CN111144618A - Demand response type customized bus network planning method based on two-stage optimization model - Google Patents

Demand response type customized bus network planning method based on two-stage optimization model Download PDF

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CN111144618A
CN111144618A CN201911225062.1A CN201911225062A CN111144618A CN 111144618 A CN111144618 A CN 111144618A CN 201911225062 A CN201911225062 A CN 201911225062A CN 111144618 A CN111144618 A CN 111144618A
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刘志远
黄迪
董润
王路濛
黄江彦
杨逊
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Southeast University
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Abstract

The invention discloses a demand response type customized public transportation network planning method based on a two-stage optimization model, which dynamically collects travel demands of users through a network platform; building a demand response type customized public transportation network framework, and initializing a customized public transportation network by using historical data; modifying the customized public transport network based on an insertion checking algorithm and a dynamic insertion algorithm according to new requirements of users; integrating all feasible temporary schemes, predicting the trip cost and the trip time of the user, providing a trip plan, and waiting for the decision of the user; calculating the probability of the user confirming the trip based on the Monte Carlo simulation process; and updating the target function and the time deviation constraint based on the travel confirmation number, and statically planning and customizing the public transportation network by adopting a graph search algorithm based on a branch-and-bound algorithm to obtain a final scheme. The invention enables the customized bus service to be more humanized and provides reliable technical support for the actual operation optimization of the customized bus.

Description

Demand response type customized bus network planning method based on two-stage optimization model
Technical Field
The invention relates to the technical field of public transport data information processing and network planning, in particular to a demand response type customized public transport network planning method based on a two-stage optimization model.
Background
In recent years, diversified, personalized, intelligent and green transportation needs have prompted a plurality of emerging public transportation means and operation modes. On this background, customized public transportation is considered to be an efficient and environmentally friendly alternative to private cars and traditional passenger transport as an efficient on-demand shared vehicle, providing highly flexible and personalized services to people with similar travel needs.
Compared with the traditional public transport and other demand response type services, the customized public transport has the unique characteristics that the user can reserve services in advance, the system can integrate the demands of a plurality of users, the optimization problem of the line is comprehensively considered, and customized and refined services are provided. In addition, under the rapid development of traffic data science, the customized public transportation service fully utilizes the intelligent network platform, receives user demand information, performs data processing, data analysis, scheme planning and decision judgment, and realizes network optimization adjustment, vehicle distribution scheduling and deep interaction with users in a very short time.
At present, the problems of route optimization and fare formulation of the customized bus at home and abroad are mainly focused on the design and optimization of a service network with known requirements, and an advanced on-demand service platform cannot be fully utilized. Therefore, the dynamic interaction process between the passenger and the operator cannot be embodied, and various problems such as information lag, operation delay, and the like are caused. Furthermore, existing research mostly separates operator and passenger analysis from the objective and does not fully cover the decision process of the dynamic phase. In summary, in order to solve the problem of customizing the bus network planning more effectively, a model which is more comprehensive and comprehensively considers the requirements of both the operator and the user needs to be established.
Disclosure of Invention
The invention aims to solve the technical problem of providing a demand response type customized bus network planning method based on a two-stage optimization model, which can improve the efficiency and accuracy of network planning, enable the customized bus service to be more humanized and provide reliable technical support for the actual operation optimization of the customized bus.
In order to solve the technical problem, the invention provides a demand response type customized public transportation network planning method based on a two-stage optimization model, which comprises the following steps:
(1) dynamically gathering user travel demands in the deadline through a network platform, wherein the user travel demands comprise information such as pickup time, pickup sites, delivery time, delivery sites and the like expected by each user;
(2) building a demand response type customized public transport network framework, and initializing a network by using historical demand data;
(3) according to new requirements of users, comprehensively considering time deviation, vehicle passenger carrying capacity and other constraints, and searching a feasible user new request insertion scheme by using an insertion checking algorithm and a dynamic insertion algorithm to solve a two-stage decision problem of a dynamic stage;
(4) integrating all feasible temporary schemes, predicting the travel cost and the travel time, sending a travel plan to the user, and waiting for the user to make a decision;
(5) calculating a probability of the user confirming the provided travel plan based on a Monte Carlo simulation process for subsequent simulation;
(6) and updating a target function and time deviation constraint of the customized bus network planning problem based on the number of the confirmed travel users, and solving the customized bus network planning problem in a static stage by adopting a graph search algorithm based on a branch-and-bound algorithm to obtain an optimal solution.
Preferably, in step (1), the requirement data mainly includes personal information of the user and the time of submitting the requirementWorkshop
Figure BDA0002301960870000021
Desired ride time
Figure BDA0002301960870000022
Desired pickup station
Figure BDA0002301960870000023
Expected delivery time
Figure BDA0002301960870000024
Desired delivery site
Figure BDA0002301960870000025
Preferably, in the step (2), the built demand response type customized bus network framework is as follows:
in (V, a), the station set is V ═ V0,v1,...,vnConsists of three subsets: pick-up station set VpDelivery site set VdAnd an origin station v0(ii) a The road section set is A { (v)i,vj):vi,vjE is V, i is not equal to j; r represents a newly emerging demand set, VrRepresenting a set of sites containing spatial information of a demand R ∈ R, i.e.
Figure BDA0002301960870000026
And
Figure BDA0002301960870000027
Figure BDA0002301960870000028
each request and expected take-over time
Figure BDA0002301960870000029
And expected delivery time
Figure BDA00023019608700000210
And (4) associating. Origin-destination point (v)i,vj) Q is the cumulative number of demands in betweenij. The fleet of homogenous vehicles is denoted as K; the passenger carrying capacity of all vehicles is cap. J. the design is a squarekRepresenting a route serviced by a vehicle K e K, which may be made up of a set of stops Vk＝{vi|(vi,vj)∈Jk,vjE.g. V.
