CN115099702A - Electric bus daytime running charging optimization method based on Lagrange relaxation algorithm - Google Patents
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Abstract
On the premise of ensuring a vehicle scheduled schedule, an electric bus daytime running charging optimization method based on a Lagrange relaxation algorithm aims at minimizing the total charging time of a system, obtains an integer optimization original problem model of a full-line network level charging scheme based on the electric quantity state of a discrete battery, converts the integer optimization original problem model into a Lagrange relaxation problem, decomposes the integer optimization original problem model into a plurality of subproblems, converts the integer optimization original problem model into a plurality of compact subproblems, obtains the optimal solution of a reduced original problem model P by solving the optimal solution of the plurality of compact subproblems, accurately describes the charging problem of a large-scale bus network, reduces the number of decision variables and constraint conditions in the model step by step, reduces the problem scale, improves the solving efficiency and carries out fast and efficient solution.
Description
Technical Field
The invention relates to an electric bus daytime running and charging optimization method based on a Lagrange relaxation algorithm.
Background
Urbanization and motorization lead to the rapid rise of vehicle ownership, which causes a great deal of environmental (such as noise and pollutant emission) and social (such as energy consumption and traffic jam) problems, the energy consumption generated in the traffic field reaches more than 25% of the total global energy consumption, the emission of greenhouse gases accounts for 27%, and the use of fuel vehicles is considered to be a serious threat to global warming.
Electric vehicles are used as substitutes for fuel vehicles, and are of great help to reduce the negative impact of urban traffic on climate and improve air quality conditions. Over the past decades, many cities around the world have provided significant ongoing investment in urban traffic electrification, with significant success particularly in public traffic electrification.
Compared with a fuel bus, the electric bus has the greatest defect that the limited battery capacity cannot meet the requirement of operation energy consumption all day long, and electricity needs to be supplemented in the daytime operation process; the non-linear relationship between the battery charging time and the electric quantity state brings a challenge to the control of the electric quantity of the bus journey.
However, in the existing research, the non-linear charging process of the electric bus and the electric quantity state tracking in the process of the journey are not considered in a fusion manner, and a quick and effective solving method is not formed by coordination of the bus operation schedule and the charging time sequence in a large-scale network.
Disclosure of Invention
The technical problem to be solved by the invention is to provide an electric bus daytime running and charging optimization strategy based on a Lagrange relaxation algorithm, according to a vehicle operation schedule and road network information, the electric quantity state of a vehicle from each station is tracked and recorded by depicting a nonlinear process of battery charging, an electric bus daytime running and charging optimization model based on the Lagrange relaxation algorithm is established, and an efficient solving algorithm is designed.
In order to solve the technical problem, the inventionThe technical scheme adopted by the invention is as follows: an electric bus daytime running charging optimization method based on a Lagrange relaxation algorithm comprises the following specific steps: s1, obtaining electric bus data and line operation data containing the number of lines, constructing a full-line network-level charging scheme integer optimization model based on the electric quantity state of a discrete battery, and obtaining an original problem model P containing coupling constraint; s2, converting the coupling constraint into an objective function of an original problem model P by introducing a Lagrange multiplier, so as to obtain a Lagrange relaxation problem P' (mu, lambda) with a new constraint condition; s3, decomposing the Lagrangian relaxation problem P' (mu, lambda) into a plurality of sub-problems P according to the line number l ' new decision variables are introduced, i.e. whether the vehicles of the respective line are charged at the respective station, so that a plurality of said sub-questions P are presented l ' conversion to multiple compact sub-problems P l "; s4, solving a plurality of compact sub-problems P l ", solving the target function of P' (mu, lambda), i.e. solving the target function of the original problem model P, and converting the optimal solution for solving the lower bound of the original problem model P into the solution of the Lagrangian dual problem P LD Solving the Lagrangian dual problem P by using a subgradient descent method LD And after each iterative solution, updating a Lagrange multiplier according to the current solution, and calculating the upper-bound optimal solution of the original problem model P by adopting a k-greedy algorithm until the upper-bound optimal solution of the original problem model P is equal to the lower-bound optimal solution, wherein the algorithm reaches a termination condition, the optimal solution of the original problem model P is obtained, namely, a daytime running charging scheme of each electric bus is obtained, and the optimization of daytime running charging of the electric buses is completed.
