CN115860299A - Coordination method for battery changing station site selection and electric vehicle path planning - Google Patents
Coordination method for battery changing station site selection and electric vehicle path planning Download PDFInfo
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Abstract
The invention discloses a method for coordinating the site selection of a power change station and the path planning of an electric vehicle, which comprises the steps of firstly, establishing a relational expression between a detour probability and accumulated mileage anxiety according to the relation between the detour probability and the electric vehicle electric quantity state; then establishing an optimization model which minimizes the construction cost of the power station and the driving cost of the electric vehicle, and minimizes the additional cost generated by the accumulated mileage anxiety of the driver in the whole journey; and finally, expressing the solution of the optimization model by using a power station site selection sequence and an electric vehicle path sequence, and performing iterative solution on the optimization model to obtain an optimal power station site selection and electric vehicle path planning scheme. The invention considers the site selection problem of the power conversion station and the cooperation behavior of both the supply and demand parties, and can effectively reduce the cost of the supply chain and improve the efficiency of the supply chain.
Description
Technical Field
The application belongs to the technical field of power station location selection-electric vehicle path planning, and particularly relates to a power station location selection and electric vehicle path planning cooperation method.
Background
Rapid development of road transportation and urbanization has exacerbated global greenhouse gas emissions, presenting a significant environmental and economic challenge. Electric vehicles are therefore widely used in the supply chain, particularly in the last mile delivery, by virtue of their low carbon emissions and maintenance costs. The electric vehicle path planning problem is an extension of the green vehicle path planning problem and aims to design an optimal path scheme for an electric vehicle. In recent years, the electric vehicle path planning problem has been expanded to the site selection of the battery replacing station-electric vehicle path planning problem, namely, the electric vehicle path planning problem and the site selection problem of the charging facility are considered at the same time.
Some unknown factors in real-world situations, such as traffic jam and different driving speeds, can cause additional power consumption of the electric vehicle. Drivers are likely to feel anxiety because the electric vehicle is not sufficiently charged to reach the destination or the battery replacement station, a phenomenon known as "range anxiety". Mileage anxiety can reduce the reliability of route planning and create additional costs, and to alleviate mileage anxiety, drivers are likely to deviate from the service customer's route to the swap station. This phenomenon is called "detour behavior" and thus increases transportation costs and reduces logistics efficiency.
The logistics company can achieve the purposes of reducing the cost and improving the service quality through the cooperation of the supply and demand parties in the transportation process. Existing research has considered the collaboration of aspects of the supply chain, such as collaboration between customers and collaboration between warehouses. However, the limited driving range of the electric vehicle and the unreasonable layout of the charging facilities lead to the cooperation of the battery changing station location-electric vehicle path planning problem being more complicated than the traditional vehicle path planning problem. Previous studies have not considered both uncertainty and cooperative behavior due to range anxiety.
Disclosure of Invention
The application aims to provide a method for coordinating site selection of a power conversion station and route planning of an electric vehicle, so that uncertainty caused by mileage anxiety of a driver is overcome, and construction cost of the power conversion station and extra cost caused by the mileage anxiety are reduced.
In order to achieve the purpose, the technical scheme of the application is as follows:
a method for site selection of a power change station and electric vehicle path planning cooperation comprises the following steps:
establishing a relational expression between the detour probability and the accumulated mileage anxiety according to the relation between the detour probability and the electric quantity state of the electric vehicle;
establishing an optimization model which minimizes the construction cost of the power change station and the driving cost of the electric vehicle, and minimizes the additional cost generated by the accumulated mileage anxiety of the driver in the whole journey;
and expressing the site selection sequence of the power station and the electric vehicle path sequence for the solution of the optimization model, and performing iterative solution on the optimization model to obtain an optimal power station site selection and electric vehicle path planning scheme.
Further, the establishing of the relational expression between the detour probability and the cumulative mileage anxiety includes:
and constructing a rectangular coordinate system by taking the detour probability as a Y axis and the driving distance as an X axis, and taking the area enclosed by the detour probability curve and the X axis as the value of the accumulated mileage anxiety.