Preferably, the two-stage decision problem, the insertion checking algorithm and the dynamic insertion algorithm in step (3) are specifically as follows:
(31) two-stage decision problem
The new request r submitted by the user includes: desired pickup station
Figure BDA00023019608700000211
Desired delivery site
Figure BDA00023019608700000212
At the actual take-over point viDesired take-over time of
Figure BDA00023019608700000213
At the actual delivery point vjDesired delivery time of
Figure BDA00023019608700000214
If there are n passengers, the station v will beiWaiting for the vehicle k, the expected pick-up time of the r-th passenger being
Figure BDA00023019608700000215
The time deviation threshold for each request r is tmaxThe operator then provides the user with a plan in which the vehicle k is at the pick-up station viThe arrival and departure times of (d) should satisfy:
Figure BDA0002301960870000031
Figure BDA0002301960870000032
vehicle k at delivery station vjTime of arrival of
Figure BDA0002301960870000033
It should satisfy:
Figure BDA0002301960870000034
for pick-up station vi∈VpIts actual ride-through time should satisfy:
Figure BDA0002301960870000035
wherein ,
Figure BDA0002301960870000036
indicating that the corresponding demand r is at the take-over point viActual ride-through time of;
Figure BDA0002301960870000037
indicating that the corresponding demand r is at the take-over point viDesired ride-through time;
Figure BDA0002301960870000038
and
Figure BDA0002301960870000039
respectively representing the vehicle k at the station viArrival time and departure time of;
for delivery site vj∈VdThe actual delivery time should satisfy:
Figure BDA00023019608700000310
when the number of confirmed passengers is less than the minimum load factor qminAt that time, a premium τ is charged0. Then the trip cost
Figure BDA00023019608700000311
Comprises the following steps:
Figure BDA00023019608700000312
wherein ,
Figure BDA00023019608700000313
to be based on site vi and vjThe fixed cost of the distance is that,
Figure BDA00023019608700000314
cost per unit distance, dijFor station vi and vjThe distance between the two or more of the two or more,
Figure BDA00023019608700000315
is the number of passengers assigned to vehicle k
Figure BDA00023019608700000316
Representing a decision variable vector;
Figure BDA00023019608700000317
representing the probability of the passenger accepting the travel plan provided by the operator; the total fee expected to be charged by the customized public transportation system after the user confirms the journey is
Figure BDA00023019608700000318
Where E (-) is the desired operator;
to achieve operator profit maximization, the objective function is:
Figure BDA0002301960870000041
the following constraints are satisfied in terms of the expressions (1) to (3):
Figure BDA0002301960870000042
Figure BDA0002301960870000043
Figure BDA0002301960870000044
Figure BDA0002301960870000045
Figure BDA0002301960870000046
Figure BDA0002301960870000047
wherein α is the unit distance operation cost, β is the fixed cost of additionally scheduling a vehicle, equations (1) - (3) are the maximum time deviation constraint, equation (8) defines the maximum passenger carrying capacity of each vehicle, equation (9) ensures that each request is served by a vehicle, equation (10) ensures that each route is a closed curve with a starting point and an ending point coincident with an originating station, equations (11) - (13) define binary variables;
OD pairs (v) in the customized public transport network N constructed by the travel schemei,vj) Travel utility of room
Figure BDA0002301960870000048
Satisfy the requirement of
Figure BDA0002301960870000049
Figure BDA00023019608700000410
wherein
Figure BDA00023019608700000411
In order to provide the expected travel costs for the passengers,
Figure BDA00023019608700000412
for passenger selectionCost savings after choosing to take a custom bus, cij(N) is a system item of,
Figure BDA00023019608700000413
is an error term, obedience is expected to equal zero, variance is equal to
Figure BDA00023019608700000414
Normal distribution of (a):
Figure BDA00023019608700000415
where λ is time, tijIs OD pair (v)i,vj) The time of flight in between is determined,
Figure BDA00023019608700000416
and
Figure BDA00023019608700000417
the time deviation is used as the punishment factor corresponding to the time deviation mu;
the probability that the passenger accepts the travel plan provided by the operator is:
Figure BDA00023019608700000418
(32) insertion checking algorithm and dynamic insertion algorithm
For new requests
Figure BDA0002301960870000051
If it is
Figure BDA0002301960870000052
And
Figure BDA0002301960870000053
already existing in the existing route JkPerforming the following steps; and is arranged at
Figure BDA0002301960870000054
And
Figure BDA0002301960870000055
where the current arrival and departure times are
Figure BDA0002301960870000056
And
Figure BDA0002301960870000057
and is
Figure BDA0002301960870000058
Within an acceptable time interval, then the request r may be inserted directly into route JkPerforming the following steps;
if the delivery point of r is requested
Figure BDA0002301960870000059
Already exists in route JkMiddle, but next to the multiplication point
Figure BDA00023019608700000510
Out of route JkIn (3), the following checks are performed: if it is currently at vmWithout demand, then vmCan be replaced by
Figure BDA00023019608700000511
Checking that the vehicle arrives at the station at this time
Figure BDA00023019608700000512
Time period of
Figure BDA00023019608700000513
Whether or not to coincide with an acceptable time period
Figure BDA00023019608700000514
Intersecting; if it is currently at vmOn demand, then vmAnd cannot be deleted. Examination of
Figure BDA00023019608700000515
Whether or not v can be insertedmAnd then. Checking that the vehicle arrives at the station at this time
Figure BDA00023019608700000516
Time period of
Figure BDA00023019608700000517
Whether or not to coincide with an acceptable time period
Figure BDA00023019608700000518
Figure BDA00023019608700000519
Intersecting;
if the pick-up point of r is requested
Figure BDA00023019608700000520
Already exists in route JkMiddle, but delivery point
Figure BDA00023019608700000521
Out of route JkIn (3), the following checks are performed: if it is currently at vmWithout demand, then vmCan be replaced by
Figure BDA00023019608700000522
Checking that the vehicle arrives at the station at this time
Figure BDA00023019608700000523
Time period of
Figure BDA00023019608700000524
Whether or not to coincide with an acceptable time period
Figure BDA00023019608700000525
Intersecting; if it is currently at vmOn demand, then vmAnd cannot be deleted. Examination of
Figure BDA00023019608700000526
Whether or not v can be insertedmThen; checking that the vehicle arrives at the station at this time
Figure BDA00023019608700000527
Time period of
Figure BDA00023019608700000528
Whether or not to coincide with an acceptable time period
Figure BDA00023019608700000529
Intersecting;
by iterating the above insertion checking algorithm as a subroutine, the following dynamic insertion algorithm can be obtained:
input historical route set JkRoute including site set VkAnd at each site vi∈VkTime of arrival of
Figure BDA00023019608700000530
And time of departure
Figure BDA00023019608700000531
Entering a new request
Figure BDA00023019608700000532
For each historical route JkApplying an insertion checking algorithm to generate a secondary V for the demand r if a feasible insertion solution cannot be found0To
Figure BDA00023019608700000533
And
Figure BDA00023019608700000534
the new route of (1);
for each insertion scheme, calculating the profit of an operator and the travel cost of a passenger, calculating the probability of the passenger selecting the scheme, and obtaining the expected profit of the scheme; keeping the insertion scheme with the highest expected profit, and updating the network;
if a new request is submitted to the operator, the input stage is switched to, and a loop is entered, otherwise, the process is ended.
