CN115879620A

CN115879620A - Demand response bus look-ahead scheduling method

Info

Publication number: CN115879620A
Application number: CN202211574144.9A
Authority: CN
Inventors: 巫威眺; 邹弘辉; 卢凯
Original assignee: South China University of Technology SCUT
Current assignee: South China University of Technology SCUT
Priority date: 2022-12-08
Filing date: 2022-12-08
Publication date: 2023-03-31

Abstract

The invention discloses a demand response bus look-ahead scheduling method. The method comprises the following steps: establishing a Markov decision process model based on a rolling time domain framework; predicting future requirements based on quantile regression, an LSTM model and a Copula function; bringing future demands into a common scheduling model, establishing a prediction-based look-ahead scheduling model, and designing error correction mechanisms for look-ahead scheduling and order cancellation respectively; designing a decision pruning strategy, and compressing a solution space to reduce the calculation time; and solving the scheduling scheme by using an approximate dynamic programming algorithm. The invention can not only reduce the cost of operators, but also obviously improve the service quality, and achieve the fine organization and management of demand response bus dispatching. Meanwhile, the algorithm has good solving characteristics and a strong practical application prospect.

Description

Demand response bus look-ahead scheduling method

Technical Field

The invention relates to the research field of a demand response bus dynamic scheduling technology, in particular to a demand response bus prospective scheduling method.

Background

Demand response buses can dynamically change routes and schedules, provide more flexible and accurate travel services for passengers, and have great development potential in future public transport systems. Fixed public transportation systems tend to be more cost effective as they have stable schedules and travel routes. However, demand response public transportation faces a huge development obstacle, and not only is the operation cost high, but also the service level is limited by real factors such as fleet scale and individual demand of passengers. On one hand, the operation cost depends on the order response quantity and the vehicle scheduling scheme, but the control of the operation cost can cause the early or late arrival of the vehicle and reduce the response rate, thereby deteriorating the service level; on the other hand, the future needs of the passengers are uncertain for planning, and the current scheduling schemes are not necessarily applicable to future needs, i.e. future needs have a potentially negative impact. With the development of personalized travel, operators increasingly need to finely organize and manage the scheduling of demand response buses, and cost reduction and efficiency improvement of services are achieved

In the dispatching problem of demand response buses, the operator demand divides the operation time into a plurality of periods, and in each period, a dispatching plan is made for all passenger travel orders led into the system, wherein the dispatching plan comprises a vehicle route, departure time, waiting time and passenger-vehicle distribution. The vehicle starts from different yards, serves passengers according to the route and the time schedule given by the scheduling plan, and finally returns to the yards.

In traditional demand response bus dispatching, operators generally need to process static orders (advance reservation type) and dynamic orders (real-time submission) and make dispatching plans and schedules in real time. In demand response bus look-ahead scheduling, the current demand is processed in real time, and the influence of future demand on the current scheduling decision is also considered. Meanwhile, the system rejects the order due to insufficient transportation resources, and the passenger temporarily cancels the order due to dissatisfaction with the price, the arrival time of the vehicle, and the route of the vehicle. Although models may be built based on deep learning methods to predict future demand, the prediction models may have errors and may have a large impact on scheduling. And because the passenger flow faced by the demand response bus is sparse and uneven, a large number of missing values and abnormal peak values are brought to prediction, and prediction errors are further aggravated. Therefore, in the demand response bus prospective scheduling model, not only a scheduling plan needs to be made in real time, but also the influence of future demands needs should be considered, so that prospective scheduling is formed.

The current demand response bus dispatching research has the following defects and shortcomings: (1) The actual scene of the demand response bus comprises the processes of collecting and processing static and dynamic demands, dynamically inserting orders and optimizing routes, rejecting demands exceeding capacity and the like, wherein the optimized routes comprise changing the existing routes and dispatching new buses, and the dispatching of the new buses needs planning of yard selection, vehicle paths, departure time, intermediate waiting time and the like. Current research lacks one or several of the above scenarios. (2) The planning model is mostly expressed in a static or pseudo-dynamic form, the former simply defines the passenger demand as an appointment type, namely, the optimal route can be obtained by solving the static demand globally once, and the planning model essentially belongs to the customized bus category; the latter is based on the initial driving route, and adopts simple means (such as penalty function, matching according to OD) to insert the real-time dynamic demand into the route so as to approach the dynamic optimization. However, the above means only respond to the dynamic demand as much as possible, but it is difficult to ensure whether the route inserted with the new demand can reach the optimum again, that is, the dynamic optimization (3) in the strict sense is not achieved, wherein a heuristic algorithm is mainly adopted in the solution algorithm, and a few precise algorithm algorithms are adopted. The demand response bus dynamic optimization problem requires that the algorithm meets the requirements of quick solution response, high-quality optimization and the like, the solution time of the accurate algorithm is not practical due to the fact that the quick response idea is violated, and the solution quality is difficult to guarantee by the heuristic algorithm, so that a quick and high-quality solution algorithm is lacked.

Disclosure of Invention

The invention mainly aims to overcome the defects and shortcomings of the prior art and provide a look-ahead scheduling method considering prediction requirements based on a rolling time domain planning frame, which solves the problem that in a demand response bus look-ahead scheduling model, not only a scheduling plan needs to be made in real time, but also the influence of the future requirements needs to be considered so as to form look-ahead scheduling by accurately predicting the future requirements.

The purpose of the invention is realized by at least one of the following technical solutions.

A demand response bus look-ahead scheduling method comprises the following steps:

s1, establishing a Markov decision process model based on a rolling time domain framework;

s2, predicting future requirements based on quantile regression, an LSTM model and a Copula function;

s3, bringing future requirements into a common scheduling model, establishing a prediction-based look-ahead scheduling model, and designing error correction mechanisms for look-ahead scheduling and order cancellation respectively;

s4, designing a decision pruning strategy, and compressing a decoding space to reduce the calculation time;

and S5, solving the scheduling scheme by using an approximate dynamic programming algorithm.

Further, in the step S1, in a rolling time domain framework, a method of delayed batch matching is adopted to allocate a periodic order to a fleet of vehicles, and the principle is to divide an operation time range into a group of periodic sets P = { P | P =1,2, \8230 |, | P | } with a duration of T, and then to introduce any periodic riding order into the system after delaying, until the period is over, the introduced order is matched to the vehicle; the matching result is accepted or rejected, and the result passes through a preset buffer time t after the period is ended _B Then the passenger is informed; the matched orders in each period can be executed in the next period, and the orders can be divided into served orders and matched but unserviced orders according to the execution state; since the passenger has been matched by the system and notified that the matched but unserviced order is not allowed to be rejected, it will be reassigned to the vehicle in the next cycle, the reassigned vehicle being either the same vehicle or another vehicle;

the rolling time domain frame comprises an order stage, a planning stage, an operation stage and a prediction stage, wherein the order stage and the prediction stage are firstly carried out to import an order into the system, then the planning stage carries out route planning on the imported order, and finally the planned route is executed in the operation stage; the scheduling plan of the current period is correlated with the execution state of the previous period; the dynamic order is not imported at the beginning of the period | P |, so that all phases except the service phase end at the end of the period | P | -1, and the vehicle v only in the service phase will still be able to enter the vehiclePlanning route planned in cycle | P | execution cycle | P | -1

A dynamic order imported with period p +1 would result in the planned route of the vehicle v being taken in/on with period p>

Incomplete execution of (2); in each subsequent cycle, the operator must not only consider the cycle p for newly introducing a passenger ≥ from the entry station i to the exit station j for a dynamic order>

Consideration is also given to matching but not served passengers->

Since the planning phase always lags behind the order phase by one cycle, a buffer time t of negligible length is set at the end of each cycle _B To plan dynamic orders; planning the route will be performed in the operational phase immediately after the buffering time.

