CN116542414A - Bus skip stop and special lane reservation method based on multi-stage random optimization - Google Patents

Abstract

The invention discloses a bus skip stop and private lane reservation method based on multi-stage random optimization, which comprises the steps of firstly, constructing a road and bus network frame, then adopting a method combining a skip stop strategy and private lane reservation to construct a multi-stage random optimization problem, and solving the problem by using a scene tree and a progressive hedging value-keeping algorithm; in each scene, the jump stop and private lane reservation strategy problem of a bus is solved by utilizing double-layer planning, the upper layer solves the hierarchy optimization problem by using a branch and bound method, and the lower layer solves the multi-mode intermodal network equalization problem by using a path-based traffic distribution algorithm and a continuous average (MSA) method. The invention can improve the efficiency of bus operation and provide reliable technical support for actual operation of bus control.

Description

Bus skip stop and special lane reservation method based on multi-stage random optimization

Technical Field

The invention relates to the field of urban traffic management and control, in particular to a bus skip stop and special lane reservation method based on multi-stage random optimization.

Background

The rapid development of urbanization brings problems of traffic jam, environmental pollution and the like. The development of public transportation systems is of great significance for relieving urban traffic pressure.

The bus stop-skipping strategy is designed for reducing the stop times in the bus running process and improving the running speed. However, in a real road environment, it is difficult for a bus to maintain a high and stable running speed due to the influence of social vehicles. In order to solve the problem, a common method is to spatially separate buses from social vehicles and to provide a bus lane. However, permanent bus lanes will inevitably reduce the road capacity, resulting in more congestion along the bus-specific road section, especially during peak hours. Therefore, it is necessary to combine the two strategies to develop a more intelligent control strategy and a hybrid bus operation scheme combining the bus lane reservation strategy and the bus skip control.

Disclosure of Invention

Aiming at the defects of the prior art, the invention aims to provide a multi-stage random optimization-based bus skip stop and dedicated lane reservation method, so that the running efficiency of a bus and the traveling experience of a bus user are improved, and a reliable technical support is provided for an actual operation control scheme of the bus.

In order to achieve the above purpose, the present invention adopts the following technical scheme:

a bus skip stop and dedicated lane reservation method based on multi-stage random optimization comprises the following steps:

(1) Constructing a road network and a bus network frame;

(2) Selecting a bus route, dividing multiple stages according to the shift number to make decisions, and controlling the jump stop and the special lane reservation strategy of a vehicle in each stage; solving the multi-stage random optimization problem by using a scene tree and a progressive hedging algorithm;

(3) In each scene, solving the decision problem of jump stop and special lane reservation of a bus by utilizing double-layer planning; the upper layer uses a branch-and-bound method to solve a hierarchical optimization problem, and the lower layer uses a path-based traffic distribution algorithm and a continuous average method to solve a multi-modal network equalization problem.

Further, the specific process of the step (1) is as follows: in the graph g= (N, a), N represents a road node, and a represents a directed edge; a bus line consisting of a fleet of vehicles is established on G; t= {1,2 …, T } represents the set of vehicles on the intersection, l= {1,2, …, L } represents the set of stops on the intersection, whereinThe head space between each schedule of each vehicle is predetermined and denoted by H;

the public transport network is composed of a group of public transport lines and stations; nodes in the public transport network represent public transport stops; for a specific bus route, after the station j station position to be jumped is determined, a special bus lane can be set at the station j station inbound (j-1, j) or station outbound (j, j+1) according to the real-time traffic condition.

Further, the specific process of the step (2) is as follows:

2.1 A multi-stage decision problem) is presented:

consider the decision problem for the aggregate T-stage, where each stage only handles the control strategy for one bus; stage T, t=1, …, T is the decision problem for handling bus T; in each stage, two groups of decision variables need to be optimized in sequence, namely whether a certain station is skipped and how to set a bus lane for the station;

the objective function of the multistage random optimization is:

the constraints are:

G ₁ (x ¹ ,y ¹ )≤d ₁ (2)

G ₂ (x ¹ ,x ² ,y ¹ ,y ² )≤d ₂ (3)

……

G _T (x ^T-1 ,x ^T ,y ^T-1 ,y ^T )≤d _T (4)

wherein x is ^t 、y ^t Reserving a vector of decision variables for jump stop and a special track of the stage t; g _t (. Cndot.) is the set of phase t correspondence constraints, d _t Is the resource parameter corresponding to stage T, t=1, …, T, S is the scene tree set;

2.2 Building a scene tree):

from the scene tree, the multi-stage stochastic optimization problem is relaxed to the following:

and add the following constraints:

wherein,,reserving vector of decision variables for jump and stop and special track of stage t under scene s, H _s 、l _s Constraint vector reserved for jump stop and special track of stage t under scene s, p _s Is the conditional probability of scene s, and is related to the temporal structure of the multi-stage process;

2.3 Using a progressive over-period warranty algorithm to solve the multi-stage random optimization problem:

2.3.1 Let k=0, ρ ⁽⁰⁾ =1, epsilon=0.001, where epsilon is a parameter that determines convergence;

solving the sub-problem in the formula (6) for each scene S epsilon S to obtain an optimal solution

Wherein S' _b(s,t) Representing a subset of the scene sequence under scene s at stage t;

calculating consensus variables using equation (8)Is a value of (2);

computing multiplierWherein->Wherein->Vector representing skip and lane reservation decision variables of stage t under scene s initialized in algorithm iterative process, +.>Representing an initialized consensus variable in an algorithm iteration process;

2.3.2 Let k=k+1;

relaxing the expected constraint by using the augmented Lagrangian relaxation, and reformulating the objective function by adding a penalty term;

wherein,,is the Lagrangian multiplier and ρ is a penalty factor;

for each scene S E S, using the objective function in equation (9) to obtain the optimal solution

Calculating consensus variables using equation (8)Updating the value of (2);

updating the Lagrangian multiplier using the following formulaAnd penalty factor ρ ^(k) :

Wherein omega ^D Representing the dual step size, ω ^P Representing the original problem step length, psi ^D(k-1) The dual gap value, ψ, representing step k-1 ^D(k-2) The dual gap value, ψ, representing step k-2 ^P(k-1) The original problem gap value, ψ, representing the kth-1 step ^P(k-2) Representing the original problem gap value of the k-2 step;

2.3.3 Check termination condition:if the termination condition is satisfied, the algorithm is terminated; if it is not formedImmediately, step 2.3.2) is continued.