Preferably, in step (5), based on the monte carlo simulation process, the probability that the user confirms the travel plan provided by the operator is obtained as follows:
Figure BDA0002301960870000061
when N → ∞ is reached,
Figure BDA0002301960870000062
wherein N is the number of times of simulation tests,
Figure BDA0002301960870000063
the number of times the travel cost can be reduced after the customized bus is selected for the user.
Preferably, in step (6), the customized bus network planning problem in the static phase and the graph search algorithm based on the branch-and-bound algorithm are detailed as follows:
after entering the static phase, the objective function should be re-expressed as:
Figure BDA0002301960870000064
the time deviation constraints (3) - (4) should be re-expressed as:
Figure BDA0002301960870000065
Figure BDA0002301960870000066
wherein ,
Figure BDA0002301960870000067
and
Figure BDA0002301960870000068
is the pick-up time and delivery time in the dynamic phase operator provisioning scheme;
the graph search algorithm based on the branch-and-bound algorithm comprises the following specific steps:
initialization
Figure BDA0002301960870000069
Figure BDA00023019608700000610
Current lowest cost cminThe best solution at present
Figure BDA00023019608700000611
Generating a current route
Figure BDA00023019608700000612
Performing graph search, and if the time deviation constraint of the expressions (20) and (21) and the passenger carrying capacity constraint of the expression (8) are not satisfied, returning; if the current theoretical minimum cost is higher than the cost of the optimal solution, returning; if it is
Figure BDA00023019608700000613
And
Figure BDA00023019608700000614
if it is empty, the total cost is calculated by equation (19); if the current cost is lower than the current lowest cost, updating the current lowest cost cmin＝ccurrentAnd the current best solution Ropt＝Rcurrent(ii) a Returning; if it is
Figure BDA00023019608700000615
Adding the new request, calling a graph search algorithm, from
Figure BDA00023019608700000616
And
Figure BDA00023019608700000617
deletion of viIn a
Figure BDA00023019608700000618
To which v is addedi(ii) a If it is
Figure BDA00023019608700000619
Call graph searchAlgorithm, from
Figure BDA00023019608700000620
Deletion of viAnd is incorporated in
Figure BDA00023019608700000621
To which v is addedi(ii) a If it is
Figure BDA00023019608700000622
For null, update the current solution RcurrentAnd cost ccurrentIn a
Figure BDA00023019608700000623
To which v is added0Invoking a graph search algorithm, from
Figure BDA0002301960870000071
Deletion of v0。
The invention has the beneficial effects that: the invention fully utilizes the Internet on-demand service platform, and provides a feasible solution for customizing the problems of incapability of embodying the dynamic interaction process of the user and the operator, information lag, operation delay and the like which possibly occur in the actual operation of the bus; the requirements and the interactivity of an operator and a user are comprehensively considered, the analysis is more comprehensive, and the decision process of the dynamic stage is basically and completely covered; the method creatively adopts a two-stage optimization method, dynamically processes the online requirements of users and rapidly provides a feasible travel scheme, and the comprehensive road network can be statically planned after the users confirm the travel, so that the efficiency and the accuracy of network planning are improved, the customized public transportation service is more humanized, and reliable technical support is provided for the actual operation optimization of the customized public transportation.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention.
Detailed Description
As shown in fig. 1, a demand response type customized bus network planning method based on a two-stage optimization model includes the following steps:
(1) dynamically collecting user travel demands in the deadline through a network platform;
the demand data is mainly acquired by a webpage of a customized bus related operation management department or mobile phone software, and the map navigation software provides related regional map information so as to mark related stops and routes. The demand data mainly comprises personal information of the user and the time for submitting the demand
Figure BDA0002301960870000072
Desired ride time
Figure BDA0002301960870000073
Desired pickup station
Figure BDA0002301960870000074
Expected delivery time
Figure BDA0002301960870000075
Desired delivery site
Figure BDA0002301960870000076
(2) Building a demand response type customized public transportation network framework, and initializing a customized public transportation network by using historical demand data;
in (V, a), the station set is V ═ V0,v1,...,vnThe road section set is A { (v)i,vj):vi,vjE.g., V, i ≠ j). The site set V includes three subsets: pick-up station set VpDelivery site set VdAnd an origin station v0. Furthermore, R represents a newly emerging demand set, VrRepresenting a set of sites containing spatial information of a demand R ∈ R, i.e.