Further, in the above-mentioned case, the optimization model is expressed by the following formula:
wherein, c B Shows the construction cost of the power station, V B Representing an alternative set of swapping stations; y is i Representing a binary variable, if an ith seat conversion station is built, the binary variable is equal to 1, otherwise, the binary variable is 0; epsilon represents the driving cost of the electric vehicle per unit distance, V represents the set of all nodes, and V E Representing a set of electric vehicles; x is the number of ijk Represents a binary variable, equal to 1 if the arc (i, j) is travelled by vehicle k, and 0 otherwise; s ij Represents the distance between nodes i and j; a. The ijk (ζ) represents the accumulated range anxiety of the driver of vehicle k while traveling in arc (i, j); σ represents the additional cost of anxiety per unit accumulated mileage.
Further, the optimization model is subjected to iterative solution to obtain an optimal power station location and electric vehicle path planning scheme:
f1, initializing a power station address selection sequence and an electric vehicle path sequence;
step F2, judging whether a stagnation standard is met, if so, applying a local search strategy to the currently recorded optimal power conversion station site selection sequence, otherwise, updating the power conversion station site selection sequence by adopting a position updating mechanism to obtain a new power conversion station site selection sequence;
f3, adopting the destroy operator and the insert operator to destroy and repair the electric vehicle path sequence respectively, and generating a new electric vehicle path sequence;
step F4, judging whether the new electric vehicle path sequence is superior to the currently recorded optimal electric vehicle path sequence, if so, entering step F5, otherwise, returning to step F3;
f5, updating the weights and the fractions of the destroy operator and the insert operator;
step F6, taking the new electric vehicle path sequence as the currently recorded optimal electric vehicle path sequence, and taking the new power change station site selection sequence as the currently recorded optimal power change station site selection sequence;
and F7, judging whether the maximum iteration times are reached, if so, stopping iteration, and outputting an optimal power station location selection sequence and an electric vehicle path sequence, otherwise, returning to the step F2 and continuing to iterate.
Further, the position updating mechanism updates the position of the site selection sequence of the power swapping station by adopting the following formula:
wherein,
represents the speed of the d element in the ith conversion station addressing sequence at the t +1 th iteration, and is/are selected>
Represents the position of the d element in the ith conversion station addressing sequence at the t +1 th iteration, and/or is selected>
Representing the position of the d element in the ith power station addressing sequence at the t iteration, and rand () is a random number subject to uniform distribution between 0 and 1.
Further, the initializing a path sequence of the electric vehicle further includes:
dividing the initial electric vehicle path sequence into sub-sequences corresponding to all warehouses according to the distance from the customer to each warehouse;
and according to a preset rule, selecting nodes from each subsequence or/and the power station address selection sequence, adding the nodes into the feasible solution of the corresponding warehouse, obtaining the feasible solution of each warehouse, and forming a final initial electric vehicle path sequence.
Further, according to the preset rule, the following formula is satisfied:
wherein S is n Represents the nth warehouse D n The feasible solution of (a) to (b),
the nearest neighbor client representing the jth client node as the (j + 1) th client node, B j+1 Represents the nearest power change station of the (j + 1) th client node, s (j+1)r Represents the (j + 1) th customer node to the nearest power change station B j+1 Distance of(s) jD Representing the jth client node to the warehouse D n Distance of(s) j(j+1) Denotes the distance between nodes j and j +1, q j Represents the electric vehicle electric quantity p at the node j j+1 Represents the demand of the (j + 1) th customer, w j Represents the electric vehicle load at node j, and>
representing a binary variable, e representing the energy consumption rate.
According to the method for site selection of the power change station and electric vehicle path planning cooperation, the site selection problem of the power change station and the cooperation behaviors of both a supply party and a demand party are considered, and the constructed CELRP-BSS-RA model can effectively reduce the cost of a supply chain and improve the efficiency of the supply chain by searching the optimal path of site selection of the power change station and an electric vehicle.
Drawings
FIG. 1 is a flow chart of a method for site selection and electric vehicle path planning cooperation of a power change station according to the present application;
FIG. 2 is a schematic diagram illustrating a relationship between a detour probability and a state of charge of an electric vehicle and a cumulative mileage anxiety according to the present application;
FIG. 3 is a flow chart of the present application for solving an optimization model;
FIG. 4 is a schematic representation of an embodiment of the present application;
FIG. 5 is a comparison of the performance of the method of the present application and the prior art method at different population scales;
FIG. 6 is a comparison of the results of an iterative trajectory experiment of the method of the present application with a prior art method.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
The facility location-vehicle path planning problem consists of a classical facility location problem and a vehicle path planning problem, uncertainty and cooperation behaviors brought by mileage anxiety are not considered simultaneously in the current research on the power station location-electric vehicle path planning problem, and the application aims to provide a power station location-electric vehicle path planning cooperation model (radio-electric vehicle location with battery-switching status high-definition network, referred to as cell-BSS-RA) considering the mileage anxiety. It is worth noting that the purpose of the present application is not only to optimize the location of the battery replacement station and reduce the driving cost of the electric vehicle, but also to minimize the extra cost caused by the anxiety of mileage during the trip. The method considers the cooperative behaviors of supply and demand parties in a supply chain, adopts a detour probability function to process uncertainty of mileage anxiety, and provides a new mileage anxiety function to evaluate accumulated mileage anxiety in the driving process.