Further, the DRT scheduling problem is modeled as a Markov Decision Process (MDP), as follows:

defining a state variable:

/>

in the formula (1), the first and second groups of the compound,

a state variable representing phase k of cycle p; />

Represents the state of the upper stop of order r in phase k of period p, if the passenger has already got on the car, then->

Otherwise, is greater or less>

Represents the state of the departure station of order r in phase k of cycle p, if a passenger has arrived->

Otherwise, is greater or less>

Representing the position of the vehicle v in phase k of the cycle p; />

Representing the remaining driving mileage of the vehicle v in the period p and the period k; />

Representing the remaining passenger capacity of the vehicle v in the period p phase k; />

Represents the accumulated travel time of the vehicle v in the period p phase k; />

Representing an overcycle time of the vehicle v at the cycle p, if the travel time of the vehicle exceeds a cycle time T->

Otherwise, is greater or less>

Represents a running route of the vehicle v at a period p;

|K ^p the specific values of | per cycle are as follows:

due to planning of the route

May exceed a cycle time T; the execution time may only cover a part of the stations in the planned route, i.e. the vehicle cannot execute the planned route of the period p in the next period p +1, so that the state variable information is confused; in order to solve this problem, a supercycle time ^ of the vehicle v in the period p phase k is introduced>

If the travel time of the vehicle exceeds a cycle time T @>

Otherwise, is greater or less>

Defining a decision variable:

in equation (3), if a vehicle v located in the yard m is used in the period p phase k, then

If not, then the mobile terminal can be switched to the normal mode,

if an order r is assigned to a vehicle v in a period p in phase k @>

Otherwise, is greater or less>

If the vehicle v goes from station i to station j in phase k of period p @>

Otherwise, is greater or less>

Representing the waiting time of the vehicle v at the station j in the period p and the period k;

the construction scenario is as follows:

scenario 1:

this scenario shows that a vehicle v in the yard waits for a period of time

Since the vehicle waits in the yard, the station j to which the vehicle goes at the current stage is still the yard m to which the vehicle v belongs _v ；

If the vehicle is at the earliest time ET for getting on the vehicle as declared by order r _r Get ahead to its station, the vehicle needs to go to station i _r Waiting; and enabling the vehicle to wait in the parking lot, wherein the waiting time is calculated as follows:

in the formula (4), d _ij Represents the shortest distance from station i to station j;

represents the running speed of the vehicle and>

represents the accumulated travel time of the vehicle v in the period p and the period k;

scenario 2:

/>

this scenario indicates that an outbound vehicle v travels from station i to station j, where it may wait; an in-transit vehicle v heading for station j may have the following status:

1) The vehicle is empty before going to the station;

2) The vehicle has passengers in front of the station;

3) The vehicle goes forward to a station;

since the time window of the lower station is not specified, the third state will not be discussed; assuming that there are passengers in the vehicle before going to the passenger station, if the vehicle is at the earliest time ET _r Before arriving at the upper station, the vehicle must wait for a period of time; however, waiting at the boarding station is undesirable to the passengers on the car; more importantly, in the framework of rolling horizon planning of DRT scheduling, when the vehicle v waits at station j in period p phase k

If long enough, the period time T may be exceeded, causing the decision for that period to be invalid; therefore, when there is a passenger on the vehicle, a boarding station that needs to wait should be avoided; for this purpose, the following limitations are introduced:

in state variables before making scheduling decisions

The travel route of the vehicle v at the period p has been recorded; if->

Including a disembarking station corresponding to the serviced boarding station, i.e. no passenger is present, the vehicle can go to any boarding station and the waiting time ÷ for the vehicle v at station j in phase k of period p>

Calculated by formula (4); otherwise, the vehicle is allowed to go to the boarding point which arrives in the time window only if passengers exist on the vehicle; if the vehicle arrives at the station in advance on the premise that the passengers are in the vehicle, the planned route is wrong;

scenario 3:

the scenario shows that the vehicle v returns to the place m _v 。

Further, a constraint is defined:

/>

wherein the constraint condition (5) requires that each yard has the maximum number of available vehicles; the constraint (6) requires that each vehicle can only be used at most once per cycle; constraints (7) ensure that all submitted orders are imported into the system; the constraint (8) ensures that all orders are processed at the beginning of the period | P |; constraint (9) ensuresOrders with import should be in the final stage

Is sent from the upper station to the corresponding lower station; the constraint (10) indicates that from cycle 1 to cycle | P | -1, the order r can be decided twice at most; due to the route decision of each stage>

Only one boarding or disembarking station containing order r and each order can be serviced by only one vehicle, so there are two &'s associated with order r in each cycle>

The decision of (1); due to>

And &>

Form a tuple, so>

There are at most two decisions; constraint (11) indicates that there is no decision within period | P |; the constraint (12) and constraint (13) ensure that the allocated order does not exceed the remaining travel distance and the remaining capacity of the vehicle, respectively; the constraint (14) requires that the vehicle be late not to exceed a threshold value->

The constraint (15) defines a duration constraint of the overcycle time; constraints (16) - (19) describe the nature of decision variables which are @, if a vehicle v located in the yard m is used in a period p phase k>

Otherwise, is greater or less>

If the vehicle v goes from station i to station j in phase k of period p @>

Otherwise, is greater or less>

Defining a state transition equation:

(3) Phase state transition equation

Phase state transition equation

The change of each attribute of the state variable under different decision variables is described, and the purpose is to plan the route of each period;

state variables of period p phase k

The transfer function of each attribute in (b) depends on the context of the decision variables, as follows:

/>

in equations (21) and (22), once the vehicle is dispatched to the entering station or the leaving station,

and &>

Are respectively updated; equation (23) specifies the position of the vehicle v; in the formula (24), the remaining travel distance of the vehicle v is not changed for the scenario 1; 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 yard; in equation (25), the remaining capacity of the vehicle v is unchanged for scenario 1; for scenario 2, the remaining capacity of vehicle v is reduced by the number of passengers for order r; for scenario 3, when the vehicle returns to the yard, the capacity is updated to maximum passenger capacity; in the formula (26), for scenario 1, the accumulated travel time of the vehicle v increases the waiting time at the yard; 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, accumulating travel time increases travel time, wait time, and service time;

(4) Periodic state transfer equation

Albeit phase state transition equation

Status variable which uses the period p phase k>

The route is planned for each cycle, but since the planned route of the vehicle v is ≥ in cycle p>

Has not yet been executed, so a state variable>

Does not change, the travel route of the vehicle v in the period p +1 +>

The planned route ≥ for period p only executes the period p within time T of period p +1>

Can be determined later; therefore, a periodic state transition equation is required>

External information G with period p changed to period p +1 ^p Can be based on the planned route

And the cycle time T is obtained; an initial status variable for the next cycle>

The equation may be transferred by the cycle state>

To iteratively calculate; based on this principle, the external information G between cycles ^p Can be obtained as follows;

the actual available travel time of the vehicle v in the period p is

External information G ^p From available travel time>

A route execution length;

specifically, first determining the available travel time is

When the vehicle runs out, which station the vehicle runs to, each station on the way and the station form a running route>

Status variable ≥ on the next cycle>

Can be determined by calculating the driving route pair>

The resulting change.