Figure BDA0002301960870000077
And
Figure BDA0002301960870000078
Figure BDA0002301960870000079
each request is also multiplied by the expected take-over time
Figure BDA00023019608700000710
And expected delivery time
Figure BDA00023019608700000711
And (4) associating. Origin-destination point (v)i,vj) Q is the number of accumulated demandsijAnd (4) showing. The fleet of homogenous vehicles is denoted as K; all vehicles have the same passenger capacity cap. J. the design is a squarekRepresenting a route served by a vehicle K e K, which may be served by a set of stops Vk,Vk＝{vi|(vi,vj)∈Jk,vjE.g. V.
(3) According to the new requirements of the current user, the constraints such as time, vehicle passenger carrying capacity and the like are comprehensively considered, a feasible user new request insertion scheme is searched by using an insertion checking algorithm and a dynamic insertion algorithm, and the two-stage decision problem of the dynamic stage is solved;
31) two-stage decision problem
For the real-time requests newly submitted by users, two processing methods are available, namely, the real-time requests are inserted into the existing customized public transportation network or new service routes are planned according to the new requests. Each request r includes: desired pickup station
Figure BDA0002301960870000081
Desired delivery site
Figure BDA0002301960870000082
At the actual take-over point viDesired take-over time of
Figure BDA0002301960870000083
At the actual delivery point vjDesired delivery time of
Figure BDA0002301960870000084
The default user request is processed according to the first-come first-serve principle; the time difference between the user receiving the feedback and making the decision is ignored.
In the scenario provided by the operator to the user, tmaxIndicating the time deviation threshold corresponding to each request r, vehicle k arriving at station viTime of
Figure BDA0002301960870000085
Should be in the time period
Figure BDA0002301960870000086
In the meantime.
Suppose that an existing n passengers will be at station viWaiting for vehicle k.
Figure BDA0002301960870000087
And
Figure BDA0002301960870000088
indicating the expected pickup time of the first and last passengers. It should be satisfied that the arrival time of the vehicle should not be later than the latest pick-up time that the first passenger can tolerate
Figure BDA0002301960870000089
The departure time of the vehicle should not be earlier than the earliest ride time that the last passenger can tolerate
Figure BDA00023019608700000810
Thus, the vehicle k is at the pick-up station viShould meet the arrival and departure time of
Figure BDA00023019608700000811
Figure BDA00023019608700000812
At delivery site vjConsider a delay penalty. The arrival time of vehicle k should be no later than the earliest desired delivery time among all requests. Thus, the arrival time of the vehicle k
Figure BDA00023019608700000813
It should satisfy:
Figure BDA00023019608700000814
for pick-up station vi∈VpIts actual ride-through time should satisfy:
Figure BDA00023019608700000815
wherein ,
Figure BDA0002301960870000091
indicating that the corresponding demand r is at the take-over point viActual ride-through time of;
Figure BDA0002301960870000092
indicating that the corresponding demand r is at the take-over point viDesired ride-through time;
Figure BDA0002301960870000093
and
Figure BDA0002301960870000094
respectively representing the vehicle k at the station viThe arrival time and the departure time of (c).
For delivery site vj∈VdThe actual delivery time should satisfy:
Figure BDA0002301960870000095
to ensure profitability of a custom-made public transportation system in low demand areas, when the number of confirmed passengers is less than a minimum passenger carrying factor qminAt that time, a premium τ is charged0. So the OD pair (v) corresponding to the user request ri,vj) Travel cost of
Figure BDA0002301960870000096
Comprises the following steps:
Figure BDA0002301960870000097
wherein ,
Figure BDA0002301960870000098
to be based on site vi and vjThe fixed cost of the distance is that,
Figure BDA0002301960870000099
cost per unit distance, dijFor station vi and vjThe distance between the two or more of the two or more,
Figure BDA00023019608700000910
is OD pair (v)i,vj) The number of passengers assigned to vehicle k. Therefore, in the travel scheme, the total fee T expected to be collected by the customized public transportation system is as follows:
Figure BDA00023019608700000911
according to the overall scheme of customizing the bus network planning problem, the variables can be divided into two subsets. The first set of variables are binary variables that are relevant to the design of a customized bus service route. If request r is assigned to vehicle k, then
Figure BDA00023019608700000912
Is 1, otherwise is 0. If the route traveled by vehicle k is (v)i,vj) Then, then
Figure BDA00023019608700000913
Is 1, otherwise is 0. If vehicle k is scheduled, δkIs 1, otherwise is 0.
The second set of variables is related to vehicle scheduling, including the arrival/departure time of each station.
Figure BDA00023019608700000914
Representing a decision variable vector.
Figure BDA00023019608700000915
Representing the probability of the passenger accepting the travel plan provided by the operator.
Figure BDA00023019608700000916
Represents the total fee the custom transit system is expected to charge after the user confirms the itinerary, where E (-) is the desired operator.
The objective function achieves operator profit maximization, i.e., maximization of the total cost charged by the system minus the operating cost:
Figure BDA00023019608700000917
the following constraints are satisfied in terms of the expressions (1) to (3):
Figure BDA0002301960870000101
Figure BDA0002301960870000102
Figure BDA0002301960870000103
Figure BDA0002301960870000104
Figure BDA0002301960870000105
Figure BDA0002301960870000106
where α is the unit distance operating cost and β is the fixed cost of additionally scheduling a vehicle equations (1) - (3) define the arrival/departure times at the pick-up/delivery site that meet the maximum time deviation constraint, equation (8) defines the maximum passenger carrying capacity of each vehicle equation (9) ensures that each request is serviced by a vehicle equation (10) ensures that each route coincides with a closed curve at the origin site for the origin and destination equations (11) - (13) define binary variables.