In one embodiment, as shown in fig. 1, a method for coordinating site selection of a power conversion station and path planning of an electric vehicle is provided, which includes:
s1, establishing a relational expression between the detour probability and the accumulated mileage anxiety according to the relation between the detour probability and the electric quantity state of the electric vehicle.
In order to study the relationship between driver detour behavior and accumulated mileage anxiety, the application uses a detour probability function and proposes a new mileage anxiety function.
The detour probability function considers the influence of the electric quantity state of the electric vehicle on the detour behavior of the driver, and can be used for quantifying the relation between the probability of the detour behavior and mileage anxiety, as shown in formula (1).
Wherein, P ijk (ζ) is the probability of detour when the vehicle k travels on the arc (i, j), ζ is a sensitivity coefficient between 0 and 1, which represents the psychological bearing capacity of the driver, τ is the mileage anxiety threshold, s ij Represents the distance between nodes i and j, q i And q is j And respectively representing the electric quantity of the electric vehicle at the nodes i and j, wherein e is a fixed energy consumption rate, and Q is the maximum battery capacity of the electric vehicle. When the electric vehicle has the electric quantity at the end node j not less than the threshold value tau, namely q j ＝q i -es ij When t is greater than or equal to ijk (ζ) equal to 0; when the electric quantity of the electric vehicle is low in the running processAt τ, the driver will have P ijk And (zeta) the probability goes around the circuit to the power swapping station.
As can be seen from the upper half of fig. 2, as the driving distance increases, the electric quantity of the electric vehicle linearly decreases, and the slope is constant e. As can be seen from the lower half of FIG. 2, when the travel distance reaches s τ That is, when the electric quantity of the electric vehicle starts to fall below the threshold τ, P increases with distance ijk (ζ) begins to increase convexly as the electric vehicle travels closer to the electric vehicle maximum travel distance s max When is, P ijk The value of (ζ) is close to 1.
In addition, considering that the accumulated mileage anxiety is more reflective of the accumulation of the mileage anxiety during the driving process than the mileage anxiety of a certain point, the application aims at the relationship between the detour probability and the accumulated mileage anxiety, and provides a new mileage anxiety function through the formula (2):
wherein A is ijk (ζ) is the accumulated range anxiety of the driver of vehicle k over arc (i, j). When the electric quantity of the electric vehicle at the end node j is not less than the threshold value tau, A ijk (ζ) equal to 0; when the electric quantity in the running process is lower than tau, A ijk And (ζ) starts to increase as the traveling distance of the electric vehicle increases. As shown in the lower half of fig. 2, a ijk The value of (ζ) is defined as an area enclosed by the detour probability function and the X-axis.
And S2, establishing an optimization model which comprises the steps of minimizing the construction cost of the power station and the driving cost of the electric vehicle, and minimizing the additional cost caused by the anxiety of the accumulated mileage of the driver in the whole journey.
The optimization model of the embodiment is shown in formula (3), and the objective function consists of three parts. The first part and the second part are respectively the construction cost of the minimum power change station and the driving cost of the electric vehicle, which are common objective functions in the problems of site selection of the power change station and path planning of the electric vehicle. The last part is to minimize the extra cost of the entire trip due to the driver's cumulative range anxiety.
The constraints of the model are as follows:
the constraint (4) indicates that each customer is only visited once by the electric vehicle. The constraint (5) ensures that each battery replacement station is visited by the electric vehicle at most once. Constraints (6) guarantee the conservation of traffic for each node. Constraints (7) and (8) indicate that customer demand is a non-negative constant and should not exceed the maximum load capacity of the electric vehicle. Constraints (9) and (10) track the state of the electric vehicle battery power, and ensure that the electric vehicle power is never lower than zero. Constraints (11) are used to eliminate sub-loops in the path. Finally, constraints (12) - (14) define the scope of the decision variables.