Further, an objective function is defined:

the cost of DRT scheduling includes fixed transportation cost, variable transportation cost and time penalty cost; the fixed transportation cost is related to the number of vehicles used, and the calculation formula is as follows:

/>

in the above expression, α _f Representing the fixed transportation cost per vehicle. Varying the transportation cost depending on the distance traveled; since a new path is created at each stage k, the cost of the variable transportation can be calculated as follows:

the time window violation penalty costs include early and late arrivals; late penalty system alpha _l And an early arrival penalty factor alpha _e Satisfies alpha _l >β _e (ii) a If the arrival time of the vehicle is within the specified time window, the penalty cost is 0; otherwise, the penalty cost depends on the length of the violation period; and the early and late arrival times of order r can be calculated as

And

the per-stage time window violation penalty cost is calculated as follows:

the cost function of the DRT model is related to the newly generated cost of each stage k; the cost of stage k of period p is equal to the cost of the previous stage

Plus the variable transportation costs incurred by that stage>

And a penalty cost->

As follows:

since the fixed transportation costs are at the stage of the final cycle

Calculating, adding the fixed transportation cost CF to the cost of the final stage, specifically as follows:

to represent the DRT problem as an SADP model, the following best-state cost function is proposed based on bellman's equation:

wherein the content of the first and second substances,

it is the phase k execution path policy ≥ of period p>

Best state cost function of;

predicted random order matrix under look-ahead scheduling

Is greater than or equal to>

The objective function needs to be included; to ensure iterative stability of the SADP algorithm, the @>

Indicating that the path policy is executed at stage k of period p->

The objective function is modified as follows:

passenger-vehicle assignment is crucial to route planning;

an order rejection mechanism is proposed, the rules of which are described as follows:

once the order cannot be completely matched, so that

The planning process is terminated; pick-up station i for orders r that cannot be matched _r And a lower passenger station j _r Then the stations are considered potential rejection stations and the solution is repeated after they are removed one by one until the remaining orders can be matched.

Further, in step S2, the predicting future demand based on quantile regression, the LSTM model, and the Copula function is specifically as follows:

predicting the future requirement of each OD pair in a conditional quantile equation under different quantile levels, and constructing empirical distribution to realize interval estimation;

where ζ represents the equation coefficient when the quantile level is equal to τ; when linear programming is used to solve for the optimal zeta, the conditional tau quantile equation can be obtained

For different quantiles τ, the equation (34) can be solved separately for each τ, from which the @, for different quantile levels, can be derived>

To predict future demand

History data for cycle 1 to cycle p are->

As a training data set; due to the need to predict future demand for different quantile levels, make/combine>

Representing quantile level τ _l OD requirement ofLevel set is τ _l = {5%,25%,50%,75%,95% }; therefore, the loss function of the LSTM model is modified to the optimization equation of the fractional regression in equation (35) as follows:

in this way, quantile samples of future demand for each OD pair can be obtained

Need->

Subject to the performance of the quantile sample, i.e.>

It can be expressed as an empirical distribution as follows:

thus, by empirical distribution

In (d) samples, a random prediction value @foreach OD pair may be obtained>

The method comprises the following specific steps:

by repeating the random sampling process, a plurality of prediction samples of each OD pair can be obtained; thus, by sampling all OD pairs, a random OD matrix of period p is obtained

Its dimension is | S- ² The method comprises the following steps:

the edge distributions of different OD pairs may be correlated, while the joint distribution may capture this correlation;

therefore, the edge distribution is merged into a joint demand distribution by using a copula, which is as follows:

order to

Respectively representing the need of each OD pair>

Cumulative Distribution Functions (CDFs); based on a multivariate CDF, random vector &basedon the composition of the respective variables>

Can be expressed as follows:

for each OD pair, it can be determined by empirical distribution

The middle sample gets a random demand>

Giving the edge distribution of each OD pair

I.e. is>

CDF of (1), and according to the Copula theory of sklarMachine vector->

May be defined as an edge distribution @ofthe respective vector>

And a Copula function, as follows:

gaussian copolas was used as follows:

wherein, C _G Denotes Gaussian Copula, phi _σ A joint CDF representing a multivariate normal distribution with a covariance matrix of σ and a mean of 0;

using C _G Can be selected from

Obtaining a future demand sample in the joint distribution; when doing so, it is selected>

First from C _G In and then converts the sample into->

Finally, Φ is mapped to the chosen samples by inverse mapping of the edge CDFs, as follows:

finally, a joint distribution function phi is obtained _σ Will be

Substituted into phi _σ The joint occurrence probability is obtained>

Further, in step S3, bringing the future demand into a common scheduling model, establishing a prediction-based look-ahead scheduling model, and designing error correction mechanisms for look-ahead scheduling and order cancellation respectively, specifically as follows:

unlike ordinary scheduling, look-ahead scheduling not only takes into account

And &>

Also taking into account the predicted future demand of the upcoming period p + 1; in this scheduling mode, future demands for the next cycle->

Is predicted in advance at period p and is combined with->

And &>

Optimizing together; therefore, training to predict future demand should be done periodically on a rolling basis; at period p, in order to predict future demand for period p +1, the training data set should include the demands of the previous and current periods, i.e., { - } { ->

Further, in step S3, a correction mechanism is proposed to reduce the negative effect of the prediction error;

planned path due to vehicle performing look-ahead scheduling at the end of period p

The route cannot be adjusted within the time T of the next period; thus, only when the vehicle v arrives at the upper station i _r Can only then check the remaining passenger load>

Whether a real number of passengers can be accommodated;

thus, the prediction error can be classified into two types, i.e., the predicted value is larger than the actual value, i.e.

And less than actual value i>

In the former case, the remaining passenger capacity can accommodate the number of passengers, so that it is only necessary to set the original remaining passenger capacity

Updated to the correct value->

For the latter, the planned route is invalid;

to avoid wasting consumed travel distance and travel time, only the requests which are separable are connected

Individual passenger, but redundant>

The passenger can act as a new dynamic order, at the end of the period p +1 and ≥>

Importing and planning together; in contrast, for an inseparable order, if the remaining passenger capacity is insufficient, the order must be rejected;

for canceling orders, the prediction error can be classified into two types, namely:

the predicted future demand is not cancelled, but is actually cancelled;

the predicted future demand is cancelled, but not actually;

for the former, the wrong state variables can be updated directly; for the latter, there are three states of 'not arriving at the boarding point', 'just arriving at the boarding point', and 'having traveled past the boarding point'; the prediction errors of the first two states can be directly updated; and for the 'has traveled past the pick-up point' state, another vehicle needs to be dispatched to service at the end of the period p + 1.