OD pairs (v) in the customized public transport network N constructed by the travel schemei,vj) Travel utility of room
Figure BDA0002301960870000107
Satisfy the requirement of
Figure BDA0002301960870000108
Figure BDA0002301960870000109
wherein
Figure BDA00023019608700001010
In order to provide the expected travel costs for the passengers,
Figure BDA00023019608700001011
for passengers at OD pairs (v)i,vj) Cost saving after choosing to take the customized bus, cij(N) is a system item of,
Figure BDA00023019608700001012
is an error term, obedience is expected to equal zero, variance is equal to
Figure BDA00023019608700001013
Normal distribution of (a):
Figure BDA00023019608700001014
where λ is time, tijIs OD pair (v)i,vj) The time of flight in between is determined,
Figure BDA00023019608700001015
and
Figure BDA00023019608700001016
and mu is a penalty factor corresponding to the time deviation.
The probability that the passenger accepts the travel plan provided by the operator is equal to the probability that the travel utility is greater than zero:
Figure BDA00023019608700001017
32) insertion checking algorithm and dynamic insertion algorithm
Inputting: new request
Figure BDA00023019608700001018
Step 1: if it is
Figure BDA00023019608700001019
And
Figure BDA00023019608700001020
already existing in the existing route JkPerforming the following steps; and is arranged at
Figure BDA00023019608700001021
And
Figure BDA00023019608700001022
where the current arrival and departure times are
Figure BDA0002301960870000111
And
Figure BDA0002301960870000112
and is
Figure BDA0002301960870000113
Within an acceptable time interval, then request r may be inserted directly into route JkIn (1). If this occurs, it is recorded as a viable insertion solution.
Step 2: if the delivery point of r is requested
Figure BDA0002301960870000114
Already exists in route JkMiddle, but next to the multiplication point
Figure BDA0002301960870000115
Out of route JkIn, then pair
Figure BDA0002301960870000116
Applying the inspection procedure in step 2.1 and scanning route JkAll existing sites v inm∈VkTo realize
Figure BDA0002301960870000117
Insertion of (2):
step 2.1: if it is currently at vmWithout demand, then vmCan be replaced by
Figure BDA0002301960870000118
From JkDeletion of vmAnd add in
Figure BDA0002301960870000119
At which time the vehicle arrives at the station
Figure BDA00023019608700001110
The time period of (d) may be expressed as:
Figure BDA00023019608700001111
checking whether the time period is equal to an acceptable time period
Figure BDA00023019608700001112
And (4) intersecting. If so, it is recorded as a viable insertion solution.
Step 2.2: if it is currently at vmOn demand, then vmAnd cannot be deleted. Examination of
Figure BDA00023019608700001113
Whether or not v can be insertedmAnd then. At which time the vehicle arrives at the station
Figure BDA00023019608700001114
The time period of (d) may be expressed as:
Figure BDA00023019608700001115
checking whether the time period is equal to an acceptable time period
Figure BDA00023019608700001116
And (4) intersecting. If so, it is recorded as a viable insertion solution.
And step 3: if the pick-up point of r is requested
Figure BDA00023019608700001117
Already exists in route JkMiddle, but delivery point
Figure BDA00023019608700001118
Out of route JkIn, then pair
Figure BDA00023019608700001119
Applying the inspection procedure in step 3.1 and scanning route JkAll existing sites v inm∈VkTo realize
Figure BDA00023019608700001120
Insertion of (2):
step 3.1: if it is currently at vmWithout demand, then vmCan be replaced by
Figure BDA00023019608700001121
From JkDeletion of vmAnd add in
Figure BDA00023019608700001122
At which time the vehicle arrives at the station
Figure BDA00023019608700001123
The time period of (d) may be expressed as:
Figure BDA00023019608700001124
check that this time period isWhether and acceptable time period
Figure BDA00023019608700001125
And (4) intersecting. If so, it is recorded as a viable insertion solution.
Step 3.2: if it is currently at vmOn demand, then vmAnd cannot be deleted. Examination of
Figure BDA00023019608700001126
Whether or not v can be insertedmAnd then. At which time the vehicle arrives at the station
Figure BDA00023019608700001127
The time period of (d) may be expressed as:
Figure BDA00023019608700001128
checking whether the time period is equal to an acceptable time period
Figure BDA00023019608700001129
And (4) intersecting. If so, it is recorded as a viable insertion solution.
With the above insertion checking algorithm as a subroutine, the following dynamic insertion algorithm can be obtained:
step 1: initialization
Inputting the existing route set JkRoute including site set VkAnd at each site vi∈VkTime of arrival of
Figure BDA0002301960870000121
And time of departure
Figure BDA0002301960870000122
Inputting a newly received request r, a take-over point
Figure BDA0002301960870000123
And delivery point
Figure BDA0002301960870000124
And desired ride time
Figure BDA0002301960870000125
And delivery time
Figure BDA0002301960870000126
Step 2: seeking a viable insertion solution
Step 2.1: for each historical route JkApplying an insertion checking algorithm to record a feasible insertion scheme;
step 2.2: if no feasible insertion scheme can be found in the insertion checking process, a secondary originating station v is generated for the demand r0To
Figure BDA0002301960870000127
And
Figure BDA0002301960870000128
the new route of (1).
And step 3: evaluating feasible insertion schemes
Step 3.1: calculating the profit of the operator and the trip cost of the passenger for each feasible insertion plan obtained in step 2, calculating the probability of the passenger selecting the plan, and then obtaining the expected profit of the plan;
step 3.2: storing the insertion scheme with the highest expected profit and updating the historical route JkRoute including site set VkAnd at each site vi∈VkTime of arrival of
Figure BDA0002301960870000129
And time of departure
Figure BDA00023019608700001210
And 4, step 4: if a new request is submitted to the operator, turning to step 1; then, the process ends.
By applying the algorithm, a new set of routes can be planned. Meanwhile, the passenger receives the travel plan from the operator, and decides whether to confirm the plan and receive subsequent services.
