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 PDFInfo
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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
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 requirementWorkshopDesired ride timeDesired pickup stationExpected delivery timeDesired delivery site
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.And each request and expected take-over timeAnd expected delivery timeAnd (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 stationDesired delivery siteAt the actual take-over point viDesired take-over time ofAt the actual delivery point vjDesired delivery time of
If there are n passengers, the station v will beiWaiting for the vehicle k, the expected pick-up time of the r-th passenger beingThe 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:
for pick-up station vi∈VpIts actual ride-through time should satisfy:
wherein ,indicating that the corresponding demand r is at the take-over point viActual ride-through time of;indicating that the corresponding demand r is at the take-over point viDesired ride-through time;andrespectively representing the vehicle k at the station viArrival time and departure time of;
for delivery site vj∈VdThe actual delivery time should satisfy:
when the number of confirmed passengers is less than the minimum load factor qminAt that time, a premium τ is charged0. Then the trip costComprises the following steps:
wherein ,to be based on site vi and vjThe fixed cost of the distance is that,cost per unit distance, dijFor station vi and vjThe distance between the two or more of the two or more,is the number of passengers assigned to vehicle kRepresenting a decision variable vector;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 isWhere E (-) is the desired operator;
to achieve operator profit maximization, the objective function is:
the following constraints are satisfied in terms of the expressions (1) to (3):
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 roomSatisfy the requirement of
wherein In order to provide the expected travel costs for the passengers,for passenger selectionCost savings after choosing to take a custom bus, cij(N) is a system item of,is an error term, obedience is expected to equal zero, variance is equal toNormal distribution of (a):
where λ is time, tijIs OD pair (v)i,vj) The time of flight in between is determined,andthe 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:
(32) insertion checking algorithm and dynamic insertion algorithm
For new requestsIf it isAndalready existing in the existing route JkPerforming the following steps; and is arranged atAndwhere the current arrival and departure times areAndand isWithin 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 requestedAlready exists in route JkMiddle, but next to the multiplication pointOut of route JkIn (3), the following checks are performed: if it is currently at vmWithout demand, then vmCan be replaced byChecking that the vehicle arrives at the station at this timeTime period ofWhether or not to coincide with an acceptable time periodIntersecting; if it is currently at vmOn demand, then vmAnd cannot be deleted. Examination ofWhether or not v can be insertedmAnd then. Checking that the vehicle arrives at the station at this timeTime period ofWhether or not to coincide with an acceptable time period Intersecting;
if the pick-up point of r is requestedAlready exists in route JkMiddle, but delivery pointOut of route JkIn (3), the following checks are performed: if it is currently at vmWithout demand, then vmCan be replaced byChecking that the vehicle arrives at the station at this timeTime period ofWhether or not to coincide with an acceptable time periodIntersecting; if it is currently at vmOn demand, then vmAnd cannot be deleted. Examination ofWhether or not v can be insertedmThen; checking that the vehicle arrives at the station at this timeTime period ofWhether or not to coincide with an acceptable time periodIntersecting;
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 ofAnd time of departureEntering a new request
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 found0ToAndthe 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:
when N → ∞ is reached,wherein N is the number of times of simulation tests,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:
the time deviation constraints (3) - (4) should be re-expressed as:
wherein ,andis 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:
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 isAndif 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 isAdding the new request, calling a graph search algorithm, fromAnddeletion of viIn aTo which v is addedi(ii) a If it isCall graph searchAlgorithm, fromDeletion of viAnd is incorporated inTo which v is addedi(ii) a If it isFor null, update the current solution RcurrentAnd cost ccurrentIn aTo which v is added0Invoking a graph search algorithm, fromDeletion 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 demandDesired ride timeDesired pickup stationExpected delivery timeDesired delivery site
(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.And each request is also multiplied by the expected take-over timeAnd expected delivery timeAnd (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 stationDesired delivery siteAt the actual take-over point viDesired take-over time ofAt the actual delivery point vjDesired delivery time ofThe 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 ofShould be in the time periodIn the meantime.
Suppose that an existing n passengers will be at station viWaiting for vehicle k.Andindicating 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 tolerateThe departure time of the vehicle should not be earlier than the earliest ride time that the last passenger can tolerateThus, the vehicle k is at the pick-up station viShould meet the arrival and departure time of
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 kIt should satisfy:
for pick-up station vi∈VpIts actual ride-through time should satisfy:
wherein ,indicating that the corresponding demand r is at the take-over point viActual ride-through time of;indicating that the corresponding demand r is at the take-over point viDesired ride-through time;andrespectively 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:
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 ofComprises the following steps:
wherein ,to be based on site vi and vjThe fixed cost of the distance is that,cost per unit distance, dijFor station vi and vjThe distance between the two or more of the two or more,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:
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, thenIs 1, otherwise is 0. If the route traveled by vehicle k is (v)i,vj) Then, thenIs 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.Representing a decision variable vector.Representing the probability of the passenger accepting the travel plan provided by the operator.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:
the following constraints are satisfied in terms of the expressions (1) to (3):
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 roomSatisfy the requirement of
wherein In order to provide the expected travel costs for the passengers,for passengers at OD pairs (v)i,vj) Cost saving after choosing to take the customized bus, cij(N) is a system item of,is an error term, obedience is expected to equal zero, variance is equal toNormal distribution of (a):
where λ is time, tijIs OD pair (v)i,vj) The time of flight in between is determined,andand 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:
32) insertion checking algorithm and dynamic insertion algorithm
Step 1: if it isAndalready existing in the existing route JkPerforming the following steps; and is arranged atAndwhere the current arrival and departure times areAndand isWithin 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 requestedAlready exists in route JkMiddle, but next to the multiplication pointOut of route JkIn, then pairApplying the inspection procedure in step 2.1 and scanning route JkAll existing sites v inm∈VkTo realizeInsertion of (2):
step 2.1: if it is currently at vmWithout demand, then vmCan be replaced byFrom JkDeletion of vmAnd add inAt which time the vehicle arrives at the stationThe time period of (d) may be expressed as:checking whether the time period is equal to an acceptable time periodAnd (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 ofWhether or not v can be insertedmAnd then. At which time the vehicle arrives at the stationThe time period of (d) may be expressed as:checking whether the time period is equal to an acceptable time periodAnd (4) intersecting. If so, it is recorded as a viable insertion solution.