Further, in step S4, a pruning strategy for decision is designed, and a decoding space is compressed to reduce the calculation time, which specifically includes:

the lower bound pruning of the vehicle remaining distance is as follows:

since the vehicle v must transport all passengers in the vehicle to the corresponding departure point, if it is possible to move ahead along the arc (i, j) ∈ a to a new departure point j = i _r Before, it is very meaningful to judge whether the remaining cruising distance of the vehicle can meet the mileage requirement of a subsequent path;

theorem 1: vehicle v goes to pick-up point j = i at phase k of cycle p _r When the time is long, the residual cruising distance always has a lower bound

Theorem 2: compared with the standard dynamic programming algorithm, after the pruning operation is adopted, the saved state space in all the stages in the period p is achieved

The waiting time is optimized specifically as follows:

the vehicle can wait when being located the parking lot to optimize the departure time, prevent that it from producing great time penalty cost when going to first point of getting on bus. Get-on vehicle needing service after waitingPoint i _r The vehicle is decided, and the subsequent path of the vehicle-entering point cannot be observed, so that the arrival time of the vehicle at the vehicle-entering point is optimized; waiting time

The optimal value of (c) is calculated as shown in equation (43): />

Calculating an optimal penalty cost by (44)

The method comprises the following specific steps:

returning to the parking lot for pruning, which is concretely as follows:

when the vehicle is at the point of departure after a visit, and there are no remaining passengers on the vehicle, the vehicle will face two decisions:

(e) Go to another boarding point;

(f) Returning to the affiliated parking lot m _v ；

The pruning strategy is as follows: when in use

When a decision is made as to path (f); when +>

A decision is made as to path (e).

Further, in step S5, the scheduling scheme is solved by using an approximate dynamic programming algorithm, which specifically includes:

in the first place

On a second iteration, the operator uses the ^ h->

Merit function after a sub-iteration->

Makes a decision->

The estimated value of the state after the approximate decision is obtained by adopting a time sequence difference updating method

Sub-iteration makes->

Converge on>

When λ =0 in TD (λ), there is a special case as shown in equation (48):

unbiased sample estimation due to end stage

Involving a cost function of the initial phase of the next cycle

However, status +>

Is often not +>

The direct iteration results in a ≧ greater or lesser status of the decision, incomplete execution of the planned path, or>

A large deviation occurs, so a cost function rolling strategy needs to be adopted;

suppose that

Sub-iteration, planned path of period p @>

Is actually performed by the vehicle to +>

Then the initial state for period p +1 is substantially equal to &' s>

I.e. is>

To ensure stability of the state cost function updates at the beginning and end of adjacent cycles, the ^ th greater or lesser than the maximum value>

Status after a sub-iteration->

Is rolled to->

As in equation (49): />

First, the

Sub-iteration, end state->

Although related to->

But initial status of the next cycle>

Inherit the status of the period->

So that its calculation should be added to +>

Makes a decision->

The value of (A):

in the same way, the method for preparing the composite material,

the cost function approximation of (c) may use the medium TD (λ) and TD (0) methods of equation (51).

In the initial stage of the period p, n period p +1 random OD matrixes given by a prediction model are introduced, and then under n random demandsSample decisions made

The method comprises the following specific steps:

when the sample is in the state

Run to>

N sample planning paths are formed; to evaluate the impact of random demand on each sample planned path, the value of each sample path is approximated using TD (λ) and TD (0) methods:

due to random OD matrix

In conjunction with a probability of occurrence>

There is a difference in the value function->

Searching a minimum expected value function, and respectively taking the minimum expected value function and the corresponding random demand as a value function under a look-ahead strategy and an optimal random demand of a period p + 1:

compared with the prior art, the invention has the following advantages and effects:

the invention establishes a Markov decision process model under a rolling time domain framework; predicting future requirements based on quantile regression, an LSTM model and a Copula function; bringing future demands into a common scheduling model, establishing a prediction-based look-ahead scheduling model, and designing error correction mechanisms for look-ahead scheduling and order cancellation respectively; a decision pruning strategy is designed, and the decoding space is compressed to reduce the calculation time; and solving the scheduling scheme by using an approximate dynamic programming algorithm. The demand response bus dispatching fine organization and management are achieved, and cost reduction and efficiency improvement of service are achieved.

Drawings

FIG. 1 is a flow chart of a demand response bus look-ahead scheduling method in an embodiment of the present invention;

FIG. 2 is a flow chart of scheduling in an embodiment of the present invention;

FIG. 3 is a diagram of a rolling time domain scheduling framework in an embodiment of the invention;

FIG. 4 is a graphical representation of overcycle time in an embodiment of the invention;

FIG. 5 is a schematic diagram of decision variables in an embodiment of the present invention;

FIG. 6 is a diagram of a cost function scrolling and look-ahead strategy in an embodiment of the invention;

FIG. 7 is a distribution diagram of the "pieced Bus" project Bus stops and yards in accordance with an embodiment of the present invention;

FIG. 8 is a schematic diagram illustrating the calculation result of EAUC in the "Ping Bus" project in the embodiment of the present invention;

FIG. 9 is a diagram illustrating the calculation results of EAPM in the "Pin Bus" project in accordance with an embodiment of the present invention;

FIG. 10 is a diagram illustrating the calculation results of MURs in the "Pin Bus" project in accordance with an embodiment of the present invention;

FIG. 11 is a diagram illustrating the results of RR calculations in the "Pin Bus" project in an embodiment of the present invention;

FIG. 12 is a diagram illustrating LR calculation results in the "Bus" project according to an embodiment of the present invention;

FIG. 13 is a diagram illustrating the calculation of ALT in the "Pinyin Bus" project in accordance with an embodiment of the present invention.

Detailed Description

The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto. First, in order to facilitate the following description of the mathematical model, table 1 lists symbolic variables related to the present invention.

TABLE 1 symbolic variables

/>

/>

A demand response bus look-ahead scheduling method is shown in fig. 1 and 2, and comprises the following steps:

as shown in fig. 3, the rolling time domain frame includes an order stage, a planning stage, an operation stage and a prediction stage, wherein the order stage and the prediction stage are performed to import an order into the system, the planning stage performs route planning on the imported order, and the planned route is performed in the operation stage; the scheduling plan of the current period is correlated with the execution state of the previous period; the dynamic order is not imported at the beginning of the period | P |, and only the vehicles v in the operation stage execute the planned route in the period | P |

A dynamic order introduced at period p +1 results in the planned route of vehicle v being ≥ n at period p>

Consideration is also given to matching but not served passengers->

defining the state variables:

|K ^p the specific values of | per cycle are as follows:

as shown in FIG. 4, the planned route of cycle 1 is

But the execution time of cycle 2 is only between station 2 and station 3. That is, when the vehicle has not arrived at station 3, the system will import a new order and re-generate a route. One reasonable improvement is to have the vehicle continue to station 3 in the previously planned route, and then the 1 st cycle travel route is taken from ≧ greater than or equal to>

Is changed into->

Wherein the time which is consumed more by the travel to the station 3 is recorded as the supercycle time ≥>

Defining decision variables:

as shown in fig. 5, the decision scenario is constructed as follows:

scenario 1:

scenario 2:

scenario 3:

if the vehicle is at the earliest time ET for getting on the vehicle as declared by order r _r Forward to its upper station where vehicles need to go i _r Waiting; it is reasonable to let the vehicle wait in the parking lot, and the waiting time is calculated as follows:

further, an objective function is defined:

in the above expression, β _f Representing the fixed transportation cost per vehicle.