(4) Integrating all feasible temporary schemes, estimating the trip cost of the user, constraining and estimating the trip time according to the time deviation, sending a trip plan to the user, and waiting for a decision result of the user;
(5) calculating a probability of the user confirming the provided travel plan based on a Monte Carlo simulation process for subsequent simulation;
each simulation test on the user request r is based on
Figure BDA00023019608700001211
Is sampled by the distribution function of (a). Let N be the number of times the simulation experiment was repeated,
Figure BDA00023019608700001212
the number of times the travel cost can be reduced after the customized bus is selected for the passenger. Then the probability that the user confirms the travel plan provided by the operator is:
Figure BDA00023019608700001213
when N → ∞ is reached,
Figure BDA0002301960870000131
(6) updating a target function and time deviation constraint of a customized bus network planning problem based on the number of users with confirmed travel, and solving the customized bus network planning problem in a static stage by adopting a graph search algorithm based on a branch-and-bound algorithm to obtain an optimal solution;
61) static phase customized bus network planning problem
After entering the static phase, no new requests are made to join the current network and the routing of all passengers is determined. Then the total revenue for the system in equation (7) is fixed and known and the objective function can be re-expressed as:
Figure BDA0002301960870000132
the time deviation constraints (3) - (4) should be re-expressed as:
Figure BDA0002301960870000133
Figure BDA0002301960870000134
wherein ,
Figure BDA0002301960870000135
and
Figure BDA0002301960870000136
is the pick-up time and delivery time in the dynamic phase operator provisioning scheme. The remaining constraints are the same as equations (8) - (13).
62) Graph search algorithm based on branch-and-bound algorithm
Based on branch-and-bound (B)&B) The algorithm can adopt a graph search algorithm to solve the problem of customized bus network planning in a static stage. In this algorithm, the route is represented by a sequence of integers of the take-over point and the delivery point.
Figure BDA0002301960870000137
For a set of multiply points that have not been visited,
Figure BDA0002301960870000138
for a set of passengers that have not yet arrived at the destination,
Figure BDA0002301960870000139
is a list of sites for the current path. At each site viThe following three possible operations may be considered as branches of the search tree:
(a) adding a new request: in that
Figure BDA00023019608700001310
And
Figure BDA00023019608700001311
to which v is addediFrom
Figure BDA00023019608700001312
Deletion of vi；
(b) Sending a request: in that
Figure BDA00023019608700001313
To which v is addediFrom
Figure BDA00023019608700001314
Deletion of vi。
(c) Dispatching a new vehicle: if it is
Figure BDA00023019608700001315
If it is empty, then it is
Figure BDA00023019608700001316
To which v is added0。
The route may be generated using a depth-first search strategy under the condition that the passenger carrying capacity constraint of equation (8) and the time deviation constraint of equations (20) and (21) are satisfied. The current solution is compared to the optimal solution and if the theoretical lowest cost of the current solution is higher than the cost of the optimal solution, the current solution is discarded. The theoretical minimum cost may be calculated based on a predetermined minimum cost of service to satisfy a request, and the cost of the current solution and the minimum cost of servicing the remaining requests. In the case of multiple vehicles, a vehicle counter k is applied to record the number of vehicles processed, and when the vehicle completes a trip, an additional branch will be added. The specific steps of recursively using the graph search algorithm are as follows:
step 1: initialization
Is provided with
Figure BDA0002301960870000141
Figure BDA0002301960870000142
Current lowest cost cminThe best solution at present
Figure BDA0002301960870000143
Generating a current route
Figure BDA0002301960870000144
Step 2: graph search
Step 2.1: checking feasibility of generating routes
If the time deviation constraints of the expressions (20) and (21) and the passenger carrying capacity constraint of the expression (8) are not met, returning; if the current theoretical minimum cost is higher than the cost of the optimal solution, return is made.
Step 2.2: check if there are any remaining requests
If it is
Figure BDA0002301960870000145
And
Figure BDA0002301960870000146
if it is empty, the total cost is calculated by equation (19). If the current cost is lower than the current lowest cost, updating the current lowest cost cmin＝ccurrentAnd the current best solution Ropt＝Rcurrent(ii) a And returning.
Step 2.3: for each site
Figure BDA0002301960870000147
Generating all possible route combinations
If it is
Figure BDA0002301960870000148
Adding the new request, calling a graph search algorithm, from
Figure BDA0002301960870000149
And
Figure BDA00023019608700001410
deletion of viIn a
Figure BDA00023019608700001411
To which v is addedi(ii) a If it is
Figure BDA00023019608700001412
Calling a graph search algorithm from
Figure BDA00023019608700001413
Deletion of viAnd is incorporated in
Figure BDA00023019608700001414
To which v is addedi(ii) a If it is
Figure BDA00023019608700001415
For null, update the current solution RcurrentAnd cost ccurrentIn a
Figure BDA00023019608700001416
To which v is added0Invoking a graph search algorithm, from
Figure BDA00023019608700001417
Deletion of v0。
The invention can improve the efficiency and accuracy of network planning, enables the customized bus service to be more humanized and provides reliable technical support for the actual operation optimization of the customized bus.

Claims (6)

1. A demand response type customized bus network planning method based on a two-stage optimization model is characterized by comprising the following steps:
(1) dynamically gathering user travel demands in the deadline through a network platform, wherein the user travel demands comprise pickup time, pickup sites, delivery time and delivery site information expected by each user;
(2) building a demand response type customized public transport network framework, and initializing a network by using historical demand data;
(3) according to new requirements of users, comprehensively considering time deviation and vehicle passenger carrying capacity constraint, and searching a feasible new user request insertion scheme by using an insertion checking algorithm and a dynamic insertion algorithm to solve a two-stage decision problem of a dynamic stage;
(4) integrating all feasible temporary schemes, predicting the travel cost and the travel time, sending a travel plan to the user, and waiting for the user to make a decision;
(5) calculating a probability of the user confirming the provided travel plan based on a Monte Carlo simulation process for subsequent simulation;
(6) and updating a target function and time deviation constraint of the customized bus network planning problem based on the number of the confirmed travel users, and solving the customized bus network planning problem in a static stage by adopting a graph search algorithm based on a branch-and-bound algorithm to obtain an optimal solution.