And step 3: if the pick-up point of r is requestedAlready exists in route JkMiddle, but delivery pointOut of route JkIn, then pairApplying the inspection procedure in step 3.1 and scanning route JkAll existing sites v inm∈VkTo realizeInsertion of (2):
step 3.1: if it is currently at vmWithout demand, then vmCan be replaced byFrom JkDeletion of vmAnd add inAt which time the vehicle arrives at the stationThe time period of (d) may be expressed as:check that this time period isWhether and acceptable time periodAnd (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 ofWhether or not v can be insertedmAnd then. At which time the vehicle arrives at the stationThe time period of (d) may be expressed as:checking whether the time period is equal to an acceptable time periodAnd (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 ofAnd time of departureInputting a newly received request r, a take-over pointAnd delivery pointAnd desired ride timeAnd delivery time
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 r0ToAndthe 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 ofAnd time of departure
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 onIs sampled by the distribution function of (a). Let N be the number of times the simulation experiment was repeated,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:
(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:
the time deviation constraints (3) - (4) should be re-expressed as:
wherein ,andis 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.For a set of multiply points that have not been visited,for a set of passengers that have not yet arrived at the destination,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:
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
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 isAndif 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.
If it isAdding the new request, calling a graph search algorithm, fromAnddeletion of viIn aTo which v is addedi(ii) a If it isCalling a graph search algorithm fromDeletion of viAnd is incorporated inTo which v is addedi(ii) a If it isFor null, update the current solution RcurrentAnd cost ccurrentIn aTo which v is added0Invoking a graph search algorithm, fromDeletion 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 demandDesired ride timeDesired pickup stationExpected delivery timeDesired delivery site
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.Andeach request and expected take-over timeAnd expected delivery timeAssociated, 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 stationDesired delivery siteAt the actual take-over point viDesired take-over time ofAt the actual delivery point vjDesired delivery time of
If there are n passengers, the station v will beiWaiting for the vehicle k, the expected pick-up time of the r-th passenger beingThe 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:
for pick-up station vi∈VpIts actual ride-through time should satisfy:
wherein ,Indicating that the corresponding demand r is at the take-over point viActual ride-through time of;indicating that the corresponding demand r is at the take-over point viDesired ride-through time;andrespectively representing the vehicle k at the station viArrival time and departure time of;
for delivery site vj∈VdThe actual delivery time should satisfy:
when the number of confirmed passengers is less than the minimum load factor qminAt that time, a premium τ is charged0Then trip costComprises the following steps:
wherein ,to be based on site vi and vjThe fixed cost of the distance is that,cost per unit distance, dijFor station vi and vjThe distance between the two or more of the two or more,is the number of passengers assigned to vehicle kRepresenting a decision variable vector;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 isWhere E (-) is the desired operator;
to achieve operator profit maximization, the objective function is:
the following constraints are satisfied in terms of the expressions (1) to (3):
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 roomSatisfy the requirement of
wherein In order to provide the expected travel costs for the passengers,cost savings for passengers after choosing to take a customized bus, cij(N) is a system item of,is an error term, obedience is expected to equal zero, variance is equal toNormal distribution of (a):
where λ is time, tijIs OD pair (v)i,vj) The time of flight in between is determined,andthe 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:
(32) insertion checking algorithm and dynamic insertion algorithm
For new requestsIf it isAndalready existing in the existing route JkPerforming the following steps; and is arranged atAndwhere the current arrival and departure times areAndand isWithin 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 requestedAlready exists in route JkMiddle, but next to the multiplication pointOut of route JkIn (3), the following checks are performed: if it is currently at vmWithout demand, then vmCan be replaced byChecking that the vehicle arrives at the station at this timeTime period ofWhether or not to coincide with an acceptable time periodIntersecting; if it is currently at vmOn demand, then vmIndelible, checkWhether or not v can be insertedmThereafter, the arrival of the vehicle at the station at the time is checkedTime period ofWhether or not to coincide with an acceptable time period Intersecting;
if the pick-up point of r is requestedAlready exists in route JkMiddle, but delivery pointOut of route JkIn (3), the following checks are performed: if it is currently at vmWithout demand, then vmCan be replaced byChecking that the vehicle arrives at the station at this timeTime period ofWhether or not to coincide with an acceptable time periodIntersecting; if it is currently at vmOn demand, then vmIndelible, checkWhether or not v can be insertedmThen; checking that the vehicle arrives at the station at this timeTime period ofWhether or not to coincide with an acceptable time periodIntersecting;
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 ofAnd time of departureEntering a new request
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 found0ToAndthe 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:
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:
the time deviation constraints (3) - (4) should be re-expressed as:
wherein ,andis 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:
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 isAndif 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 isAdding the new request, calling a graph search algorithm, fromAnddeletion of viIn aTo which v is addedi(ii) a If it isCalling a graph search algorithm fromDeletion of viAnd is incorporated inTo which v is addedi(ii) a If it isFor null, update the current solution RcurrentAnd cost ccurrentIn aTo which v is added0Invoking a graph search algorithm, fromDeletion of v0。
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