In some embodiments, the electric bus data includes the maximum charging times of each bus at each station, the minimum electric quantity protection value of each bus, and the electric bus electric quantity state, and the route operation data includes the route station, the arrival and departure schedule of each station, and the number of charging piles at each station.
In some embodiments, the objective function of the original problem model P in step S1 is specifically:
s.t.
wherein,
s.t. represents the constraint condition is;
n and L respectively represent the position and the number of bus stations, L represents the L-th bus line, L belongs to L, N represents the N-th bus station, N belongs to N, and N l Represents the total number of stations of route l;
a l,j scheduled arrival time, d, at jth stop for vehicles representing route l l,j The vehicles on the line l are scheduled to leave the station at the jth station for a predetermined time, j e { 1, …, N l -1 }, discretizing the planning time interval T into intervals in units of Δ tmin, T, T', T "each being a certain time point within the planning time interval T, the charging scheme being determined by a decision variable u l,j tt’ Or u l,j t’t” Is expressed when the vehicle is in time interval t, t']Or [ t', t "]When charging u is positive at jth station of line l l,j tt’ =1 or u l,j t’t” =1；
S is a discrete set, S represents an electric bus electric quantity state SOC, S = {0,1,2, …, Q }, each value S e S in the set S represents an electric quantity state reached after the vehicle starts to be charged from the SOC =0 state for S time intervals Δ t, i.e., S =0 represents an electric quantity reached by the battery after the vehicle is charged for Δ t duration, S =2 represents an electric quantity reached by the battery after the vehicle is charged for 2 Δ t duration, time required for the battery to be fully charged from the state of SOC =0 is H hours, Q represents an electric quantity state Q, i.e., a full state, and Q =60H Δ t;
station j =1, …, N for all routes of route l l Of variable v l,j,s Whether the electric quantity state of the vehicle is s or not when the vehicle leaves the jth station is shown, when the variable is 1, the electric quantity state is shown to be s, and when the variable is 0, the electric quantity state is not shown to be sQuantity v l,1,Q =1 denotes the state of charge of the vehicle on route l leaving the 1 st station is Q, variable v l,j-1,s Indicating whether the electric quantity state of the vehicle when leaving the j-1 th station is s or not;
g is an electric public transport network, G = (N, L), and the minimum electric quantity protection value of the vehicle of each line L is G l ；N l Represents the total number of stations of the route l, N (1, j) represents the jth station of the route l, N (1, j) is equal to N l ；
D l,j Representing the amount of power consumed by a vehicle on route l for its journey from jth to j +1 th stop, D l,j-1 Represents the amount of power consumed by the vehicle on route l for its trip from the jth-1 st station to the jth station;
the maximum number of times of charging permitted by the vehicles on the line l at each station is U l And the number of charging piles of each station N belonging to N is M n 。
In some embodiments, the lagrangian relaxation problem P' (μ, λ) is specifically:
s.t.
wherein, mu l,j And λ n,t Is the lagrange multiplier described in step S2.
In some embodiments, the sub-problem has | L | sub-problems P l Is a compound of
A variable 0 to 1 and
a bar-constrained 0-1 integer programming model, where | S | represents the number of elements in a discrete set S, a l,n Indicating the scheduled arrival time of the vehicle at the n stations on the route l, d l,n Indicating the scheduled departure time of the vehicle on the line l at the n stations, the l sub-question P l ' described as:
s.t.
wherein the charging scheme is determined by a decision variable u l,n tt’ Or u l,n t’t” Denotes when the vehicle is in time interval t, t']Or [ t', t "]Then, u is charged at the nth station of the line l l,n tt’ =1 or u l,n t’t” =1。
In some embodiments, the sub-problem P is presented to l ' New decision variables are introduced into
，
Represents [ t, t +1 ]]When the vehicle on line l is charging at its jth station, and the vehicle on line l is not charging at jth station,
wherein j =1, …, N l ，t∈｛a l,j ,…,d l,j H, solve the subproblem P l ' equivalent transformation compact sub-problem P l ", compact sub-problem P l "have | L | number, L th compact sub-problem P l "may be described as:
s.t.
wherein, variable
Representing the battery state of charge of the vehicle on line l as it leaves the jth station,
representing the battery state of charge of the vehicle on line i when it leaves the 1 st station,
representing the battery state of charge of the vehicle on line i as it leaves the j-1 st station,
is a new decision variable, which when it is 1, indicates [ t, t +1 ]]The vehicle on line l is charging at its j-1 st station.