Further, the specific process of the step (3) is as follows:

3.1 Establishing a double layer planning problem:

defining variables and constraints related to the double-layer planning problem;

waiting time of bus t at station iWherein->Is the number of passengers boarding bus t at station i and +.> Is the number of passengers getting off bus t at stop i and +.>a and b are constants representing an average time for getting off or on each passenger on average;

wherein,,indicating whether the bus t skips the station at the station i, if 1 indicates that the station is skipped, 0 indicates that the station is not skipped;Representing the number of passengers waiting at station i desiring to get off at station j to take bus t;Indicating whether the bus t skips the station at the station l, if the bus t skips the station at the station l, the bus t is 1, and if the bus t is 0, the bus t does not skip the station;

departure time of bus t at station iEqual to the arrival time of bus t at stop i +.>Adding the waiting time of the bus t at the station i:Representing waiting time of the bus t at the station i; arrival time of bus t at stop i +.>Equal to the departure time of bus t at station i-1 +. >Plus the path travel time of bus t after leaving the last stop i-1 +.>Acceleration time->Deceleration time->I.e. The time interval between the bus t and the bus t-1 at the station i is equal to the arrival time of the bus t>Departure time from bus t-1 +.>The difference is:Gamma represents the deceleration or acceleration time of the bus at the platform;

the number of passengers skipped by bus t at station i and desiring to get off at station t is: wherein (1)>Is the number of passengers taking bus t, boarding at station i, and desiring to get off at station j; and->Wherein->Is the number of people selecting bus t at station i and desiring to get off at station j,is determined by the lower layer planning; the total number of passengers arriving at station i is +.>λ _i Indicating the arrival rate of the passenger;

the path travel time of cars and buses is represented by a modified BPR function:

wherein,,and->Travel time representing inbound or outbound link of car and bus at station i, +.>And->Free-stream travel time, alpha, representing inbound or outbound links of a car and bus at station i, respectively ^car And alpha ^bus BPR linear adjustment parameters respectively representing car and bus, beta ^car And beta ^bus BPR index adjustment parameters for cars and buses, respectively, < > >And->Flow values, n, representing inbound or outbound links of a car and bus, respectively, at station i _i The number of lanes representing the station i link or the station out link, M represents that one bus corresponds to M cars in flow conversion, and cap _i Representing the capacity of a single lane between station i-1 and station i; y is _i The number of bus lanes between the station i-1 and the station i is represented;

avoiding too long waiting time of passengers, the bus operation should satisfy the following constraints:

(a) Two consecutive buses are prohibited from skipping the same station:

(b) One bus is prohibited from continuously skipping two stations:

(c) The bus is prohibited from skipping the start station and the end station on the line:

when the bus t skips the i station, the inbound and outbound links of the i station are considered as candidate links of the bus lane reservation; with binary variablesAnd->A lane reservation scheme of the bus t is represented; jumping station i, if the inbound link of station i is reserved for bus t +.>Otherwise-> The prescribed bus lane may be reserved only on the outbound route, or both:

3.3.1 Upper layer problem):

the passengers waiting at the station consist of two parts, namely the passenger skipped by the previous bus and the passenger arriving between t and t-1; the total passenger waiting time may be expressed as:

The total in-vehicle time is the sum of the travel time between two stations and the two-station residence time, namely:

wherein,,representing the travel time of a bus between stop l-1 and stop l +.>Representing waiting time of the bus t at the station l;

the total travel time is:

similar to the cost of bus passengers, the total travel cost of the automobile user is:

skipping the station i, reserving the negative influence of the bus lane on the incoming and outgoing linesThe following can be calculated:

wherein,,and->Indicating the transit time and the traffic volume of the car after reserving the bus lane on the inbound link of station i,And->Indicating the transit time and the traffic volume of the car when no bus lane is reserved on the inbound link of station i,And->Indicating the transit time and the car flow after reserving the bus lane on the inbound link of station i,and->Indicating the transit time and the traffic of the car when the bus lane is not reserved on the inbound link of the station i; x is X _t A decision vector for reserving a bus lane for the bus t is represented;

the overall negative impact is:

the total cost of the system is as follows:

Z＝π _w Z _w +π _v Z _v +π _bus Z _bus +π _car Z _car +π _l Z _l (27)

wherein pi _w Linear adjustment coefficient, pi, representing total passenger waiting time _v Linear adjustment coefficient, pi, representing total in-vehicle time _bus Linear adjustment coefficient pi representing bus trip cost _car Linear adjustment coefficient pi representing car travel cost _l A linear adjustment coefficient indicative of a negative impact;

3.1.2 Lower layer problem):

the superscript m epsilon { car, bus } is used for distinguishing two modes of a car and a bus;representing the demand for selecting pattern m from site i to site j at stage τ; the total demand from site i to site j at stage τ is:

the car road traffic between stations i-1 and i at stage τ is:

wherein, when the path p passes through the road section between the station i-1 and the station i,otherwise-> Representing car traffic on path p;

the bus section flow between the station i-1 and the station i in the tau phase is as follows:

wherein,,representing bus flow of a path between a station i and a station j in the tau phase;

the road section travel time between the station i-1 and the station i of the car and the bus in the tau stage is as follows:

wherein,,representing the car free flow transit time between stage tau-1 station i-1 and station i,represents the bus free flow transit time between station i-1 and station i at stage τ -1,Indicating whether bus lane is set on outbound link of station i>Indicating arrangement, and->Indicating no setting;

the generalized travel cost of the automobile driver at the tau stage is as follows:

Wherein,,a car transit time representing an inbound link or an outbound link at station l;

for a public transport user, considering in-car congestion, the generalized travel cost of passengers between the station i-1 and the station i can be expressed as:

wherein eta ₁ And eta ₂ Is a parameter related to congestion in a vehicle, wherein C represents a capacity of the bus and F represents a departure frequency of the bus;

assuming that passengers arriving at a bus stop obey uniform distribution, the general trip cost for taking bus t at station i is as follows:

wherein,,bus traffic representing a phase τ station l inbound link or outbound link;

the user equalization problem can be described as follows:

wherein the method comprises the steps ofRepresenting the minimum generalized route travel cost of a traveler traveling in an m-way from station i to station j>Balanced generalized route travel cost representing travel of travelers in m-way, +.>Representing the set of paths between travel site i to site j in m-way,Representing the road section flow between the travel station i and the station j in an m mode;

demand for cars and buses according to the logic t-split functionThe method comprises the following steps of:

wherein θ is the standard deviation of perceived errors when selecting buses and cars;for adjusting selection preferences between the bus and the car; / >Is the total number of passengers from station i to station j;Representing minimum generalized route travel cost of traveler traveling in a car manner from station i to station j,/->The minimum generalized route travel cost of a traveler traveling from a station i to a station j in a bus mode is represented;

the objective function of the lower layer planning is:

constraint is formulas (28) - (35), (37) - (39) and (41);

wherein,,representing a set of paths from site i to site j;

3.2 Branch-and-bound method:

in each scenario, an upper bound is generated by assuming that any site is skipped, i.e Assuming that the first class car skips all even stations except the starting station and the end station to obtain an initial feasible solution X _current The method comprises the steps of carrying out a first treatment on the surface of the For the subsequent buses, determining the position of the skipped station through a greedy strategy according to constraint formulas (16) - (18);

after the station jump scheme is designed, the reserved bus lane is selected:

3.2.1 Initializing Y ⁽⁰⁾ ＝{y _r ＝0|r＝1,2,…S }, indicating that no bus lane is reserved for bus t;

3.2.2 Invoking branch delimitation and obtaining optimal jump strategy X _t The method comprises the steps of carrying out a first treatment on the surface of the Let w=0, and Y ^(w) ＝{y _r ＝0|r∈X _t }；

3.2.3 Y) to be Y ^(ω) Inputting the total negative income into the lane reservation optimization problem and the lower planning problem, and calculating to obtain the total negative incomeLet w=w+1; let Y ^(w-1) W is equal to 1 and obtain Y ^(w) ；

3.2.4 Returning to step 3.2.2); if it isY is then ^(w) ＝Y ^(w-1) And goes to step 3.2.5); otherwise, returning to the step 3.2.3);

3.2.5 If w= |x _t I, stop algorithm; otherwise, returning to the step 3.2.4);

3.3 Multi-mode traffic distribution algorithm):

3.3.1 Make the road section flowTraffic demand-> Path flow->Make the road section travel time +.>And->Is free flow time and n=1;

wherein,,and->Respectively representing the road traffic of a car and a bus, < >>And->Representing traffic demands of car and bus, respectively, < ->And->Represents the path flow of car and bus respectively, < ->And->The road section travel time of the car and the bus is respectively represented, and the upper mark k represents the kth path;

3.3.2 Updating the link travel time using equations (31) and (32);

3.3.3 Finding the shortest between OD pair r-s; the bus route is unique; the travel costs of the shortest car route and the shortest bus route are respectivelyAnd->Wherein, the OD pair represents a trip starting point and a trip ending point;

3.3.4 For each OD pair r-s, if ThenOtherwise the first set of parameters is selected,

wherein,,represents the traffic demand of OD on the kth path between r-s, Q _rs Indicating the total traffic demand between OD and r-s, < ->Representing the minimum cost of the kth routing car between OD versus r-s, < > >Representing the minimum cost of representing the kth routing bus between OD versus r-s, +.>Representing the total set of car paths between OD versus r-s, +.>Represents the total set of bus paths between OD and r-s, < ->Representing the set of paths that have been used by the car between OD versus r-s, +.>Representing a set of paths that have been used by the bus between OD pairs r-s;

3.3.5 Small between each OD pair r-sThe flow rate of the automobile is Bus flow between each OD pair r-s is +.> Calculating the road section flow through the formula (29) and the formula (30); for each OD pair r-s, calculating car flow +.>And bus traffic +.>

3.3.6 If n=n _max Or alternatively Terminating the algorithm; otherwise, let n=n+1 and return to step 3.3.2);

wherein N is _max Representing the total number of iterations and,representing the total cost of the kth path car in the path set p,the total cost of the kth path bus in the path set p is represented, and Q represents the total travel demand.

The invention has the beneficial effects that: the invention fully utilizes the advantages of the bus stop jump scheme and the bus lane, combines the two, and provides a feasible solution for the problem that the permanent bus lane affects the social vehicle passing efficiency; comprehensively considering the requirements and interactions of both operators and users, and analyzing more comprehensively; the multi-stage random optimization method is creatively adopted, randomness of user demands is considered, overall robustness of the control scheme is stronger, and reliable technical support is provided for actual operation control of buses.

Drawings

FIG. 1 is a flow chart of a method according to an embodiment of the invention.

Detailed Description

The present invention will be further described with reference to the accompanying drawings, and it should be noted that, while the present embodiment provides a detailed implementation and a specific operation process on the premise of the present technical solution, the protection scope of the present invention is not limited to the present embodiment.

The embodiment provides a bus skip stop and dedicated lane reservation method based on multi-stage random optimization, and provides a multi-stage random optimization problem in consideration of uncertainty of passenger demands. The evolution of uncertainty is explained by a scene tree, and the multi-stage problem is solved by using a progressive method based on the set period guard, and the large-scale optimization problem is decomposed into sub-problems. As shown in fig. 1, the method comprises the steps of:

(1) Constructing a road network and a bus network frame;

in the graph g= (N, a), N represents a road node, and a represents a directed edge. A bus route consisting of a fleet of buses is established on G. T= {1,2 …, T } represents the set of buses on the bus, l= {1,2, …, L } represents the set of stops on the bus, wherein The head space between each schedule of each vehicle is predetermined and denoted by H.