2. The demand response type customized bus network planning method based on two-stage optimization model as claimed in claim 1, wherein in step (1), the demand data mainly comprises personal information of users and time for submitting demand
Figure FDA0002301960860000011
Desired ride time
Figure FDA0002301960860000012
Desired pickup station
Figure FDA0002301960860000013
Expected delivery time
Figure FDA0002301960860000014
Desired delivery site
Figure FDA0002301960860000015
3. The demand response type customized bus network planning method based on the two-stage optimization model as claimed in claim 1, wherein in the step (2), the built demand response type customized bus network framework is as follows:
in (V, a), the station set is V ═ V0,v1,...,vnConsists of three subsets: pick-up station set VpDelivery site set VdAnd an origin station v0(ii) a The road section set is A { (v)i,vj):vi,vjE is V, i is not equal to j; r represents a newly emerging demand set, VrRepresenting a set of sites containing spatial information of a demand R ∈ R, i.e.
Figure FDA0002301960860000016
And
Figure FDA0002301960860000017
each request and expected take-over time
Figure FDA0002301960860000018
And expected delivery time
Figure FDA0002301960860000019
Associated, origin-destination (v)i,vj) Q is the cumulative number of demands in betweenijThe fleet of homogenous vehicles is denoted as K; the passenger carrying capacity of all vehicles is cap, JkRepresenting a route serviced by a vehicle K e K, which may be made up of a set of stops Vk＝{vi|(vi,vj)∈Jk,vjE.g. V.
4. The demand response type customized bus network planning method based on the two-stage optimization model as claimed in claim 1, wherein the two-stage decision problem, the insert inspection algorithm and the dynamic insert algorithm in the step (3) are specifically as follows:
(31) two-stage decision problem
The new request r submitted by the user includes: desired pickup station
Figure FDA0002301960860000021
Desired delivery site
Figure FDA0002301960860000022
At the actual take-over point viDesired take-over time of
Figure FDA0002301960860000023
At the actual delivery point vjDesired delivery time of
Figure FDA0002301960860000024
If there are n passengers, the station v will beiWaiting for the vehicle k, the expected pick-up time of the r-th passenger being
Figure FDA0002301960860000025
The time deviation threshold for each request r is tmaxThe operator then provides the user with a plan in which the vehicle k is at the pick-up station viThe arrival and departure times of (d) should satisfy:
Figure FDA0002301960860000026
Figure FDA0002301960860000027
vehicle k at delivery station vjTime of arrival of
Figure FDA0002301960860000028
It should satisfy:
Figure FDA0002301960860000029
for pick-up station vi∈VpIts actual ride-through time should satisfy:
Figure FDA00023019608600000210
wherein ,
Figure FDA00023019608600000211
Indicating that the corresponding demand r is at the take-over point viActual ride-through time of;
Figure FDA00023019608600000212
indicating that the corresponding demand r is at the take-over point viDesired ride-through time;
Figure FDA00023019608600000213
and
Figure FDA00023019608600000214
respectively representing the vehicle k at the station viArrival time and departure time of;
for delivery site vj∈VdThe actual delivery time should satisfy:
Figure FDA00023019608600000215
when the number of confirmed passengers is less than the minimum load factor qminAt that time, a premium τ is charged0Then trip cost
Figure FDA00023019608600000216
Comprises the following steps:
Figure FDA0002301960860000031
wherein ,
Figure FDA0002301960860000032
to be based on site vi and vjThe fixed cost of the distance is that,
Figure FDA0002301960860000033
cost per unit distance, dijFor station vi and vjThe distance between the two or more of the two or more,
Figure FDA0002301960860000034
is the number of passengers assigned to vehicle k
Figure FDA0002301960860000035
Representing a decision variable vector;
Figure FDA0002301960860000036
representing the probability of the passenger accepting the travel plan provided by the operator; the total fee expected to be charged by the customized public transportation system after the user confirms the journey is
Figure FDA0002301960860000037
Where E (-) is the desired operator;
to achieve operator profit maximization, the objective function is:
Figure FDA0002301960860000038
the following constraints are satisfied in terms of the expressions (1) to (3):
Figure FDA0002301960860000039
Figure FDA00023019608600000310
Figure FDA00023019608600000311
Figure FDA00023019608600000312
Figure FDA00023019608600000313
Figure FDA00023019608600000314
wherein α is the unit distance operation cost, β is the fixed cost of additionally scheduling a vehicle, equations (1) - (3) are the maximum time deviation constraint, equation (8) defines the maximum passenger carrying capacity of each vehicle, equation (9) ensures that each request is served by a vehicle, equation (10) ensures that each route is a closed curve with a starting point and an ending point coincident with an originating station, equations (11) - (13) define binary variables;
OD pairs (v) in the customized public transport network N constructed by the travel schemei,vj) Travel utility of room
Figure FDA00023019608600000315
Satisfy the requirement of
Figure FDA00023019608600000316
Figure FDA00023019608600000317
wherein
Figure FDA0002301960860000041
In order to provide the expected travel costs for the passengers,
Figure FDA0002301960860000042
cost savings for passengers after choosing to take a customized bus, cij(N) is a system item of,
Figure FDA0002301960860000043
is an error term, obedience is expected to equal zero, variance is equal to
Figure FDA0002301960860000044
Normal distribution of (a):
Figure FDA0002301960860000045
where λ is time, tijIs OD pair (v)i,vj) The time of flight in between is determined,
Figure FDA0002301960860000046
and
Figure FDA0002301960860000047
the time deviation is used as the punishment factor corresponding to the time deviation mu;
the probability that the passenger accepts the travel plan provided by the operator is:
Figure FDA0002301960860000048
(32) insertion checking algorithm and dynamic insertion algorithm
For new requests
Figure FDA0002301960860000049
If it is
Figure FDA00023019608600000410