In some embodiments, the step S4 is specifically: step S41, let the number of charging times U of the vehicle on the route l at the jth station l,j Number of vehicles charged simultaneously m in each station t interval =0 n,t = 0; step S42, traversing interval t epsilon [ a ∈ ] l,j +1，d l,j ]If at all
And is
In time, let U l,j + 1; traversal interval t e [ a ] l,j ，d l,j ]，
(ii) a Step S43, and obtaining
，
N is N, T is T, the target function of the Lagrangian relaxation problem P' (mu, lambda) is
In some embodiments, step S45 specifically includes: step S01, the Lagrangian dual problem P is processed LD Initializing, setting the current iteration number i =0, initializing Lagrangian multipliers mu and lambda, and setting an initial lower bound lb = - ∞ and an initial upper bound ub = + ∞; step S02, update multipliers mu, lambda and solve compact subproblems P using a commercial solver l ", obtain the optimal solution
，
(ii) a Step S03, calculating U by using the steps S41-S44 l,j (i) And m n,t (i) And obtaining P l "objective function value obj of LR (i) Solving the original problem by using a k-greedy algorithm and obtaining an objective function value obj corresponding to a feasible solution (i) Recording the current iteration result, if the constraint is relaxed, namely U l,j (i) ≤U l And m n,t (i) ≤M n If both are satisfied, the upper and lower bounds are checked and updated: if obj LR (i) If lb is greater than lb, update lower bound lb = obj LR (i) (ii) a If obj (i) If the sub is less than the sub, the upper bound ub is updated to be = obj (i) (ii) a Step S04, updating the lagrangian multiplier by using the secondary gradient, making the update step of the multiplier δ =1/2(n +1), and updating the multiplier by using the following formula: mu.s l,j (i+1) =max{μ l,j (i) +δ·△μ l,j (i) ，0}，λ n,t (i+1) =max{λ n,t (i) +δ·△λ n,t (i) 0} in which
Step S05, judging whether the algorithm termination condition is satisfied, if all the complementary relaxation conditions are satisfied, the μ l,j (i+1) (U l,j (i) -U l ) =0 and λ n,t (i+1) (m n,t (i) -M n ) =0, the algorithm is terminated, and at this time, the optimal solution corresponding to the lagrangian relaxation problem is the optimal solution of the original problem, and the superscripts (i) and (i +1) respectively represent the ith iteration and the (i +1) th iteration; when lb = ub, the algorithm is terminated, and the optimal solution corresponding to the Lagrangian relaxation problem is the optimal solution of the original problem; when the iteration number I exceeds the maximum iteration number I max When the algorithm is ended, outputting a target function and an optimal solution corresponding to the upper and lower bounds; if the three conditions are not met, the step S01-the step S05 are circulated, the iteration times are +1 in sequence, the optimal solution of the original problem is obtained until one of the three conditions is met, the daytime running charging scheme of each electric bus is obtained, and the daytime running charging of the electric buses is optimized.
The scope of the present invention is not limited to the specific combinations of the above-described features, and other embodiments in which the above-described features or their equivalents are arbitrarily combined are also intended to be encompassed. For example, the above features and the technical features (but not limited to) having similar functions disclosed in the present application are mutually replaced to form the technical solution.
Due to the application of the technical scheme, compared with the prior art, the invention has the following advantages: the invention provides an electric bus daytime running charge optimization method based on a Lagrange relaxation algorithm, which aims at minimizing the total charging time of a system on the premise of ensuring a preset schedule of a vehicle, obtains a full-line network level charging scheme integer optimization original problem model based on the electric quantity state of a discrete battery, converts the integer optimization original problem model into a Lagrange relaxation problem, decomposes the Lagrange relaxation problem into a plurality of subproblems, and finally converts the integral optimization original problem model into a plurality of compact subproblems.
Drawings
FIG. 1 is a schematic flow diagram of an electric bus daytime running charging optimization strategy based on a Lagrange relaxation algorithm;
FIG. 2 is a flow chart of the k-greedy algorithm of the present invention.