The public transport network is composed of a group of public transport lines and public transport stops. Nodes in the public transport network represent public transport stops. For a specific bus route, after the station j position of the station to be jumped is determined, a special bus lane can be arranged at the station j of the station j (j-1, j) or the station j (j, j+1) according to the real-time traffic condition.

(2) Selecting a bus route, dividing multiple stages according to the shift number to make decisions, and controlling the skip stop and the special lane reservation strategy of a bus in each stage; solving the multi-stage stochastic optimization problem using a scene tree and a progressive hedging algorithm (the progressive hedging algorithm, PHA);

2.1 A multi-stage decision problem) is presented:

consider the decision problem of totaling T phases, where each phase only deals with the control strategy of one bus. Stage T (t=1, …, T) deals with the decision problem of bus T. In each stage, two sets of decision variables need to be optimized in turn, whether to skip a certain station and how to set a bus lane for the station.

The objective function of the multistage random optimization is:

the constraints are:

G ₁ (x ¹ ,y ¹ )≤d ₁ (2)

G ₂ (x ¹ ,x ² ,y ¹ ,y ² )≤d ₂ (3)

……

G _T (x ^T-1 ,x ^T ,y ^T-1 ,y ^T )≤d _T (4)

wherein c ^t 、y ^t Reserving a vector of decision variables for jump stop and a special track of the stage t; g _t (. Cndot.) is the set of phase t correspondence constraints, d _t Is the resource parameter corresponding to phase t, t=1,…, T, S are scene tree sets.

2.2 Building a scene tree):

the present embodiment uses scene trees to interpret the information structure of the problem, describing the evolution of uncertainty. Information phase ζ of the first phase corresponding to the root node (s=0) ¹ ，ξ ¹ Is known in advance. Each node of the t-phase represents ζ ^t Is described herein). Each node of the t-phase is connected by a unique node (except the root node) through the arc of phase t-1. The probability of the node s being related to the information state is p _s . The path from the root node to the terminal node corresponds to a scene and is also the joint realization of parameters of each stage of the problem. The probability of each scene may be obtained by using the conditional probability of the corresponding path. The passenger demands at the same time in different dates are clustered into a plurality of scenes, and the probability of occurrence of a certain scene is given by the ratio of the number of samples of the scene to the total number of samples, so as to generate a scene tree.

From the scene tree, the multi-stage stochastic optimization problem is relaxed to the following:

and add the following constraints:

wherein,,reserving vector of decision variables for jump and stop and special track of stage t under scene s, H _s 、l _s Constraint vector reserved for jump stop and special track of stage t under scene s, p _s Is the conditional probability of the scene s, and is related to the temporal structure of the multi-stage process.

2.3 Using a progressive over-period warranty algorithm to solve the multi-stage random optimization problem:

2.3.1 Let k=0, ρ ⁽⁰⁾ ＝1，ε＝0.001，Wherein epsilon is a parameter for judging convergence;

solving the sub-problem in the formula (6) for each scene S epsilon S to obtain an optimal solution

Wherein S' _b(s,t) Representing a subset of the sequence of scenes under scene s at stage t.

Calculating consensus variables using equation (8)Is a value of (2);

computing multiplierWherein->Wherein->Vector representing skip and lane reservation decision variables of stage t under scene s initialized in algorithm iterative process, +.>Representing the consensus variable initialized during the algorithm iteration.

2.3.2 Let k=k+1;

the objective function is reformulated by adding a penalty term using the augmented lagrangian relaxation to relax the expected constraint.

Wherein,,is the Lagrangian multiplier and ρ is a penalty factor. />

For each scene S E S, using the objective function in equation (9) to obtain the optimal solution

Calculating consensus variables using equation (8)Updating the value of (2);

updating the Lagrangian multiplier using the following formulaAnd penalty factor ρ ^(k) :

Wherein omega ^D Representing the dual step size, ω ^P Representing the original problem step length, psi ^D(k-1) The dual gap value, ψ, representing step k-1 ^D(k-2) The dual gap value, ψ, representing step k-2 ^P(k-1) The original problem gap value, ψ, representing the kth-1 step ^P(k-2) The original problem gap value of the k-2 step is shown.

2.3.3 Check termination condition:if the termination condition is satisfied, the algorithm is terminated; if not, proceed to step 2.3.2).

(3) In each scene, the jump stop and special lane reservation decision problem of a bus is solved by utilizing double-layer planning. The upper layer uses a branch-and-bound method to solve a hierarchical optimization problem, and the lower layer uses a path-based traffic distribution algorithm and a continuous average (MSA) method to solve a multi-modal intermodal network equalization problem.

3.1 Establishing a double layer planning problem:

variables and constraints involved in the double-layer planning problem are defined.

Waiting time of bus t at station iWherein->Is the number of passengers boarding bus t at station i and +.> Is the number of passengers getting off bus t at stop i and +.>a and b are constants representing an average time for getting off or on each passenger on average;

wherein,,indicating whether bus t skips the stop at station i, if 1 indicates that it skips the stop, 0 indicates that it does not skip the stop.Indicating that waiting for a desired presence at site ij number of passengers getting off bus t. / >Indicating whether bus t skips the stop at stop l, if 1 indicates that the stop is skipped, 0 indicates that the stop is not skipped.

Departure time of bus t at station iEqual to the arrival time of bus t at stop i +.>Adding the waiting time of the bus t at the station i: Representing waiting time of the bus t at the station i; arrival time of bus t at stop i +.>Equal to the departure time of bus t at station i-1 +.>Plus the path travel time of bus t after leaving the last stop i-1 +.>Acceleration time->Deceleration time->I.e. The time interval between the bus t and the bus t-1 at the station i is equal to the arrival time of the bus t>Departure time from bus t-1 +.>The difference is:Gamma represents the deceleration or acceleration time of the bus at the stop.