The symbols used in this application are described below:
V C representing a set of customers;
V D representing a warehouse collection;
V B representing an alternative set of swapping stations;
v' represents a dummy node set, wherein the dummy node is a virtual node and is used for establishing a virtual power station changing node when a model is constructed;
and V represents all node sets, and the nodes refer to all nodes, namely warehouse nodes, client nodes, power station changing nodes and dummy nodes.
V E Representing a set of electric vehicles;
w represents the maximum load capacity of the electric vehicle;
q represents a maximum battery capacity of the electric vehicle;
w i representing the electric vehicle load amount at the node i;
p i representing the demand of customer i;
e represents the energy consumption rate (per unit distance);
q i representing the electric vehicle electric quantity at the node i;
s ij representing between nodes i and jA distance;
epsilon represents the driving cost of the electric vehicle per unit distance;
c B the construction cost of the power conversion station is shown;
P ijk (ζ) represents the probability of detour of vehicle k when traveling in arc (i, j) under range anxiety, ζ being a non-negative coefficient of sensitivity;
A ijk (ζ) represents the accumulated range anxiety for the driver of vehicle k while traveling in arc (i, j);
τ represents a mileage anxiety threshold;
σ represents the additional cost of anxiety per unit accumulated mileage;
x ijk represents a binary variable, equal to 1 if the arc (i, j) is travelled by vehicle k, and 0 otherwise;
y i representing a binary variable, if an ith seat conversion station is built, the binary variable is equal to 1, otherwise, the binary variable is 0;
And S3, expressing the solution of the optimization model by using a power station site selection sequence and an electric vehicle path sequence, and performing iterative solution on the optimization model to obtain an optimal power station site selection and electric vehicle path planning scheme.
The method and the device for searching the optimal path of the electric vehicle and the power station selection are expected to search the optimal path of the electric vehicle and the power station selection according to the optimization model, so that the cost of the supply chain is effectively reduced, and the efficiency of the supply chain is improved. The process of searching the optimal path of the electric vehicle and the site selection of the battery replacing station is the process of carrying out iterative solution on the optimization model. The solution of the optimization model is represented by a power station location selection sequence and an electric vehicle path sequence.
The optimization model is iteratively solved, a discrete Binary Particle Swarm Optimization (BPSO) is improved, and an EBPSO method is provided for updating the site selection sequence of the power station. The electric vehicle path sequence is then updated using a large neighborhood search Algorithm (ALNS). That is, the EBPSO and the aln algorithms are fused, and a new solution method is proposed, which is referred to as the HALNS algorithm in the present application, as shown in fig. 3, and includes the following steps:
and F1, initializing a power station address selection sequence and an electric vehicle path sequence.
In the EBPSO method proposed in the present application, as with the BPSO, a particle population is obtained by initialization, and then an initial particle is randomly selected from the particle population, and subsequent iterative update is performed. As shown in fig. 4, the particle representation (solution representation) trades the station addressing sequence. For the site selection sequence of the power change station, 1 represents that the corresponding power change station needs to be built, and 0 represents that the corresponding power change station does not need to be built. And selecting initial particles from the initial particle population, namely an initial power station address changing sequence.
In a specific embodiment, in order to obtain a better initial feasible solution, the method for initializing the electric vehicle path sequence further includes:
step 1), dividing the initial electric vehicle path sequence into subsequences corresponding to all warehouses according to the distance from the customer to each warehouse.
Site selection sequence Y of power station is traded to this embodiment B ＝{y 1 ,y 2 ,...,y B },y i And =1 (i ∈ {1, 2.,. B }) represents that the ith replacement station is built, and is 0 otherwise. For a path sequence of an electric vehicle, X C ＝{x 1 ,x 2 ,...,x C },x j = C (j e {1, 2.,. C }) represents serving the C-th customer. As shown in fig. 4 (a), five battery stations are built, and the other four battery stations are not built, and a path sequence of the electric vehicle is randomly generated.
In the optimization model, the cooperative behavior of the supply and demand parties ensures that the warehouse and the electric vehicle can serve different types of customers. Thus, to obtain a better initial feasible solution, the path sequence X in the electric vehicle C In the method, a method of customer clustering is adopted, the customer may be assigned to the nearest warehouse. Assuming that there are N warehouses in the model, after adopting the customer clustering method, X C Is divided into several subsequences, i.e.