Detailed Description
As shown in fig. 1, the electric bus daytime running charging optimization method based on the lagrangian relaxation algorithm includes the following steps:
step S1: acquiring electric bus data and line operation data containing line quantity, wherein the electric bus data comprise the maximum charging times of each bus at each station and the minimum electric quantity protection value of the bus, the line operation data comprise route stations, arrival and departure schedules of each station and the number of charging piles of each station, a full-line network-level charging scheme integer optimization model based on the electric quantity state of a discrete battery is constructed, and an original problem model P containing coupling constraint is obtained, and specifically:
s.t.
wherein s.t. represents the constraint condition of,
The original problem model P has two types of decision variables, which are respectively a charging schedule of the electric bus and an optimal battery state when the electric bus leaves a station, and the original problem model P has three types of constraints, which are respectively constraints related to a route schedule, battery electric quantity state constraints and coupling constraints.
Step S2, by introducing Lagrange multiplier mu l,j And λ n,t And mu l,j ≥0，λ n,t And ≧ 0, converting the coupling constraint condition into an objective function of the original problem P, thereby obtaining a Lagrangian relaxation problem P '(μ, λ) with a new constraint condition, wherein the Lagrangian relaxation problem P' (μ, λ) is specifically:
s.t.
step S03, apply the constant term in the above-mentioned lagrangian relaxation problem P' (μ, λ) objective function, i.e. the constant term
Removing and then decomposing the Lagrangian relaxation problem P' (mu, lambda) into | L | subproblems according to the number of lines, wherein each subproblem is respectively the decision optimization of each line charging scheme, and the first subproblem P l ' may be described as: first sub-problem P l ' described as:
s.t.
the charging scheme is determined by a decision variable u l,n tt’ Or u l,n t’t” Is expressed when the vehicle is in time interval t, t']Or [ t', t "]Then, u is charged at the nth station of the line l l,n tt’ =1 or u l,n t’t” =1, sub-problem P l Is a compound of
A variable 0 to 1 and
the strip constrained 0-1 integer programming model is extremely difficult to solve in a large-scale problem when the running schedule of each line is long in duration, so that new decision variables are continuously introduced
，
Represents [ t, t +1 ]]When the vehicle on line i is charging at its jth station, otherwise
Wherein j =1, …, N l ，t∈｛a l,j ,…,d l,j }; variables of
Representing the battery state of charge of the vehicle on line l as it leaves the jth station,
representing the battery state of charge of the vehicle on route i when it leaves the 1 st station,
representing the battery state of charge of the vehicle on line i as it leaves the j-1 st station,
is a new decision variable, which when it is 1, indicates [ t, t +1 ]]Then the vehicle on line l is charging at the j-1 st station; thereby solving a plurality of the sub-questions P l ' equivalent transformation compact sub-problem P l ", compact sub-problem P l "is described as:
s.t.
step S4, solving a plurality of compact sub-problems P by using a sub-gradient descent method l ", each iteration is followed byThe Lagrange multiplier is updated by the previous solution until the algorithm reaches a termination condition, and the optimal solution of the original problem model P is obtained, and the method specifically comprises the following steps:
step S41, let the number of charging times U of the vehicle on the route l at the jth station l,j =0, number m of vehicles charged simultaneously in each station t interval n,t =0；
Step S42, traversing interval t epsilon [ a ∈ l,j +1，d l,j ]If, if
And is provided with
When making U l,j + 1; traversal interval t e [ a ] l,j ，d l,j ]，
；
Step S43, and obtaining
The objective function of the Lagrangian relaxation problem P' (μ, λ) is then
Is equal to
The objective function formula of the original problem model P
Is equal to
；
Step S44, respectively using μ and λ to represent vectors formed by lagrangian multipliers in the lagrangian relaxation problem P '(μ, λ), and making L (μ, λ) represent an optimal solution corresponding to the lagrangian relaxation problem P' (μ, λ), so that the solution of the lower bound of the original problem model P can be converted into a solution of a lagrangian dual problem:
step S45, the Lagrangian dual problem P is processed LD Initializing, setting the current iteration number i =0, initializing Lagrangian multipliers mu and lambda, and setting an initial lower bound lb = - ∞ and an initial upper bound ub = + ∞; updating multipliers mu, lambda and solving compact subproblems P using a commercial solver l ", obtain the optimal solution
，
Calculating U by using the steps S41-S44 l,j (i) And m n,t (i) And obtaining P l "objective function value obj of LR (i) Solving the original problem by using a k-greedy algorithm and obtaining an objective function value obj corresponding to a feasible solution (i) The k-greedy algorithm solution is shown in fig. 2, the current iteration result is recorded, and if the constraint is relaxed, U is obtained l,j (i) ≤U l And m n,t (i) ≤M n If both are satisfied, the upper and lower bounds are checked and updated: if obj LR (i) If lb is greater than lb, update lower bound lb = obj LR (i) (ii) a If obj LR (i) If lb is greater than lb, update lower bound lb = obj LR (i) (ii) a Updating the Lagrange multiplier by using the secondary gradient, enabling the updating step of the multiplier to be delta =1/2(n +1), and updating the multiplier by adopting the following formula:
wherein
Judging whether the algorithm termination condition is satisfied, if all the complementary relaxation conditions are satisfied, the mu value is l,j (i+1) (U l,j (i) -U l ) =0 and λ n,t (i+1) (m n,t (i) -M n ) =0, the algorithm is terminated, and the optimal solution corresponding to the Lagrange relaxation problem is the optimal solution of the original problem at this time; when lb = ub, the algorithm is terminated, and the optimal solution corresponding to the Lagrangian relaxation problem is the optimal solution of the original problem; when the iteration number I exceeds the maximum iteration number I max When the algorithm is ended, outputting a target function and an optimal solution corresponding to an upper boundary and a lower boundary; if the three conditions are not met, the step S01-the step S05 are circulated, the iteration times are +1 in sequence, the optimal solution of the original problem is obtained until one of the three conditions is met, the daytime running charging scheme of each electric bus is obtained, and the daytime running charging of the electric buses is optimized.
The embodiment is as follows: in the embodiment, public transport network and daytime operation data (including station positions, vehicle travel schedules and the like) disclosed by a website are used, a planning time range T is divided into 600 time intervals delta T, each time interval represents 1min, the vehicle battery capacity Cap =100, and the battery minimum electric quantity protection value G l And (5). Because of the original problem P and the transformed sub-problem P l ' and compact sub-problem P l "all are described as integer programming models, and all can be solved directly by using commercial solvers (e.g., Cplex, Gurobi, etc.).
To highlight the effectiveness of the protocol of the present application, the examples compare: 1) directly solving the original problem P using Gurobi, and 2) solving the compact sub-problem P therein using steps S41-S45 l "optimal solution and solution efficiency using Gurobi for both methods, the results are shown in Table 1:
in Table 1, the value of N, L, M is calculated n 、U l Respectively represent: the total number of stations, the total number of lines and the number M of charging piles of each station N belonging to N in the network n The maximum number of charging times allowed by the vehicles on each route l at each station is U l (ii) a The objective function column represents an objective function value corresponding to the optimal solution, and the time consumed for solving is the CPU calculation time in seconds. The result shows that the scheme provided by the application can effectively solve the problem of optimizing the daytime running and charging of the electric bus, and the solving efficiency is obviously superior to that of a solution scheme directly using a Gurobi solver; and when the number of stations and the number of lines respectively reach 300/150, Gurobi cannot solve due to large problem scale, and the scheme still shows excellent solving capability, so that the scheme is more stable and efficient than the conventional method.
The above embodiments are merely illustrative of the technical ideas and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and implement the present invention, and not to limit the protection scope of the present invention. All equivalent changes and modifications made according to the spirit of the present invention should be covered in the protection scope of the present invention.
Claims (8)
1. An electric bus daytime running charging optimization method based on a Lagrange relaxation algorithm is characterized by comprising the following steps: the method comprises the following specific steps:
s1, obtaining electric bus data and line operation data containing the number of lines, constructing a full-line network-level charging scheme integer optimization model based on the electric quantity state of a discrete battery, and obtaining an original problem model P containing coupling constraint;
s2, converting the coupling constraint into an objective function of an original problem model P by introducing a Lagrange multiplier, so as to obtain a Lagrange relaxation problem P' (mu, lambda) with a new constraint condition;
s3, decomposing the Lagrangian relaxation problem P' (mu, lambda) into a plurality of sub-problems P according to the line number l ' new decision variables are introduced, i.e. whether the vehicles of the respective line are charged at the respective station, so that a plurality of said sub-questions P are presented l ' converting into multiple compact sub-problems P l ”；
S4, solving a plurality of compact sub-problems P l ", the objective function of P' (mu, lambda) is solved, that is, the objective function of the original problem model P is solved,
converting the optimal solution for solving the lower bound of the original problem model P into the solution of the Lagrangian dual problem P LD Solving the Lagrangian dual problem P by using a sub-gradient descent method LD And updating the Lagrange multiplier according to the current solution after each iteration solution,
calculating the upper-bound optimal solution of the original problem model P by adopting a k-greedy algorithm,
and obtaining the optimal solution of the original problem model P until the optimal solution of the upper bound of the original problem model P is equal to the optimal solution of the lower bound, and obtaining the optimal solution of the original problem model P, namely obtaining the daytime running charging scheme of each electric bus to complete the optimization of the daytime running charging of the electric buses.