The cost of variable transportation for each stage k can be calculated as follows:

the time penalty cost per phase k can be calculated as follows:

the cost function of the DRT model is related to the newly generated cost for each stage k; the cost of phase k of period p is equal to the cost of the previous phase

Plus the variable transportation costs incurred by that stage>

And a penalty cost->

As follows:

since the fixed transportation costs are at the stage of the final cycle

wherein the content of the first and second substances,

it is the phase k execution path policy ≥ of period p>

Best state cost function of;

predicted random order matrix under look-ahead scheduling

Is greater than or equal to>

The objective function needs to be included; make->

Indicating that the path policy is executed at stage k of period p->

The objective function is modified as follows:

once the order cannot be completely matched, so that

S2, predicting future requirements based on quantile regression, an LSTM model and a Copula function, and specifically comprising the following steps:

predicting the future requirement of each OD pair in a conditional quantile equation under different quantile levels so as to construct empirical distribution to realize interval estimation, wherein an optimization model of quantile regression is modified into a formula (35) as follows:

the method adopts the LSTM model to predict future requirements

The loss function is modified as follows:

in this way, quantile samples of future demand for each OD pair can be obtained

Need->

Subject to the performance of the quantile sample, i.e.>

It can be expressed as an empirical distribution as follows:

/>

by empirical distribution

Medium sample, a random predictor value @, for each OD pair may be obtained>

The method comprises the following specific steps:

Its dimension is | S- ² The method comprises the following steps:

edge distributions of different ODs are merged into a joint demand distribution by using a copula, which is as follows:

gaussian copolas was used as follows:

map Φ to the chosen samples by inverse mapping of the edge CDFs, as follows:

finally, a joint distribution function phi is obtained _σ Will be

Substituted into phi _σ The joint occurrence probability is obtained>

S3, bringing future requirements into a common scheduling model, establishing a prediction-based look-ahead scheduling model, and designing error correction mechanisms for look-ahead scheduling and order cancellation respectively, wherein the error correction mechanisms are as follows:

look-ahead scheduling simultaneous optimization

And a predicted future demand for the upcoming cycle p + 1; as shown in fig. 3, the future demand of the next cycle +>

Is predicted in advance at period p and is associated with->

And &>

Are optimized together. Meanwhile, when the dynamic order of the next period is imported, the prediction error is corrected; for example, cycle 2, first on a dynamic order->

Correction time period t ₀ -T,t ₀ ]Is/is>

And obtain a matching but unserviced order &>

At the same time, during the prediction time period t ₀ ,t ₀ +T]Is based on a future need->

Then will->

And &>

In a time period t ₀ ,t ₀ +t _B ]Plan together and then schedule the vehicle for a time period t ₀ +t _B ,t ₀ +T]Performing;

The route cannot be adjusted within the time T of the next period; thus, only when the vehicle v arrives at the upper station i _r Can only check the remaining passenger capacity->

Whether a real number of passengers can be accommodated;

And less than the actual value, i.e.>

In the former case, the remaining passenger capacity can accommodate the number of passengers, so that only the original remaining passenger capacity needs to be used

Updated to the correct value->

For the latter, the planned route is invalid;

to avoid wasting consumed travel distance and travel time, only those requests that can be split are received

Individual passenger, but redundant>

The passenger can act as a new dynamic order in conjunction with the end of period p +1>

the predicted future demand is not cancelled, but is actually cancelled;

the predicted future demand is cancelled, but not actually;

for the former, the wrong state variables may be updated directly; for the latter, there are three states of 'not arriving at the boarding point', 'just arriving at the boarding point', and 'having traveled past the boarding point'; the prediction errors of the first two states can be directly updated; for the 'has traveled past the departure point', another vehicle needs to be dispatched to service at the end of the period p + 1.

S4, designing a decision pruning strategy, and compressing a decoding space to reduce the calculation time, wherein the method specifically comprises the following steps:

the lower bound pruning of the vehicle remaining distance is as follows:

the lower bound of the remaining range is uniformly expressed as shown in formula (20).

The decision that the residual driving distance is smaller than the lower bound can be eliminated by utilizing the lower bound pruning of the residual driving distance of the vehicle, and the decision cannot be a decision selected on the optimal path because the decisions are smaller than the lower bound, namely, the optimal solution is guaranteed not to be pruned.

The waiting time is optimized specifically as follows:

the arrival time of the vehicle at the station can be optimized when the vehicle is located in the parking lot. Waiting time

The optimal value of (2) is calculated as shown in equation (21):

calculating an optimal penalty cost by (22)

The method comprises the following specific steps:

returning to the parking lot for pruning, which is concretely as follows:

when in use

When a decision is made, as path (f); when/is>

A decision is made as to path (e).

S5, solving the scheduling scheme by using an approximate dynamic programming algorithm, which comprises the following specific steps:

in the first place

Sub-iteration, operator uses a th &>

Merit function after a sub-iteration->

Makes a decision->

/>

Sub-iteration makes->

Converge on>

When λ =0 in TD (λ), there is a special case as shown in equation (25):

in order to ensure the stability of the state cost function update at the beginning and the end of the adjacent period, the method

Status after sub-iteration>

Is rolled to->

As in equation (26):

first, the

Sub-iteration, end state>

Although related to->

But the initial status of the next cycle->

Inherits the status of the cycle @>

Therefore, it should be calculated to add->

Makes a decision->

The value of (A):

in the same way, the method has the advantages of,

the cost function approximation of (c) may use the medium TD (λ) and TD (0) methods of equation (28).

All steps of the cost function rolling strategy are summarized in table 2.

TABLE 2 VALUE FUNCTION ROLLING POLICY PSEUDO-CODE

/>

In the initial stage of the period p, n period p +1 random OD matrixes given by a prediction model are introduced, and then sample decisions are made under n random demands

The method comprises the following specific steps:

when the sample is in the state

Run to>

due to random OD matrix

In conjunction with a probability of occurrence>

There is a difference in the value function of the samples n>

Medium search minimum expectationAnd the value function and the corresponding random demand are respectively used as the value function under a prospective strategy and the optimal random demand of the period p + 1:

example 1:

in this embodiment, the Guangzhou public transportation company has established 68 upper stations and 100 lower stations for the "Pinbus" project in the region through a real demand response public transportation project, namely the "Pinbus" project in Guangzhou university City. The spatial distribution of bus stations and yards is shown in fig. 7.