As shown in fig. 4 (b), the path sequence of the electric vehicle is divided into three sub-sequences according to the distance from the customer to each warehouse.
And 2) selecting nodes from each subsequence or/and the power station address selection sequence according to a preset rule, adding the nodes into the feasible solution of the corresponding warehouse, obtaining the feasible solution of each warehouse and forming a final initial electric vehicle path sequence.
The nearest neighbor method (NN for short) can generate a good initial feasible solution, and thus is widely applied to the conventional vehicle path planning problem. However, in the optimization model of the present application, due to the battery capacity constraint, the load capacity constraint and the detour behavior of the driver of the electric vehicle, the generation of the initial feasible solution is more complex than the conventional vehicle path planning problem, so that the original NN method is no longer applicable. Therefore, the present application proposes an ENN method for updating the nth warehouse D using a preset rule formula (15) n Initial feasible solution S of n 。
Wherein S is n Represents the nth warehouse D n The feasible solution of (a) to (b),
the nearest neighbor client representing the jth client node as the (j + 1) th client node, B j+1 Represents the nearest power change station of the (j + 1) th client node, s (j+1)r Represents the (j + 1) th customer node to the nearest power change station B j+1 Distance of(s) jD Representing the jth client node to the warehouse D n Distance of(s) j(j+1) Represents the distance between nodes j and j +1, q j Represents the electric vehicle electric quantity p at the node j j+1 Represents the demand of the (j + 1) th customer, w j Represents the electric vehicle load at node j, and>
representing a binary variable, e representing the energy consumption rate.
Selection using the ENN method
In the jth client node, is based on a fact that the nearest neighbor client->
As the (j + 1) th client node. s (j+1)r Represents the (j + 1) th customer node to the nearest power change station B j+1 S, of jD Representing the jth client node to the warehouse D n The distance of (c). When the battery capacity and load capacity constraints are met and no detour behavior of the vehicle occurs, based on the status of the battery>
Will be added to S n Performing the following steps; additionally, if a detour behaviour of the vehicle k occurs, i.e. </OR >>
The vehicle will visit B first j+1 To re-serve the customer
If the electric vehicle is about to be insufficient, namely the electric quantity from the jth customer node to the (j + 1) customer node to the latest power change station is consumed to be larger than the residual electric quantity of the vehicle, namely e(s) j(j+1) +s (j+1)r )＞q j If the electric vehicle is in service customer->
Access B before j+1 (ii) a If the load capacity constraint is not satisfied, i.e. p j+1 ＞w j Then the electric vehicle will return to the warehouse D n Reloading and then serving the customer; if neither the battery capacity nor the load capacity constraints are satisfied, i.e., es jD ＞q j And p j+1 ＞w j The electric vehicle must be charged at the battery replacement station before visiting the warehouse and the customer.
When the final initial electric vehicle path sequence is generated in this step, a power station switching node is selected from the power station switching address sequence in the initial particle and inserted.
As can be seen from fig. 4 (c), the ENN method generates an initial feasible solution by adjusting the order of the service clients and inserting the power station nodes, where the initial feasible solution is an electric vehicle path sequence at the beginning of iteration, and the initial feasible solution needs to be generated first, then the sequence is updated by using a destroy/insert operator on the basis of the initial feasible solution, and if the new path sequence is better than the initial feasible solution, the path sequence is updated (i.e., the original sequence is replaced by the new path sequence), otherwise, the path sequence is kept unchanged.
In an embodiment of the application, according to a preset rule, selecting a node from each subsequence or/and the power conversion station address selection sequence to add into a feasible solution of a corresponding warehouse, to obtain a feasible solution of each warehouse, including:
step F1.1, inputting a site selection sequence Y of the power station B And a sequence of electric vehicle paths serving the nth depot
Step F1.2, according to a preset rule
Or/and power station site selection sequence Y B In which the nearest neighbor client that selects the jth node->
Or/and the nearest battery replacement station B j+1 Initial feasible solution S for adding to nth warehouse n And the node is selected from
Or/and power station site selection sequence Y B Deleting;
step F1.3, judgment
Whether the current warehouse is an empty set or not, and if the current warehouse is the empty set, outputting an initial feasible solution S of the nth warehouse n Otherwise, returning to the step F1.2.
Therefore, the method obtains the initial electric vehicle path sequence and the initial feasible solutions S corresponding to all warehouses n The final initial electric vehicle path sequence is composed as shown in fig. 4 (c).