2. The electric bus daytime running charging optimization method based on the Lagrangian relaxation algorithm as claimed in claim 1, wherein: the electric bus data comprise the maximum charging times of each bus at each station, the minimum electric quantity protection value of the bus and the electric bus electric quantity state, and the line operation data comprise the approach stations, the arrival and departure timetables of the stations and the charging pile number of the stations.
3. The electric bus daytime running charging optimization method based on the Lagrangian relaxation algorithm as claimed in claim 2, wherein the method comprises the following steps: target of original problem model P in step S1The function is specifically:
s.t.
wherein,
s.t. represents the constraint condition is;
n and L respectively represent the position and the number of bus stations, L represents the L-th bus line, L belongs to L, N represents the N-th bus station, N belongs to N, and N l Represents the total number of stations of route l;
a l,j scheduled arrival time, d, at jth stop for vehicles representing route l l,j The scheduled departure time of the vehicle representing the line l at the jth station, j epsilon { 1, …, N l -1 }, discretizing the planning time interval T into intervals in units of Δ tmin, T, T', T "each being a certain time point within the planning time interval T, the charging scheme being determined by a decision variable u l,j tt’ Or u l,j t’t” Denotes when the vehicle is in time interval t, t']Or [ t', t "]When charging u is positive at jth station of line l l,j tt’ =1 or u l,j t’t” =1；
S is a discrete set, S represents an electric bus electric quantity state SOC, S = {0,1,2, …, Q }, each value S e S in the set S represents an electric quantity state reached after the vehicle starts to be charged from the SOC =0 state for S time intervals Δ t, i.e., S =0 represents an electric quantity reached by the battery after the vehicle is charged for Δ t duration, S =2 represents an electric quantity reached by the battery after the vehicle is charged for 2 Δ t duration, time required for the battery to be fully charged from the state of SOC =0 is H hours, Q represents an electric quantity state Q, i.e., a full state, and Q =60H Δ t;
station j =1, …, N for all routes of route l l Of variable v l,j,s Whether the electric quantity state of the vehicle is s or not when the vehicle leaves the jth station is shown, when the variable is 1, the electric quantity state is shown to be s, and when the variable is 0, the electric quantity state is not shown to be s l,1,Q =1 denotes the state of charge of the vehicle on route l leaving the 1 st station is Q, variable v l,j-1,s Indicating whether the electric quantity state of the vehicle when leaving the j-1 th station is s or not;
g is an electric public transport network, G = (N, L), and the minimum electric quantity protection value of the vehicle of each line L is G l ；N l Represents the total number of stations of the route l, N (1, j) represents the jth station of the route l, N (1, j) is epsilon N l ；
D l,j Representing the amount of power consumed by a vehicle on route l for its journey from jth to j +1 th stop, D l,j-1 Represents the amount of power consumed by the vehicle on route l for its trip from the jth-1 st station to the jth station;
the maximum allowable charging times of the vehicles on the line l at each station are U l And the number of charging piles of each station N belonging to N is M n 。
4. The electric bus daytime running charging optimization method based on the Lagrangian relaxation algorithm as claimed in claim 3, wherein: the lagrangian relaxation problem P' (μ, λ) is specifically:
s.t.
wherein, mu l,j And λ n,t Is the lagrange multiplier described in step S2.
