modified to the optimization equation of quantile regression in formula (36), as follows: In this way, quantile samples of future demand for each OD pair are obtained. Real needs The distribution follows the quantile sample performance, i.e. It can be represented by the following empirical distribution: Therefore, by analyzing empirical distributions Mid-sampling is used to obtain random predicted values ​​for each OD pair. The details are as follows: By repeating the random sampling process, multiple predicted samples are obtained for each OD pair; by sampling all OD pairs, the periodicity is obtained. random OD matrix Its dimensions are The details are as follows: A copula is used to merge the marginal distributions into a joint demand distribution, and finally the joint occurrence probability is obtained. ; S3. Incorporate future demand into the Markov decision process model to establish a forecast-based forward scheduling model, and design error correction mechanisms for forward scheduling and order cancellation respectively; specifically as follows: Unlike ordinary scheduling, look-ahead scheduling not only considers and Also considering the upcoming cycle Forecasting future demand; under this scheduling model, the future demand for the next cycle. In the cycle Predicted in advance, and with and Optimize together; For period From the station Get off at the station Matched but unserved passengers Therefore, training to predict future demand should be conducted periodically on a rolling basis; in the period... In order to predict the cycle To meet future needs, the training dataset should include requirements from previous and current cycles, i.e. ; The prediction error will be corrected when the dynamic orders are imported in the next cycle; in the second cycle, the prediction error will be corrected first based on the dynamic orders. Correct the time period middle The prediction error, and obtain matched but unserved orders. Meanwhile, during the predicted time period Future demand in After that, , and In time period Plan together, and then schedule vehicles within a time period. Execution in; among which, Indicates buffer time; S4. Pruning strategies for design decisions: Compressing the solution space to reduce computation time; S5. Solve the scheduling scheme using an approximate dynamic programming algorithm.

2. The demand-response bus forward scheduling method according to claim 1, characterized in that, In step S1, within the rolling time-domain framework, a delayed batch matching method is used to allocate orders for one cycle to the fleet. The principle is to divide the operating time range into a group of durations... periodic set The system then delays the import of ride orders for any given period until the end of that period, at which point the imported orders are matched with vehicles. The matching result can be either acceptance or rejection, and this result is subject to a pre-set buffer period after the end of the period. The passenger will then be notified; orders matched in each cycle will be executed in the next cycle, and will be divided into served orders and matched but unserved orders based on their execution status; since they have been matched by the system and the passenger has been notified, matched but unserved orders cannot be rejected, and will be reassigned to a vehicle in the next cycle. The reassigned vehicle can be either the same vehicle or a different vehicle. The rolling time-domain framework includes an order phase, a planning phase, an operation phase, and a forecasting phase. The phase sequence is as follows: first, the order and forecasting phases import orders into the system; then, the planning phase plans routes for the imported orders; finally, the operation phase executes the planned routes. The scheduling plan for the current cycle is correlated with the execution status of the previous cycle; dynamic orders are managed within the cycle. Importing stops at the start time, therefore all phases except the operational phase are within the cycle. Termination at the end, only vehicles in the operational phase remain. It will also be in the cycle Execution cycle Planned route ;cycle Imported dynamic orders will cause cycle vehicle Planning route Incomplete execution; in each subsequent cycle, the operator must consider not only the cycle itself. New imported dynamic orders from the boarding station Get off at the station Passengers We also need to consider the cycle. From the station Get off at the station Matched but unserved passengers ; Since the planning phase always lags behind the order phase by one cycle, a buffer period of negligible length is set at the end of each cycle. To plan dynamic orders; The planned route will be implemented immediately after the buffer period during the operational phase.

3. The demand-response bus forward scheduling method according to claim 1, characterized in that, Define constraints: in, For maximum driving range, For vehicle passenger capacity, For orders The upper bound of the time window Let r be the number of passengers in order r. For orders The boarding station; arc set ,in and Represents a parking lot or bus stop. For use as a meeting point for parking lots and bus stops; Constraint (5) requires each parking lot to have a maximum number of available vehicles; Constraint (6) requires each vehicle to be used at most once per cycle; Constraint (7) ensures that all submitted orders are imported into the system; Constraint (8) ensures that all orders are processed within the cycle. The initial processing time is determined by constraint (9), which ensures that all imported orders should be processed in the final stage. From the boarding station to the corresponding alighting station; constraint (10) indicates from period 1 to period ,Order It can be decided at most twice; due to the route decision at each stage. Includes only orders A single boarding or alighting station, and each order can only be served by one vehicle, therefore there are two vehicles with orders in each cycle. Related The decision; due to and This forms a tuple, so There are at most two decisions; constraint (11) states that during the period No decision is made; constraints (12) and (13) ensure that the assigned orders do not exceed the vehicle's remaining driving distance and remaining capacity, respectively; constraint (14) requires that the vehicle's lateness does not exceed a threshold. Constraint (15) defines the duration constraint of the overcycle time; Constraints (16)-(19) describe the properties of the decision variables, if located in the parking lot vehicles In the cycle stage If used, then ;otherwise, If the vehicle In the cycle stage From the station Head to Station ,but ;otherwise, ; Define state transition equations, including stage state transition equations and periodic state transition equations.