The number of passengers skipped by bus t at station i and desiring to get off at station j is: wherein (1)>Is the number of passengers taking bus t, getting on at station i, and desiring to get off at station j. And->Wherein->Is the number of people selecting bus t at station i and desiring to get off at station j, +.>Is determined by the underlying plan. The total number of passengers arriving at station i is +.>λ _i Indicating the arrival rate of the passenger.

The path travel time of cars and buses is represented by a modified BPR function:

Wherein,,and->Travel time representing inbound or outbound link of car and bus at station i, +.>And->Free-stream travel time, alpha, representing inbound or outbound links of a car and bus at station i, respectively ^car And alpha ^bus BPR linear adjustment parameters respectively representing car and bus, beta ^car And beta ^bus BPR index adjustment parameters for cars and buses, respectively, < >>And->Flow values, n, representing inbound or outbound links of a car and bus, respectively, at station i _i The number of lanes representing the station i link or the station out link, M represents that one bus corresponds to M cars in flow conversion, and cap _i Representing the capacity of a single lane between station i-1 and station i; y is _i Representing buses between station i-1 and station iNumber of lanes.

Avoiding too long waiting time of passengers, the bus operation should satisfy the following constraints:

(a) Two consecutive buses are prohibited from skipping the same station:

(b) One bus is prohibited from continuously skipping two stations:

(c) The bus is prohibited from skipping the start station and the end station on the line:

when bus t skips over an i station, the inbound and outbound links of the i station are considered candidate links for bus lane reservation. With binary variables And->Indicating a lane reservation scheme for bus t. Jumping station i, if the inbound link of station i is reserved for bus t +.>Otherwise->0. The prescribed bus lane may be reserved only on the outbound route, or both:

3.3.1 Upper layer problem):

the passengers waiting at the stops consist of two parts, the passenger skipped by the previous bus and the passenger arriving between t and t-1. The total passenger waiting time may be expressed as:

the total in-vehicle time is the sum of the travel time between two stations and the two-station residence time, namely:

wherein,,representing the travel time of a bus between stop l-1 and stop l +.>Indicating the waiting time of bus t at stop l.

The total travel time is:

similar to the cost of bus passengers, the total travel cost of the automobile user is:

skipping the station i, reserving the negative influence of the bus lane on the incoming and outgoing linesThe following can be calculated:

wherein,,and->Indicating the transit time and the traffic volume of the car after reserving the bus lane on the inbound link of station i,And->Indicating the transit time and the traffic volume of the car when no bus lane is reserved on the inbound link of station i,And->Indicating the transit time and the car flow after reserving the bus lane on the inbound link of station i, And->Indicating the transit time and the car flow when no bus lane is reserved on the inbound link of station i. X is X _t Decision direction for representing reserved bus lane of bus tAmount of the components.

The overall negative impact is:

the total cost of the system is as follows:

Z＝π _w Z _w +π _v Z _v +π _bus Z _bus +π _car Z _car +π _l Z _l (27)

wherein pi _w Linear adjustment coefficient, pi, representing total passenger waiting time _v Linear adjustment coefficient, pi, representing total in-vehicle time _bus Linear adjustment coefficient pi representing bus trip cost _car Linear adjustment coefficient pi representing car travel cost _l A linear adjustment coefficient representing a negative effect.

3.1.2 Lower layer problem):

the superscript m.epsilon.car, bus is used to distinguish between two modes of car and bus.Representing the demand for selecting pattern m from site i to site j at stage τ. The total demand from site i to site j at stage τ is:

the car road traffic between stations i-1 and i at stage τ is:

wherein, when the path p passes through the road section between the station i-1 and the station i,otherwise-> Representing the car traffic on path p.

The bus section flow between the station i-1 and the station i in the tau phase is as follows:

wherein,,representing the bus traffic of the path between station i and station j at stage tau.

The road section travel time between the station i-1 and the station i of the car and the bus in the tau stage is as follows:

Wherein,,representing the car free flow transit time between stage tau-1 station i-1 and station i,represents the bus free flow transit time between station i-1 and station i at stage τ -1,Indicating whether bus lane is set on outbound link of station i>Indicating arrangement, and->Indicating no setting.

The generalized travel cost of the automobile driver at the tau stage is as follows:

wherein,,indicating the car transit time of the inbound link or outbound link at station l.

For a public transport user, considering in-car congestion, the generalized travel cost of passengers between the station i-1 and the station i can be expressed as:

wherein eta ₁ And eta ₂ Is a parameter related to congestion in a vehicle, where C represents the capacity of the bus and F represents the departure frequency of the bus.

Assuming that passengers arriving at a bus stop obey uniform distribution, the general trip cost for taking bus t at station i is as follows:

wherein,,representing bus traffic for inbound or outbound links for phase τ, station l.

The user equalization problem can be described as follows:

wherein the method comprises the steps ofRepresenting the minimum generalized route travel cost of a traveler traveling in an m-way from station i to station j>Balanced generalized route travel cost representing travel of travelers in m-way, +. >Representing the set of paths between travel site i to site j in m-way,The road traffic between the travel station i to the station j in m is represented.

Demand for cars and buses according to the logic t-split functionThe method comprises the following steps of:

wherein θ is the standard deviation of perceived errors when selecting buses and cars;for adjusting selection preferences between the bus and the car;Is the total number of passengers from station i to station j;Representing minimum generalized route travel cost of traveler traveling in a car manner from station i to station j,/->The minimum generalized route travel cost of a traveler traveling from a station i to a station j in a bus mode is represented;

the objective function of the lower layer planning is:

the constraints are formulas (28) - (35), (37) - (39) and (41).

Wherein,,representing the set of paths from site i to site j.

3.2 Branch-and-bound method:

in each scenario, an upper bound is generated by assuming that any site is skipped, i.e Assuming that the first class car skips all even stations except the starting station and the end station to obtain an initial feasible solution X _current The method comprises the steps of carrying out a first treatment on the surface of the For subsequent buses, the position of the skipped station is determined by greedy strategy according to constraint formulas (16) - (18).