And F2, judging whether the stagnation standard is met, if so, applying a local search strategy to the currently recorded optimal power conversion station site selection sequence, otherwise, updating the power conversion station site selection sequence by adopting a position updating mechanism to obtain a new power conversion station site selection sequence.
The stagnation criterion in this embodiment is: if the representation of the globally optimal power station addressing sequence is not promoted after the preset iteration number iter, the stagnation standard is reached. Where iter is a preset number of iterations, e.g., iter =0.1 × maximum number of iterations.
The basic BPSO algorithm has strong global search capability, but has poor local search capability. Therefore, a local search strategy is introduced in the EBPSO algorithm of the present application to improve the local search capability. This application has adopted three kinds of operators: an exchange operator, an insert operator, and an invert operator. The swapping operator is used for selecting and swapping two elements in the swapping station address selection sequence. The insertion operator is used for randomly selecting several elements from the addressing sequence of the power conversion station and inserting the elements into the beginning of the sequence. The inversion operator is used for selecting one section from the position sequence of the power swapping station and inverting the section. The selection of which operator is selected by applying the local search strategy is a relatively mature technology in the field, and is not described herein again. According to the method and the device, a local search strategy is added in the search process, so that the local search capability of the basic BPSO algorithm is improved.
When the basic BPSO algorithm is used for iterative updating, the ith power station changing particle in the t iteration can use the position vector
And a velocity vector pick>
To indicate. In an iterative process, each particle will adjust its own velocity and position, where the velocity is updated according to equation (16) and the position is updated according to equation (17).
Where ω is an inertial parameter, c 1 And c 2 Is a learning factor, r 1 And r 2 Is a random number between 0 and 1, rand () is a random number between 0 and 1 subject to uniform distribution, sig (v) represents sigmoid transformation.
In the basic type BPSO algorithm, sigmoid transformation for updating the particle position is as shown in equation (18):
as the particle approaches the optimal position, the velocity of the particle approaches 0 to stabilize the position of the particle. However, as can be seen from the formula (18), if
Close to 0, is greater or less>
The value of (c) will be close to 0.5, resulting in a search that is always highly random, even if an excellent solution has been found. The power station swapping particle is also the address selection sequence of the power station swapping.
To this end, in the present application, a new location update mechanism is proposed to improve the convergence of the EBPSO algorithm, as shown in equations (19) and (20):
as can be seen from equation (19), when the particle velocity approaches 0,
the value of (c) also tends to 0. The particle updates the position according to equation (20) when->
Close to 0, is selected>
More likely to remain unchanged. The mechanism makes the particles with high speed more prone to change positions, and the particles with low speed more prone to remain unchanged, so that the global searching capacity and convergence of the algorithm are enhanced.
Wherein,
represents the speed of the d element in the ith conversion station addressing sequence at the t +1 th iteration, and is/are selected>
Represents the position of the d element in the ith conversion station addressing sequence at the t +1 th iteration, and/or is selected>
And the position of the d element in the ith conversion station addressing sequence at the t iteration is shown.
The site selection sequence of the power conversion station is updated through an improved BPSO algorithm. It should be noted that, in the BPSO algorithm of this embodiment, the swapping station address selection sequence is used as a particle of the BPSO algorithm. The method is mainly used for updating the site selection sequence of the power station, and then updating the electric vehicle path sequence through the following steps.
And F3, adopting a destroy operator and an insert operator to destroy and repair the electric vehicle path sequence respectively, and generating a new electric vehicle path sequence.
The ALNS algorithm is an extended version of a large neighborhood search algorithm, and the algorithm adopts different destroying operators and inserting operators to destroy and reconstruct a solution respectively. In order to obtain better search neighborhood and solution, the ALNS algorithm assigns an initial weight to each destroy operator and insert operator, and dynamically adjusts the weight according to the performance of the operators.
The present application employs two kinds of destroy operators to process the optimization model, including a random destroy operator and a worst destroy operator.
Random destroy operator removes from current solution randomly from r min To r max Proportional client node, where r min And r max Respectively, of a fixed value between 0 and 1. The worst destroy operator first calculates the change Δ f of the objective function when the ith customer is removed from the current solution i Then removing from η min To eta max Scaled client nodes resulting in a large increase of the objective function, where η min And η max Respectively, of a fixed value between 0 and 1.
The method adopts three insertion operators, namely a random operator, a greedy operator and a regret-3 insertion operator, and the removed clients are reinserted through the operators to repair the solution.