5. The electric bus daytime running charging optimization method based on the Lagrangian relaxation algorithm as claimed in claim 4, wherein the method comprises the following steps: the sub-problem has | L | pieces, sub-problem P l ' is a composition containing
A variable 0 to 1 and
0-1 integer programming model of strip constraintType, where | S | represents the number of elements in a discrete set S, a l,n Indicating a scheduled arrival time of a vehicle at n stations on route l, d l,n Indicating the scheduled departure time of the vehicle on the line l at the n stations, the l sub-question P l ' described as:
s.t.
wherein the charging scheme is determined by a decision variable u l,n tt’ Or u l,n t’t” Denotes when the vehicle is in time interval t, t']Or [ t', t "]While being on the lineCharging u at nth station of l l,n tt’ =1 or u l,n t’t” =1。
6. The electric bus daytime running charging optimization method based on the Lagrangian relaxation algorithm as claimed in claim 5, wherein: to the sub-question P l ' Internally introducing New decision variables
，
Represents [ t, t +1 ]]When the vehicle on line l is charging at its jth station, and the vehicle on line l is not charging at jth station,
wherein j =1, …, N l ，t∈｛a l,j ,…,d l,j Will sub-problem P l ' equivalent transformation compact sub-problem P l ", compact sub-problem P l "has | L | number, the L-th compact sub-problem P l "may be described as:
s.t.
wherein, variable
Representing the battery state of charge of the vehicle on line l as it leaves the jth station,
representing the battery state of charge of the vehicle on route i when it leaves the 1 st station,
representing the battery state of charge of the vehicle on line i as it leaves the j-1 st station,
is a new decision variable, which when it is 1, indicates [ t, t +1 ]]The vehicle on line l is charging at its j-1 st station.
7. The electric bus daytime running charging optimization method based on the Lagrangian relaxation algorithm as claimed in claim 6, wherein: the step S4 specifically includes: step S41, let the number of times U of charging the vehicle on the route l at the jth station l,j Number of vehicles charged simultaneously m in each station t interval =0 n,t = 0; step S42, traversing interval t epsilon [ a ∈ l,j +1，d l,j ]If at all
And is
When making U l,j + 1; traversal interval t e [ a ] l,j ，d l,j ]，
(ii) a Step S43, and obtaining
，
N is N, T is T, the target function formula of the Lagrangian relaxation problem P' (mu, lambda) is
8. The electric bus daytime running charging optimization method based on the Lagrangian relaxation algorithm as claimed in claim 7, wherein the method comprises the following steps: step S45 specifically includes: step S01, the Lagrangian dual problem P is processed LD Initializing, setting the current iteration number i =0, initializing Lagrangian multipliers mu and lambda, and setting an initial lower bound lb = - ∞ and an initial upper bound ub = + ∞; step S02, updating multipliers mu and lambda and solving compact subproblems P by using a commercial solver l ", obtain the optimal solution
，
(ii) a Step S03, calculating U by using the steps S41-S44 l,j (i) And m n,t (i) And obtaining P l "objective function value obj of LR (i) Solving the original problem by using a k-greedy algorithm and obtaining an objective function value obj corresponding to a feasible solution (i) Recording the current iteration result, if the constraint is relaxed, i.e. U l,j (i) ≤U l And m n,t (i) ≤M n If both are satisfied, the upper and lower bounds are checked and updated: if obj LR (i) If lb is greater than lb, update lower bound lb = obj LR (i) (ii) a If obj (i) If ub is less than ub, update the upper bound ub = obj (i) (ii) a Step S04, updating the lagrangian multiplier by using the secondary gradient, making the update step of the multiplier δ =1/2(n +1), and updating the multiplier by using the following formula: mu.s l,j (i+1) =max{μ l,j (i) +δ·△μ l,j (i) ，0}，λ n,t (i+1) =max{λ n,t (i) +δ·△λ n,t (i) 0} in which
Step S05, judging whether the algorithm termination condition is satisfied, if all the complementary relaxation conditions are satisfied, the μ l,j (i+1) (U l,j (i) -U l ) =0 and λ n,t (i+1) (m n,t (i) -M n ) =0, the algorithm is terminated, and at this time, the optimal solution corresponding to the lagrangian relaxation problem is the optimal solution of the original problem, and the superscripts (i) and (i +1) respectively represent the ith iteration and the (i +1) th iteration; when lb = ub, the algorithm is terminated, and the optimal solution corresponding to the Lagrangian relaxation problem is the optimal solution of the original problem; when the iteration number I exceeds the maximum iteration number I max Time, algorithmTerminating, and outputting a target function and an optimal solution corresponding to the upper and lower bounds; if the three conditions are not met, the step S01-the step S05 are repeated, the iteration times are sequentially +1, and the optimal solution of the original problem is obtained until one of the three conditions is met, namely the daytime running charging scheme of each electric bus is obtained, and the optimization of the daytime running charging of the electric buses is completed.
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