After the station jump scheme is designed, the reserved bus lane is selected:

3.2.1 Initializing Y ⁽⁰⁾ ＝{y _r = 0|r =1, 2, …, s }, indicating that no bus lane is reserved for bus t.

3.2.2 Invoking branch delimitation and obtaining optimal jump strategy X _t The method comprises the steps of carrying out a first treatment on the surface of the Let w=0, and Y ^(w) ＝{y _r ＝0|r∈X _t }。

3.2.3 Y) to be Y ^(ω) Inputting the total negative income into the lane reservation optimization problem and the lower planning problem, and calculating to obtain the total negative incomeLet w=w+1; let Y ^(w-1) W is equal to 1 and obtain Y ^(w) 。

3.2.4 Returning to step 3.2.2); if it isY is then ^(w) ＝Y ^(w-1) And goes to step 3.2.5); otherwise, returning to the step 3.2.3).

3.2.5 If w= |x _t I, stop algorithm; otherwise, returning to the step 3.2.4).

3.3 Multi-mode traffic distribution algorithm):

3.3.1 Make the road section flowTraffic demand-> Path flow->Make the road section travel time +.>And->Is free flow time and n=1.

Wherein,,and->Respectively representing the road traffic of a car and a bus, < >>And->Representing traffic demands of car and bus, respectively, < ->And->Represents the path flow of car and bus respectively, < ->And->The road travel time of the car and the bus are respectively represented, and the upper mark k represents the kth path.

3.3.2 Using equations (31) and (32) to update the link travel time.

3.3.3 Find the shortest between OD pair r-s. The bus route is unique. The travel costs of the shortest car route and the shortest bus route are respectively And->Wherein the OD pair represents a trip start point and a trip end point.

3.3.4 For each OD pair r-s, if ThenOtherwise the first set of parameters is selected,

wherein,,represents the traffic demand of OD on the kth path between r-s, Q _rs Indicating the total traffic demand between OD and r-s, < ->Representing the minimum cost of the kth routing car between OD versus r-s, < >>Representing the minimum cost of representing the kth routing bus between OD versus r-s, +.>Representing the total set of car paths between OD versus r-s, +.>Represents the total set of bus paths between OD and r-s, < ->Representing the set of paths that have been used by the car between OD versus r-s, +.>Representing the set of paths that have been used by the bus between OD versus r-s.

3.3.5 Car flow between each OD pair r-s is Bus flow between each OD pair r-s is +.> The link flow is calculated by equation (29) and equation (30). For each OD pair r-s, calculating car flow +.>And bus traffic +.>

3.3.6 If n=n _max Or alternatively The algorithm terminates. Otherwise, let n=n+1 and return to step 3.3.2).

Wherein N is _max Representing the total number of iterations and,representing the total cost of the kth path car in the path set p,representing the kth bus in the set of paths p Total cost, Q, represents total travel demand.

Various modifications and variations of the present invention will be apparent to those skilled in the art in light of the foregoing teachings and are intended to be included within the scope of the following claims.

Claims (4)

1. A bus skip stop and dedicated lane reservation method based on multi-stage random optimization is characterized by comprising the following steps:

(1) Constructing a road network and a bus network frame;

(2) Selecting a bus route, dividing multiple stages according to the shift number to make decisions, and controlling the jump stop and the special lane reservation strategy of a vehicle in each stage; solving the multi-stage random optimization problem by using a scene tree and a progressive hedging algorithm;

(3) In each scene, solving the decision problem of jump stop and special lane reservation of a bus by utilizing double-layer planning; the upper layer uses a branch-and-bound method to solve a hierarchical optimization problem, and the lower layer uses a path-based traffic distribution algorithm and a continuous average method to solve a multi-modal network equalization problem.

2. The method for bus stop-and-lane reservation based on multistage random optimization of claim 1, wherein the specific process of step (1) is as follows: in the graph g= (N, a), N represents a road node, and a represents a directed edge; a bus line consisting of a fleet of vehicles is established on G; t= {1,2 …, T } represents the set of vehicles on the intersection, l= {1,2, …, L } represents the set of stops on the intersection, wherein The head space between each schedule of each vehicle is predetermined and denoted by H;

the public transport network is composed of a group of public transport lines and stations; nodes in the public transport network represent public transport stops; for a specific bus route, after the station j station position to be jumped is determined, a special bus lane can be set at the station j station inbound (j-1, j) or station outbound (j, j+1) according to the real-time traffic condition.

3. The method for bus stop-and-lane reservation based on multistage random optimization according to claim 2, wherein the specific process of step (2) is as follows:

2.1 A multi-stage decision problem) is presented:

consider the decision problem for the aggregate T-stage, where each stage only handles the control strategy for one bus; stage T, t=1..t is the decision problem for handling bus T; at each stage, two sets of decision variables need to be optimized in turn: whether to skip a certain station or not and how to set a bus lane for the station;

the objective function of the multistage random optimization is:

the constraints are:

G ₁ (x ¹ ，y ¹ )≤d ₁ (2)

G ₂ (x ¹ ，x ² ，y ¹ ，y ² )≤d ₂ (3)

……

G _T (x ^T-1 ，x ^T ，y ^T-1 ，y ^T )≤d _T (4)

wherein x is ^t 、y ^t Reserving a vector of decision variables for jump stop and a special track of the stage t; g _t (. Cndot.) is the set of phase t correspondence constraints, d _t Is the resource parameter corresponding to stage T, t=1,..t, S is the scene tree set;

2.2 Building a scene tree):

from the scene tree, the multi-stage stochastic optimization problem is relaxed to the following:

and add the following constraints:

wherein,,reserving vector of decision variables for jump and stop and special track of stage t under scene s, H _s 、l _s Constraint vector reserved for jump stop and special track of stage t under scene s, p _s Is the conditional probability of scene s, and is related to the temporal structure of the multi-stage process;