The random insert operator randomly generates insert indices for the removed customers and reinserts them to repair the solution. The greedy insertion operator calculates the delta Δ f of the objective function when the ith removed customer is inserted to the jth position of the current solution ij Thereby inserting the customer into the position where the target function increment is minimal. Repentance c t Defined as the difference of the objective function when inserting the client p at the tth suboptimal position and the optimal position, i.e. c t ＝f(s t (p))-f(s opt (p)). In regret-3 insertion operator, consider three suboptimal positions and choose c t The insertion index I with the maximized sum is used as the insertion position of the client p, as shown in equation (21):
how to select the destroy operator and the insert operator is a well-established technique in the field and will not be described here.
And F4, judging whether the new electric vehicle path sequence is superior to the currently recorded optimal electric vehicle path sequence, if so, entering the step F5, otherwise, returning to the step F3.
And comparing the new electric vehicle path sequence objective function value with the currently recorded optimal electric vehicle path sequence objective function value, and if the new electric vehicle path sequence objective function value is less than the currently recorded optimal electric vehicle path sequence objective function value, calling that the new electric vehicle path sequence is superior to the currently recorded optimal electric vehicle path sequence. In the iteration process, a currently recorded optimal electric vehicle path sequence and a currently recorded optimal power station site selection sequence are always recorded, and are updated in step F6.
It should be noted that, as shown in fig. 3, in step F3, the initial electric vehicle path sequence is initially operated, and the solution S is the initial electric vehicle path sequence. If step F3 is executed again after the learning S is updated in step F6, the solution S is operated.
And F5, updating the weights and the scores of the destroy operator and the insert operator.
And F6, taking the new electric vehicle path sequence as the currently recorded optimal electric vehicle path sequence, and taking the new power change station site selection sequence as the currently recorded optimal power change station site selection sequence.
In the step, the new electric vehicle path sequence is superior to the original electric vehicle path sequence, and the current recorded optimal electric vehicle path sequence is updated by the new electric vehicle path sequence.
And F7, judging whether the maximum iteration times are reached, if so, stopping iteration, and outputting an optimal power station location selection sequence and an electric vehicle path sequence, otherwise, returning to the step F2 and continuing to iterate.
It should be noted that steps F3 to F6 are basic steps of the conventional aln algorithm, and belong to a relatively mature technology in the field of technology, and are not described herein again.
The application also analyzes the optimization model and the solving method (HALNS algorithm) provided by the application through a series of experimental data, and compares the HALNS algorithm with other four heuristic baseline algorithms, thereby verifying the effectiveness and performance of the HALNS algorithm. Firstly, comparing the HALNS algorithm with a hybrid algorithm fused with a basic BPSO algorithm and an ALNS algorithm and a hybrid algorithm fused with a Genetic Algorithm (GA) and the ALNS algorithm, and verifying the effectiveness of the EBPSO algorithm in solving the problem of site selection of the power station. Then, comparing the HALNS algorithm with a hybrid algorithm fusing the EBPSO algorithm and an iterative local search algorithm (ILS for short) and the HVNS algorithm, and verifying the effectiveness of the ALNS algorithm in solving the electric vehicle path planning problem. For ease of illustration, the algorithms described above are denoted BPSO-ALNS, GA-ALNS, EBPSO-ILS and HVNS, respectively.
In the prior power station location-electric vehicle path planning problem, mileage anxiety and electric vehicle cooperation behaviors are not considered at the same time, so that a reference problem example adopted by the prior research cannot be directly suitable for the model provided by the application. Therefore, the method firstly modifies 11 classic examples of the vehicle path planning problem with load limitation according to the characteristics of an optimization model of the method to generate data sets A, B and P, and then randomly generates 14 examples as a data set C through computer simulation. The number of warehouses per instance is 2 to 5. The number of the alternative power stations is 17 to 55. The customer's demand has three values, 1, 3, 5 respectively. The maximum load capacity of the electric vehicle ranges from 16 to 75. The maximum battery capacity of the electric vehicle ranges from 42 to 96. The mileage anxiety threshold is set at 30% of the maximum battery capacity. Each instance is named according to the data set, the number of nodes and the number of warehouses to which the instance belongs. For example, instance A-n34-d3 indicates that the instance belongs to data set A, which contains 34 nodes and 3 repositories.