Fig. 8 to 13 compare the actual operation, the ordinary operation and the prospective operation of the "joined BUS" project on six indexes. The common operation and the forward-looking operation are found to be superior to the actual operation in six indexes, except that the actual operation in a certain few days is slightly better than the common operation in the late time rate and the average late time. The average increase in prospective operation over 7 days compared to actual operation is as follows: the number of vehicles is reduced by 11.43%, the average cost of effective passengers is reduced by 38.35%, the average mileage of effective passengers is reduced by 23.76%, the mileage utilization rate is increased by 20.05%, the response rate is increased by 13.30%, the late time is reduced by 14.46%, and the average late time is reduced by 1.81 minutes. Then, the overall increase in the "LSTM + Quantile + Copula" model over 7 days compared to the "LSTM + Quantile" model is as follows: mean effective passenger cost (EAUC) increased by 3.73%, mean effective passenger mileage (EAPM) decreased by 11.31%, mileage Utilization (MUR) increased by 6.26%, response Rate (RR) increased by 14.09%, late point rate (LR) increased by 0.13%, mean late point time (ALT) increased by 0.02 min. Although Copula's theory worsens the late rates and average late times and thus the average cost of active passengers, this negative effect is almost negligible. However, the performance improvement of effective passenger average mileage, mileage utilization rate and response rate due to Copula capturing spatial correlation is huge, which shows that the exploration of spatial features of the reinforced prediction model can improve the service efficiency of the prospective operation with small consumption of system cost. In addition, the overall increase in the 7-day quantile + LSTM model compared to the LSTM model is as follows: the average cost of the effective passengers is reduced by 4.19%, the average mileage of the effective passengers is reduced by 17.91%, the mileage utilization rate is increased by 17.41%, the response rate is increased by 7.67%, the late time rate is reduced by 0.40%, and the average late time is reduced by 0.06 min. Due to the quantile interval estimation, the prediction uncertainty of sparse passenger flow can be overcome, and the prediction deviation caused by default values and abnormal peak values is reduced. Therefore, replacing the point estimates of the "LSTM" model with interval estimates can effectively address the challenges of sparse order data.

The result shows that the prospective scheduling method and the solving algorithm provided by the invention have good characteristics and can be popularized to practical application.

The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims

1. A demand response bus look-ahead scheduling method is characterized by comprising the following steps:

2. The demand response bus look-ahead scheduling method according to claim 1, wherein in step S1, delayed batch matching is adopted in a rolling time domain frameworkThe method comprises the steps of distributing a periodic order to a motorcade, dividing an operation time range into a group of periodic sets P = { P | P =1,2, \8230 |; | P | } with the duration T, and then leading the riding order of any period into a system after delaying, and matching the led order to a vehicle when the period is over; the matching result is accepted or rejected, and the result passes through a preset buffer time t after the period is ended _B Then the passenger is informed; the matched orders in each period can be executed in the next period, and the orders can be divided into served orders and matched but unserviced orders according to the execution state; since the passenger has been matched by the system and notified that the matched but unserviced order is not allowed to be rejected, it will be reassigned to the vehicle in the next cycle, the reassigned vehicle being either the same vehicle or another vehicle;

the rolling time domain frame comprises an order stage, a planning stage, an operation stage and a prediction stage, wherein the order stage and the prediction stage are firstly carried out to import an order into the system, then the planning stage carries out route planning on the imported order, and finally the planned route is executed in the operation stage; the scheduling plan of the current period is correlated with the execution state of the previous period; the dynamic order is not imported at the beginning of the period | P |, so that all phases except the service phase end at the end of the period | P | -1, and the vehicle v only in the service phase executes the planned route planned by the period | P | -1 at the period | P |

Also consider the piece from the boarding station i to the disembarking station j up to the period pMatched but not served passenger->

3. The demand-response bus look-ahead scheduling method of claim 2, wherein the demand-response bus (DRT) scheduling problem is a variation of a pickup vehicle routing problem with time windows, which further considers a plurality of yards, departure time optimization, latency optimization, dynamic ordering, passenger-vehicle matching and order rejection mechanisms; in the present invention, the DRT scheduling problem is modeled as a Markov Decision Process (MDP), as follows:

defining a state variable:

in the formula (1), the first and second groups of the compound,

state variables representing the p phases k of the period; />

Otherwise, is combined with>

Otherwise, is greater or less>

Representing the position of the vehicle v in phase k of the cycle p; />

Representing the remaining driving mileage of the vehicle v in the period p phase k; />

Otherwise, is combined with>

Represents a running route of the vehicle v at a period p;

then deducing the periodTotal phase of p | K ^p The numerical value of | for the sake of simplifying the symbolic representation, k is represented by the symbol k ^p I.e. k = k ^p (ii) a By symbols

Denotes the number of final stages per cycle | K ^p I | in combination>

For phase k, the system will assign the order r to the vehicle v and generate the external information ≥>

Passes the phase transfer equation->

Obtaining a state variable of the next stage; in each cycle the route is planned for all imported orders, if order r is imported in period p ≥>

If not, then,

for example, in cycle 1, since the imported order has not been serviced by the vehicle, the final number of stages | K ^p | equals the number of stations for static orders; in the 2 nd cycle to the | P | cycle, | K ^p An induction variable with a specific value per cycle equal to the number of unserviced sites for all imported orders, as follows:

due to planning of the route

Is provided withThe line time may exceed one cycle time T; the execution time may only cover a part of the stations in the planned route, i.e. the vehicle cannot execute the planned route of the period p in the next period p +1, so that the state variable information is confused; to solve this problem, a supercycle time £ of the vehicle v in the period p phase k is introduced>

If the travel time of the vehicle exceeds a cycle time T @>

Otherwise, is greater or less>

Defining a decision variable:

in the formula (3), if the vehicle v located at the yard m is used in the period p phase k, then

If not, then,

if an order r is assigned to a vehicle v in a period p phase k, then @>

Otherwise, is combined with>

If the vehicle v goes from station i to station j in phase k of period p @>

Otherwise, is greater or less>

Representing the waiting time of the vehicle v at the station j in the period p and the phase k;

the construction scenario is as follows:

scenario 1:

this scenario shows that a vehicle v in the yard waits for a period of time

Since the vehicle waits in the yard, the stop j to which the vehicle is heading at the current stage is still the yard m to which the vehicle v belongs _v ；

If the vehicle is at the earliest time ET for getting on the vehicle as declared by order r _r Get ahead to its station, the vehicle needs to go to station i _r Waiting; it is reasonable to make the vehicle wait in the parking lot, and the waiting time is calculated as follows:

indicates the vehicle running speed and is greater or less>

Scenario 2:

this scenario indicates that an outbound vehicle v travels from station i to station j, where it may wait; a vehicle v in transit heading for station j may have the following status:

1) The vehicle is empty before going to the station;

2) The vehicle has passengers in front of the station;

3) The vehicle goes forward to a station;

since the time window of the lower station is not specified, the third state will not be discussed; assuming that there are passengers in the vehicle before going to the passenger station, if the vehicle is at the earliest time ET _r Before arriving at the upper station, the vehicle must wait for a period of time; however, waiting at the bus stop is undesirable for passengers in the bus; more importantly, in the framework of rolling horizon planning of DRT scheduling, when the vehicle v waits at station j in period p phase k

in state variables before making scheduling decisions

The travel route of the vehicle v at the period p has been recorded; if->

Including the off-stop corresponding to the served on-stop, i.e. no passenger is present, the vehicle can go to any on-stop and the waiting time ≥ for station j during period p, phase k>