And
Figure FDA00023019608600000411
already existing in the existing route JkPerforming the following steps; and is arranged at
Figure FDA00023019608600000412
And
Figure FDA00023019608600000413
where the current arrival and departure times are
Figure FDA00023019608600000414
And
Figure FDA00023019608600000415
and is
Figure FDA00023019608600000416
Within an acceptable time interval, then the request r may be inserted directly into route JkPerforming the following steps;
if the delivery point of r is requested
Figure FDA00023019608600000417
Already exists in route JkMiddle, but next to the multiplication point
Figure FDA00023019608600000418
Out of route JkIn (3), the following checks are performed: if it is currently at vmWithout demand, then vmCan be replaced by
Figure FDA00023019608600000419
Checking that the vehicle arrives at the station at this time
Figure FDA00023019608600000420
Time period of
Figure FDA00023019608600000421
Whether or not to coincide with an acceptable time period
Figure FDA00023019608600000422
Intersecting; if it is currently at vmOn demand, then vmIndelible, check
Figure FDA00023019608600000423
Whether or not v can be insertedmThereafter, the arrival of the vehicle at the station at the time is checked
Figure FDA00023019608600000424
Time period of
Figure FDA00023019608600000425
Whether or not to coincide with an acceptable time period
Figure FDA00023019608600000426
Figure FDA00023019608600000427
Intersecting;
if the pick-up point of r is requested
Figure FDA00023019608600000428
Already exists in route JkMiddle, but delivery point
Figure FDA00023019608600000429
Out of route JkIn (3), the following checks are performed: if it is currently at vmWithout demand, then vmCan be replaced by
Figure FDA00023019608600000430
Checking that the vehicle arrives at the station at this time
Figure FDA00023019608600000431
Time period of
Figure FDA00023019608600000432
Whether or not to coincide with an acceptable time period
Figure FDA00023019608600000433
Intersecting; if it is currently at vmOn demand, then vmIndelible, check
Figure FDA00023019608600000434
Whether or not v can be insertedmThen; checking that the vehicle arrives at the station at this time
Figure FDA00023019608600000435
Time period of
Figure FDA00023019608600000436
Whether or not to coincide with an acceptable time period
Figure FDA00023019608600000437
Intersecting;
by iterating the above insertion checking algorithm as a subroutine, the following dynamic insertion algorithm can be obtained:
input historical route set JkRoute including site set VkAnd at each site vi∈VkTime of arrival of
Figure FDA0002301960860000051
And time of departure
Figure FDA0002301960860000052
Entering a new request
Figure FDA0002301960860000053
For each historical route JkApplying an insertion checking algorithm to generate a secondary V for the demand r if a feasible insertion solution cannot be found0To
Figure FDA0002301960860000054
And
Figure FDA0002301960860000055
the new route of (1);
for each insertion scheme, calculating the profit of an operator and the travel cost of a passenger, calculating the probability of the passenger selecting the scheme, and obtaining the expected profit of the scheme; keeping the insertion scheme with the highest expected profit, and updating the network;
if a new request is submitted to the operator, the input stage is switched to, and a loop is entered, otherwise, the process is ended.
5. The demand response type customized bus network planning method based on the two-stage optimization model as claimed in claim 1, wherein in step (5), based on the monte carlo simulation process, the probability that the user confirms the travel plan provided by the operator is obtained as follows:
Figure FDA0002301960860000056
when N → ∞ is reached,
Figure FDA0002301960860000057
wherein N is the number of times of simulation tests,
Figure FDA0002301960860000058
the number of times the travel cost can be reduced after the customized bus is selected for the user.
6. The demand response type customized bus network planning method based on the two-stage optimization model as claimed in claim 1, wherein in the step (6), the customized bus network planning problem in the static stage and the graph search algorithm based on the branch-and-bound algorithm are detailed as follows:
after entering the static phase, the objective function should be re-expressed as:
Figure FDA0002301960860000059
the time deviation constraints (3) - (4) should be re-expressed as:
Figure FDA00023019608600000510
Figure FDA00023019608600000511
wherein ,
Figure FDA00023019608600000512
and
Figure FDA00023019608600000513
is the pick-up time and delivery time in the dynamic phase operator provisioning scheme;
the graph search algorithm based on the branch-and-bound algorithm comprises the following specific steps:
initialization
Figure FDA0002301960860000061
Current lowest cost cminThe best solution at present
Figure FDA0002301960860000062
Generating a current route
Figure FDA0002301960860000063
Performing graph search, and if the time deviation constraint of the expressions (20) and (21) and the passenger carrying capacity constraint of the expression (8) are not satisfied, returning; if the current theoretical minimum cost is higher than the cost of the optimal solution, returning; if it is
Figure FDA0002301960860000064
And
Figure FDA0002301960860000065
if it is empty, the total cost is calculated by equation (19); if the current cost is lower than the current lowest cost, updating the current lowest cost cmin＝ccurrentAnd the current best solution Ropt＝Rcurrent(ii) a Returning; if it is
Figure FDA0002301960860000066
Adding the new request, calling a graph search algorithm, from
Figure FDA0002301960860000067
And
Figure FDA0002301960860000068
deletion of viIn a
Figure FDA0002301960860000069
To which v is addedi(ii) a If it is
Figure FDA00023019608600000610
Calling a graph search algorithm from
Figure FDA00023019608600000611
Deletion of viAnd is incorporated in
Figure FDA00023019608600000612
To which v is addedi(ii) a If it is
Figure FDA00023019608600000613
For null, update the current solution RcurrentAnd cost ccurrentIn a
Figure FDA00023019608600000614
To which v is added0Invoking a graph search algorithm, from
Figure FDA00023019608600000615
Deletion of v0。
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