2.3 Using a progressive over-period warranty algorithm to solve the multi-stage random optimization problem:

2.3.1 Let k=0, ρ ⁽⁰⁾ =1, epsilon=0.001, where epsilon is a parameter that determines convergence;

solving the sub-problem in the formula (6) for each scene S epsilon S to obtain an optimal solution

Wherein S' _b(s,t) Representing a subset of the scene sequence under scene s at stage t;

calculating consensus variables using equation (8)Is a value of (2);

computing multiplierWherein->Wherein->Vector representing skip and lane reservation decision variables of stage t under scene s initialized in algorithm iterative process, +.>Representing an initialized consensus variable in an algorithm iteration process;

2.3.2 Let k=k+1;

relaxing the expected constraint by using the augmented Lagrangian relaxation, and reformulating the objective function by adding a penalty term;

wherein,,is the Lagrangian multiplier and ρ is a penalty factor;

For each scene S E S, using the objective function in equation (9) to obtain the optimal solution

Calculating consensus variables using equation (8)Updating the value of (2);

updating the Lagrangian multiplier using the following formulaAnd penalty factor ρ ^(k) :

Wherein omega ^D Representing the dual step size, ω ^P Representing the original problem step length, psi ^D(k-1) The dual gap value, ψ, representing step k-1 ^D(k-2) The dual gap value, ψ, representing step k-2 ^P(k-1) The original problem gap value, ψ, representing the kth-1 step ^P(k-2) Representing the original problem gap value of the k-2 step;

2.3.3 Check termination condition:if the termination condition is satisfied, the algorithm is terminated; if not, proceed to step 2.3.2).

4. The method for bus stop-and-lane reservation based on multi-stage random optimization of claim 3, wherein the specific process of step (3) is as follows:

3.1 Establishing a double layer planning problem:

defining variables and constraints related to the double-layer planning problem;

waiting time of bus t at station iWherein->Is the number of passengers boarding bus t at station i and +.> Is the number of passengers getting off bus t at stop i, anda and b are constants representing an average time for getting off or on each passenger on average;

wherein,,indicating whether the bus t skips the station at the station i, if 1 indicates that the station is skipped, 0 indicates that the station is not skipped; / >Representing the number of passengers waiting at station i desiring to get off at station j to take bus t;Indicating whether the bus t skips the station at the station l, if the bus t skips the station at the station l, the bus t is 1, and if the bus t is 0, the bus t does not skip the station;

departure time of bus t at station iEqual to the arrival time of bus t at stop i +.>Adding the waiting time of the bus t at the station i: Representing waiting time of the bus t at the station i; arrival time of bus t at stop i +.>Equal to the departure time of bus t at station i-1 +.>Plus the path travel time of bus t after leaving the last stop i-1 +.>Acceleration time->Deceleration time->I.e. < -> The time interval between the bus t and the bus t-1 at the station i is equal to the arrival time of the bus t>Departure time from bus t-1 +.>The difference is:Gamma represents the deceleration or acceleration time of the bus at the platform;

the number of passengers skipped by bus t at station i and desiring to get off at station j is: wherein (1)>Is the number of passengers taking bus t, boarding at station i, and desiring to get off at station j; and is also provided withWherein->Is the number of people selecting bus t at station i and desiring to get off at station j, +.>Is determined by the lower layer planning; the total number of passengers arriving at station i is +. >λ _i Indicating the arrival rate of the passenger;

the path travel time of cars and buses is represented by a modified BPR function:

wherein,,and->Indicating the travel time of the car and bus in the inbound link or outbound link of station i,and->Free-stream travel time, alpha, representing inbound or outbound links of a car and bus at station i, respectively ^car And alpha ^bus BPR linear adjustment parameters respectively representing car and bus, beta ^car And beta ^bus BPR index adjustment parameters for cars and buses, respectively, < >>And->Flow values, n, representing inbound or outbound links of a car and bus, respectively, at station i _i The number of lanes representing the station i link or the station out link, M represents that one bus corresponds to M cars in flow conversion, and cap _i Representing the capacity of a single lane between station i-1 and station i; y is _i The number of bus lanes between the station i-1 and the station i is represented;

avoiding too long waiting time of passengers, the bus operation should satisfy the following constraints:

(a) Two consecutive buses are prohibited from skipping the same station:

(b) One bus is prohibited from continuously skipping two stations:

(c) The bus is prohibited from skipping the start station and the end station on the line:

when the bus t skips the i station, the inbound and outbound links of the i station are considered as candidate links of the bus lane reservation; with binary variables And->A lane reservation scheme of the bus t is represented; jumping station i, if the inbound link of station i is reserved for bus t +.>Otherwise-> The prescribed bus lane may be reserved only on the outbound route, or both:

3.3.1 Upper layer problem):

the passengers waiting at the station consist of two parts, namely the passenger skipped by the previous bus and the passenger arriving between t and t-1; the total passenger waiting time may be expressed as:

the total in-vehicle time is the sum of the travel time between two stations and the two-station residence time, namely:

wherein,,representing the travel time of a bus between stop l-1 and stop l +.>Representing waiting time of the bus t at the station l;

the total travel time is:

similar to the cost of bus passengers, the total travel cost of the automobile user is:

skipping the station i, reserving the negative influence of the bus lane on the incoming and outgoing linesThe following can be calculated:

wherein,,and->Indicating the transit time and the traffic volume of the car after reserving the bus lane on the inbound link of station i,And->Indicating the transit time and car flow when no bus lane is reserved on the inbound link at station i,and->Indicating the transit time and the traffic volume of the car after reserving the bus lane on the inbound link of station i,/ >Andindicating the transit time and the traffic of the car when the bus lane is not reserved on the inbound link of the station i; x is X _t A decision vector for reserving a bus lane for the bus t is represented;

the overall negative impact is:

the total cost of the system is as follows:

Z＝π _w Z _w +π _v Z _v +π _bus Z _bus +π _car Z _car +π _l Z _l (27)

wherein pi _w Linear adjustment coefficient, pi, representing total passenger waiting time _v Linear adjustment coefficient, pi, representing total in-vehicle time _bus Linear adjustment coefficient pi representing bus trip cost _car Linear adjustment coefficient pi representing car travel cost _l A linear adjustment coefficient indicative of a negative impact;

3.1.2 Lower layer problem):

the superscript m epsilon { car, bus } is used for distinguishing two modes of a car and a bus;representing the demand for selecting pattern m from site i to site j at stage τ; the total demand from site i to site j at stage τ is:

the car road traffic between stations i-1 and i at stage τ is:

wherein, when the path p passes through the road section between the station i-1 and the station i,otherwise->Representing car traffic on path p;

the bus section flow between the station i-1 and the station i in the tau phase is as follows:

wherein,,representing bus flow of a path between a station i and a station j in the tau phase;

the road section travel time between the station i-1 and the station i of the car and the bus in the tau stage is as follows:

Wherein,,representing the car free flow transit time between station i-1 and station i at stage τ -1,Represents the bus free flow transit time between station i-1 and station i at stage τ -1,Indicating whether bus lane is set on outbound link of station i>Indicating arrangement, and->Indicating no setting;

the generalized travel cost of the automobile driver at the tau stage is as follows:

wherein,,a car transit time representing an inbound link or an outbound link at station l;

for a public transport user, considering in-car congestion, the generalized travel cost of passengers between the station i-1 and the station i can be expressed as:

wherein eta ₁ And eta ₂ Is a parameter related to congestion in a vehicle, wherein C represents a capacity of the bus and F represents a departure frequency of the bus;

assuming that passengers arriving at a bus stop obey uniform distribution, the general trip cost for taking bus t at station i is as follows:

wherein,,bus traffic representing a phase τ station l inbound link or outbound link;

the user equalization problem can be described as follows:

wherein the method comprises the steps ofRepresents the minimum generalized route travel cost of the traveler traveling in an m-way from station i to station j,balanced generalized route travel cost representing travel of travelers in m-way, +. >Representing the set of paths between travel site i to site j in m-way,Representing the road section flow between the travel station i and the station j in an m mode;

demand for cars and buses according to the logic splitting functionSolving forThe method comprises the following steps of:

wherein θ is the standard deviation of perceived errors when selecting buses and cars;for adjusting selection preferences between the bus and the car;Is the total number of passengers from station i to station j;Representing minimum generalized route travel cost of traveler traveling in a car manner from station i to station j,/->The minimum generalized route travel cost of a traveler traveling from a station i to a station j in a bus mode is represented;

the objective function of the lower layer planning is:

constraint is formulas (28) - (35), (37) - (39) and (41);

wherein,,representing a set of paths from site i to site j;

3.2 Branch-and-bound method:

in each scenario, an upper bound is generated by assuming that any site is skipped, i.e Assuming that the first class car skips all even stations except the starting station and the end station to obtain an initial feasible solution X _current The method comprises the steps of carrying out a first treatment on the surface of the For the subsequent buses, determining the position of the skipped station through a greedy strategy according to constraint formulas (16) - (18);

after the station jump scheme is designed, the reserved bus lane is selected:

3.2.1 Initializing Y ⁽⁰⁾ ＝{y _r = 0|r =1, 2, …, s }, indicating that no bus lane is reserved for bus t;

3.2.2 Invoking branch delimitation and obtaining optimal jump strategy X _t The method comprises the steps of carrying out a first treatment on the surface of the Let w=0, and Y ^(w) ＝{y _r ＝0|r∈X _t }；

3.2.3 Y) to be Y ^(ω) Inputting the total negative income into the lane reservation optimization problem and the lower planning problem, and calculating to obtain the total negative incomeLet w=w+1; let Y ^(w-1) W is equal to 1 and obtain Y ^(w) ；

3.2.4 Returning to step 3.2.2); if it isY is then ^(w) ＝Y ^(w-1) And goes to step 3.2.5); otherwise, returning to the step 3.2.3);

3.2.5 If w= |x _t I, stop algorithm; otherwise, returning to the step 3.2.4);

3.3 Multi-mode traffic distribution algorithm):

3.3.1 Make the road section flowTraffic demand->0,r, s, path flow->Make the road section travel time +.>And->Is free flow time and n=1;

wherein,,and->Respectively representing the road traffic of a car and a bus, < >>And->Representing traffic demands of car and bus, respectively, < ->And->Represents the path flow of car and bus respectively, < ->And->The road section travel time of the car and the bus is respectively represented, and the upper mark k represents the kth path;

3.3.2 Updating the link travel time using equations (31) and (32);

3.3.3 Finding the shortest between OD pair r-s; the bus route is unique; the travel costs of the shortest car route and the shortest bus route are respectively And->Wherein, the OD pair represents a trip starting point and a trip ending point;

3.3.4 For each OD pair r-s, if ThenOtherwise the first set of parameters is selected,

wherein,,represents the traffic demand of OD on the kth path between r-s, Q _rs Indicating the total traffic demand between OD versus r-s,representing the minimum cost of the kth routing car between OD versus r-s, < >>Representing the minimum cost of representing the kth routing bus between OD versus r-s, +.>Representing the total set of car paths between OD versus r-s, +.>Represents the total set of bus paths between OD and r-s, < ->Representing the set of paths that have been used by the car between OD versus r-s, +.>Representing a set of paths that have been used by the bus between OD pairs r-s;

3.3.5 Car flow between each OD pair r-s is Bus flow between each OD pair r-s is +.> Calculating the road section flow rate through the formula (29) and the formula (30)The method comprises the steps of carrying out a first treatment on the surface of the For each OD pair r-s, calculating car flow +.>And bus traffic +.>

3.3.6 If n=n _max Or alternatively Terminating the algorithm; otherwise, let n=n+1 and return to step 3.3.2);

wherein N is _max Representing the total number of iterations and,representing the total cost of the kth road car in the set of paths p, +.>The total cost of the kth path bus in the path set p is represented, and Q represents the total travel demand.