Calculated by formula (4); otherwise, the passenger is present on the vehicle, and the vehicle is onlyAllowing the departure of the pick-up point reached within the time window; if the vehicle arrives at the station in advance on the premise that passengers exist in the vehicle, the fact that the planned route of the vehicle is wrong is indicated;

scenario 3:

the scenario shows that the vehicle v returns to the place m _v 。

4. The demand response bus look-ahead scheduling method of claim 3, wherein a constraint condition is defined:

/>

wherein the constraint condition (5) requires that each yard has the maximum number of available vehicles; the constraint (6) requires that each vehicle can only be used at most once per cycle; constraints (7) ensure that all submitted orders are imported into the system; the constraint condition (8) ensures that all orders are processed at the starting time of the period | P |; restraint stripThe member (9) ensures that all imported orders should be in the final stage

Is sent from the upper station to the corresponding lower station; the constraint (10) indicates that from cycle 1 to cycle | P | -1, the order r can be decided twice at most; due to the route decision of each stage->

Only one getting-on or getting-off station containing order r and each order can be served by only one vehicle, so there are two associated with order r in each cycle

The decision of (1); due to>

And &>

Form a tuple, so>

There are at most two decisions; constraint (11) indicates that there is no decision within period | P |; the constraint (12) and the constraint (13) ensure that the allocated order does not exceed the remaining travel distance and the remaining capacity of the vehicle, respectively; the constraint (14) requires that the vehicle be late not to exceed a threshold value->

Otherwise, is greater or less>

If the vehicle v goes from station i to station j in phase k of period p @>

Otherwise, is greater or less>

Defining a state transition equation:

(1) Phase state transition equation

Phase state transition equation

state variables of period p phase k

The transfer function of each attribute in (1) depends on the context of the decision variables, as follows:

/>

and &>

Are respectively updated; equation (23) specifies the position of the vehicle v; in the formula (24), the remaining travel distance of the vehicle v is not changed for the scenario 1; 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 yard; in equation (25), the remaining capacity of the vehicle v is unchanged for scenario 1; for scenario 2, the remaining capacity of vehicle v is reduced by the number of passengers for order r; for scenario 3, when the vehicle returns to the yard, the capacity is updated to maximum passenger capacity; in equation (26), for scenario 1, the cumulative travel time of vehicle v increases the waiting time at the yard; 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, accumulating travel time increases travel time, wait time, and service time;

(2) Periodic state transition equation

Albeit phase state transition equation

Status variable ≥ using period p phase k>

Has not yet been executed, so a state variable>

Is not changed, the travel route of the vehicle v is/are based on the period p +1>

And the cycle time T is obtained; an initial state variable->

Can be combined by a periodic state transition equation>

To iterate the calculation; based on this principle, the external information G between cycles ^p Can be obtained as follows;

the actual available travel time of the vehicle v in the period p is

External information G ^p From available travel time>

A route execution length;

specifically, first determining the available travel time is

Status variable ≥ on the next cycle>

Can be determined by calculating the travel route pair->

The resulting change.

5. The demand response bus look-ahead scheduling method of claim 4, wherein an objective function is defined:

in the above expression, β _f Representing the fixed transportation cost of each vehicle; varying the transportation cost depending on the distance traveled; due to the fact that at each stepIf segment k generates a new path, the cost of the alternate transport can be calculated as follows:

the time window violation penalty costs include early and late arrivals; in general, late arrival is more dangerous than early arrival, so late arrival penalizes the system β _l And early arrival penalty factor beta _e Satisfies beta _l >β _e (ii) a If the arrival time of the vehicle is within the specified time window, the penalty cost is 0; otherwise, the penalty cost depends on the length of the violation period; and the early and late arrival times of order r can be calculated as

And &>

The per-stage time window violation penalty cost is calculated as follows:

the cost function of the DRT model is related to the newly generated cost for each stage k; the cost of stage k of period p is equal to the cost of the previous stage

Plus altered transportation costs incurred for that stage>

And a penalty cost->

As follows:

since the fixed transportation costs are at the stage of the final cycle

wherein the content of the first and second substances,

stage k execution path policy that is period p @>

Best state cost function of;

predicted random order matrix under look-ahead scheduling

Is greater than or equal to>

The objective function needs to be included; however, only the future demand of cycle P +1 can be predicted, not for all subsequent cycles (from cycle P +1 to | P | phase); to ensure iterative stability of the SADP algorithm, the @>

Indicating that the path policy is executed at stage k of period p->

The objective function is modified as follows: />

Passenger-vehicle assignment is crucial to route planning;

however, due to supply limitations, such as fleet size and vehicle remaining passenger capacity, imported orders cannot always be fully matched; an order rejection mechanism is proposed, the rules of which are described as follows:

decision variables when all imported orders can be matched within period p

Can be expressed by a phase state transition equation

Iterating to a final state variable>

Namely, it is

However, once the order cannot be completely matched, so that

The planning process is terminated; pick-up station i for orders r that cannot be matched _r And a guest drop-off station j _r Then the stations are considered potential rejection stations and the solution is repeated after they are removed one by one until the remaining orders can be matched.

6. The demand response bus look-ahead scheduling method according to claim 1, wherein in step S2, the future demand is predicted based on quantile regression, an LSTM model, and a Copula function, specifically as follows:

predicting the future requirement of each OD pair through a conditional quantile equation under different quantile levels, thereby constructing empirical distribution to realize interval estimation;

in general, a regression problem can be expressed as an optimization model; by finding a functional relationship

Bringing a desired demand and a real demand->

The difference between them is minimal, namely:

wherein

Is a dependent variable>

The conditional expectation equation of (c);

however, equation (34) only applies to the case where the residuals of the two side sample points are equally weighted, i.e. median (τ = 0.5) regression; for regression of quantile τ, it is necessary to rely on

And &>

The magnitude relationship between τ and 1- τ; therefore, the optimization model of quantile regression isModified to equation (35), specifically as follows:

where ζ represents the equation coefficient when the quantile level is equal to τ; when linear programming is used to solve to the optimal zeta, the conditional tau quantile equation can be obtained

For different quantiles τ, the equation (35) can be solved separately for each τ, from which the @, at different quantile levels, can be derived>

To predict future demand

History data for cycle 1 to cycle p are->

As a training data set; due to the need to predict future demands at different quantile levels, let @>

Representing quantile level τ _l OD requirement at, and a quantile level set of τ _l = 5%,25%,50%,75%,95% }; therefore, the loss function of the LSTM model is modified to the optimization equation of the fractal regression in equation (36), as follows:

in this way, quantile samples of future demand for each OD pair can be obtained

Need->

Subject to the performance of the quantile sample, i.e.>

It can be expressed as an empirical distribution as follows:

thus, by empirical distribution

Medium sample, a random predictor value @, for each OD pair may be obtained>

The method comprises the following specific steps:

Its dimension is | S- ² The method comprises the following steps:

order to

Respectively representing the need of each OD pair>

Cumulative Distribution Functions (CDFs); based on the multivariate CDF, random vector @, consisting of the respective variables>