4. The demand-response bus forward scheduling method according to claim 3, characterized in that, Define the objective function: The cost of DRT scheduling includes fixed transportation costs, variable transportation costs, and time window violation penalty costs. Fixed transportation costs are related to the number of vehicles used, and the calculation formula is as follows: In equation (27), This represents a fixed transportation cost per vehicle; variable transportation costs depend on the distance traveled; due to the varying costs at each stage... New routes will be generated, and the variable transportation costs will be calculated as follows: The penalty cost for violating the time window includes arriving early and arriving late; the penalty coefficient for lateness. Early arrival penalty coefficient satisfy ;in The cost is per unit mileage; if the vehicle's arrival time falls within the specified time window, the penalty cost is 0; otherwise, the penalty cost depends on the length of the violation period; and the order... The early and late arrival times can be calculated as follows: and ; Calculate the penalty cost for violations within the time window of each stage. ; The value function of the DRT model and each stage Related to newly generated costs; cycle stage The cost equals the cost of the previous stage. In addition to the variable transportation costs incurred during this stage and time window penalty costs As shown below: Because fixed transportation costs occur in the final stage of the cycle. Therefore, the final stage cost should include fixed transportation costs. The details are as follows: To formulate the DRT problem as a SADP model, the following optimal state-value function is proposed based on the Bellman equation: in, It is a cycle stage Execution path strategy The optimal state value function; Under look-ahead scheduling, the predicted random order matrix probability value of occurrence It needs to be included in the objective function; let Indicates the period stage Execution path strategy The optimal state value function and the objective function are modified as follows: An order rejection mechanism is proposed, with the following rules: When all imported orders can be completed within the cycle When internal matching occurs, decision variables Through the stage state transition equation Iterate to the final state variable ,Right now However, if orders cannot be fully matched, it makes... If so, the planning process will be terminated; For orders that cannot be matched boarding station and the drop-off station If a station is identified as a potential rejection station, it is removed one by one, and the solution is repeated until the remaining orders can be matched.

5. The demand-response bus forward scheduling method according to claim 1, characterized in that, In step S3, a correction mechanism is proposed to mitigate the negative effects of prediction errors; Due to the vehicle's cycle The planned path for executing lookahead scheduling at the end time. The route in the next cycle Internal adjustments are not possible; Therefore, only when the vehicle Arrive at the station Only then can the remaining passenger capacity be checked. Can it accommodate the number of actual passengers? Therefore, prediction errors are divided into two types: predicted values ​​are greater than actual values. and less than the actual value, i.e. ;in Let r be the number of passengers in order r; For the former, the remaining passenger capacity can accommodate the number of passengers, so it is only necessary to adjust the original remaining passenger capacity. Update to the correct value ; For the latter, route planning is ineffective; To avoid wasting already traveled distance and time, only accept requests that can be separated. One passenger, and the extra Passengers, as new dynamic orders, in the cycle End time and Import and plan together; in contrast, for inseparable orders, if the remaining passenger capacity is insufficient, the order must be rejected. There are two types of order cancellations: a) The predicted future demand was not cancelled, but it was actually cancelled; b) Forecasted future demand was cancelled, but it was not actually cancelled; In scenario a), the predicted future demand has not been cancelled, indicating that passengers... It has already been included in the route by the system; the vehicle may have just arrived or may not have arrived at the boarding station yet; Therefore, the error state variable can be updated directly; In scenario b), the predicted future demand is cancelled, meaning the order does not exist in the planned route; however, since the actual order is not cancelled, the vehicle exists in three states: 'not yet at the pick-up point,' 'just arrived at the pick-up point,' and 'has already passed the pick-up point.' The prediction error for the first two states can be directly updated as in scenario a); however, for the state of 'has already passed the pick-up point,' it needs to be updated within the cycle." At the end of the service, another vehicle will be dispatched to provide service.

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