Can be expressed as follows:

for each OD pair, it can be determined by empirical distribution

The middle sample gets a random demand>

Giving the edge distribution of each OD pair

I.e. is>

And according to sklar's Copula theory, the random vector ≥ is>

May be defined as an edge distribution @ofthe respective vector>

And a Copula function, as follows: />

Gaussian copolas was used as follows:

wherein, C _G Denotes Gaussian Copula, phi _σ A joint CDF representing a multivariate normal distribution with covariance matrix σ and mean 0; note C _G There is no analytical formula, and numerical integration is needed to approximate the calculation;

use of C _G Can be selected from

Obtaining a future demand sample in the joint distribution; in so doing, it is possible to do so,

first from C _G And then convert the sample to->

Finally, Φ is mapped to the chosen sample by inverse mapping of the edge CDFs, as follows:

finally, a joint distribution function phi is obtained _σ Will be

Substituted into phi _σ The joint occurrence probability is obtained>

7. The demand response bus look-ahead scheduling method according to claim 1, wherein in step S3, future demands are brought into a common scheduling model, a look-ahead scheduling model based on prediction is established, and error correction mechanisms are respectively designed for look-ahead scheduling and order cancellation, specifically as follows:

unlike ordinary scheduling, look-ahead scheduling not only takes into account

And &>

Also taking into account the predicted future demand of the upcoming period p + 1; in this scheduling mode, the future demand of the next cycle->

Is predicted in advance at period p and is associated with->

And

optimizing together; therefore, training to predict future demand should be done periodically on a rolling basis; for example, at cycle p, in order to predict future demand for cycle p +1, the training data set should include the demands of the previous and current cycles, i.e., { (R) }>

When the dynamic order of the next period is imported, the prediction error is corrected; in cycle 2, first, according to the dynamic order

Correction time period t ₀ -T,t ₀ ]In or>

And obtains a matching but unserviced order @>

Then will >>

And &>

At a time period t ₀ ,t ₀ +t _B ]Plan together and then schedule the vehicle for a time period t ₀ +t _B ,t ₀ +T]Performing;

notwithstanding predicted future demand

The method is deterministic when planning is carried out at the end time of a period p, but errors may exist in quantile regression and LSTM model prediction, and great influence can be generated on planning; assume that a remaining passenger load of the vehicle v is +>

From the loading station i _r Get to the station j _r Predicted passenger number of c _r =1; due to prediction errors only a real order is introduced at the end of the period p +1 @>

Only then can it be known that, if the number of real passengers exceeds the remaining passenger capacity of the vehicle, for example c _r =2, i.e. specifying planned route ≥>

Are invalid, which can lead to inefficient consumption of remaining travel distance and deterioration of subsequent decisions.

8. The demand response bus look-ahead scheduling method according to claim 7, wherein in step S3, a correction mechanism is proposed to reduce the negative effect of the prediction error;

Whether a real number of passengers can be accommodated;

thus, the prediction error can be divided into two types, i.e. the predicted value is larger than the actual value, i.e. the prediction error is larger than the actual value

And is less than the actual value i.e

Updated to the correct value->

For the latter, the planned route is not valid;

Individual passenger, but redundant>

in practice, passengers may temporarily cancel orders because of dissatisfaction with changes in price, vehicle arrival time, and vehicle route; different from the route planned by the operator

Timely and active order rejection and dynamic order reservation>

The cancellation of (b) is actively and temporarily initiated by the passenger; the order is already planned by the system in the vehicle route before it is cancelled; in order to ensure the stability of the vehicle route, the cancelled order should be deleted from the planned route in real time;

if orders are cancelled before the system plans a route, the orders can be directly removed from the imported dynamic orders; planned route under look-ahead scheduling

Already planned, the vehicle may be due to the order being cancelled by the passengerThe station can arrive or not arrive; similar to the error correction mechanism of the predicted order, the invention can update the incorrect state variable; under a look-ahead schedule, based on a look-ahead schedule>

And &>

All are imported into the system at the end of the period p; and the passenger cancels the order>

And &>

In the period p +1 and the period p +2, respectively; thus, there are two cases of look-ahead scheduling, namely:

a) The predicted future demand is not cancelled, but is actually cancelled;

b) The predicted future demand is cancelled, but not actually;

for case a), the predicted future demand is not cancelled, indicating that the passenger is

Has been planned into the line by the system; the vehicle may have just arrived or not yet arrived at the upper station; thus, the wrong state variables can be updated directly;

for case b), the predicted future demand is cancelled, i.e. the order is not present in the planned route; however, since the actual order is not cancelled, the vehicle has three states of 'not arriving at the boarding point', 'just arriving at the boarding point', and 'having traveled past the boarding point'; while the prediction errors of the first two states can be updated directly as in case a); and for the 'has traveled past the pick-up point' state, another vehicle needs to be dispatched to service at the end of the period p + 1.

9. The demand response bus look-ahead scheduling method according to claim 1, wherein in step S4, a pruning strategy of the decision is designed, and a decoding space is compressed to reduce the calculation time, specifically comprising:

the lower bound pruning of the vehicle residual distance is as follows:

since vehicle v must deliver all passengers in the vehicle to the corresponding departure point, if it can go ahead along arc (i, j) e a to a new departure point j = i _r Before, it is very meaningful to judge whether the remaining cruising distance of the vehicle can meet the mileage requirement of a subsequent path; the following theorem is given along with its proof:

The waiting time is optimized specifically as follows:

the vehicle can be waited when being positioned in a parking lot, so that the departure time is optimized, and the large time penalty cost is prevented from being generated when the vehicle goes to a first boarding point; due to the point i of getting on bus needing service after waiting _r The vehicle is decided, and the subsequent path of the vehicle-entering point cannot be observed, so that the arrival time of the vehicle at the vehicle-entering point is optimized; waiting time

The optimal value of (c) is calculated as shown in equation (45):

calculating an optimal penalty by (46)Penalty cost

The method comprises the following specific steps:

returning to the parking lot for pruning, which is concretely as follows:

when a vehicle is visiting a departure point and there are no remaining passengers on the vehicle, the vehicle will face two decisions:

(e) Go to another boarding point;

(f) Returning to the affiliated parking lot m _v ；

Because the lower bound pruning of the vehicle remaining distance can eliminate partial wrong vehicle paths, the path (e) discussed in this subsection is premised on that the vehicle remaining distance is sufficient, and the vehicle decision is pruned and optimized from the cost perspective;

without considering the time window penalty, the cost of path (f) must be higher than path (e) even if the fixed cost of use of the vehicle is ignored; however, in actual operation, the time penalty must be considered, if the vehicle makes the boarding point passenger wait too long, a new vehicle is not dispatched from the parking lot to go to the service, so that the time cost is reduced, and the total cost is lower than the former; based on the above principle, the pruning strategy is as follows: when the temperature is higher than the set temperature

When a decision is made as to path (f); when/is>

A decision is made as to path (e).

10. The demand response bus look-ahead scheduling method according to any one of claims 1 to 9, wherein in step S5, the scheduling scheme is solved by using an approximate dynamic programming algorithm, specifically as follows:

in general, the VFA strategy of period p starts in an initial state, iterating along the simulated sample planning path