To validate the HALNS algorithm, the present application performed multiple sets of experiments. First, to verify the robustness of the HALNS algorithm in solving the CELRP-BSS-RA model, five algorithms were compared on the "C-n19-d2" example at population scales of 5 to 15, respectively. As shown in fig. 5, the HALNS algorithm can get a better solution and is more stable than the other four baseline algorithms as the population size changes. This experiment shows that the HALNS algorithm is robust in solving the model proposed herein.
Subsequently, on the "C-n19-d2" example, the HALNS algorithm was compared to the other four baseline algorithms at different iterations, and the iteration traces of the five algorithms are shown in FIG. 6. As can be seen from fig. 6, compared with the other four baseline algorithms, the HALNS algorithm converges faster, and an optimal solution can be obtained in a smaller number of iterations. This experiment shows that the HALNS algorithm has a stronger convergence and local search capability than other baseline algorithms.
Finally, the HALNS algorithm was compared to the four baseline algorithms on the baseline problem example. The five algorithms were run in duplicate 10 times for each instance. Table 1, table 2 and table 3 give the experimental results of the five algorithms. The optimum, mean and standard deviation of the objective function values are reported in tables 1 and 2. Table 3 records the average run time of the five algorithms in seconds. As can be seen from tables 1 and 2, in 25 cases, the HALNS algorithm yielded an average of 23 out of the other four baseline algorithms, and 22 cases with standard deviations no greater than the other baseline algorithms, indicating that the HALNS algorithm is more efficient and stable in solving the CELRP-BSS-RA model. Table 3 shows that the HALNS algorithm takes more time to solve 17 of the 25 instances than the other baseline algorithms due to the local search strategy, but the time taken is still within acceptable limits. In addition, with the continuous development of computing technologies such as parallel computing and cloud computing, the running time of the HALNS algorithm can be greatly shortened.
TABLE 1 optimal, mean and standard deviation of the five algorithms (first part)
TABLE 2 optimal, mean and standard deviation of the five algorithms (second part)
TABLE 3 average run time of the five algorithms
The application provides a new CELRP-BSS-RA model for solving the problem of power station site selection-electric vehicle path planning considering cooperation behavior and mileage anxiety at the same time. The model improves the supply chain efficiency through the cooperative behaviors of the supply and demand parties, and provides a new mileage anxiety function to solve the problem of mileage anxiety in the driving process. In order to effectively solve the model, the HALNS hybrid algorithm fusing the EBPSO algorithm and the ALNS algorithm is provided, and experimental results show that the HALNS algorithm is superior to other four baseline algorithms when the CELRP-BSS-RA model is solved.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (7)
1. A method for coordinating site selection of a power change station and path planning of an electric vehicle is characterized in that the method for coordinating site selection of the power change station and path planning of the electric vehicle comprises the following steps:
establishing a relational expression between the detour probability and the accumulated mileage anxiety according to the relation between the detour probability and the electric quantity state of the electric vehicle;
establishing an optimization model which minimizes the construction cost of the power change station and the driving cost of the electric vehicle, and minimizes the additional cost generated by the accumulated mileage anxiety of the driver in the whole journey;
and expressing the site selection sequence of the power station and the electric vehicle path sequence for the solution of the optimization model, and performing iterative solution on the optimization model to obtain an optimal power station site selection and electric vehicle path planning scheme.
2. The method as claimed in claim 1, wherein the establishing of the relational expression between the detour probability and the accumulated mileage anxiety comprises:
and constructing a rectangular coordinate system by taking the detour probability as an axis Y and the driving distance as an axis X, and taking the area enclosed by the detour probability curve and the axis X as the value of the accumulated mileage anxiety.
3. The method for site selection of a power conversion station and cooperation of path planning of an electric vehicle according to claim 1, wherein the optimization model is represented by the following formula:
wherein, c B Shows the construction cost of the power station, V B Representing an alternative set of swapping stations; y is i Representing a binary variable, if an ith seat conversion station is built, the binary variable is equal to 1, otherwise, the binary variable is 0; epsilon represents the driving cost of the electric vehicle per unit distance, V represents the set of all nodes, and V E Representing a set of electric vehicles; x is the number of ijk Represents a binary variable, equal to 1 if arc (i, j) is driven by vehicle k, and 0 otherwise; s ij Represents the distance between nodes i and j; a. The ijk (ζ) represents the driver of vehicle k traveling in arc (i, j)Cumulative mileage anxiety of (a); σ represents the additional cost of anxiety per unit accumulated mileage.
4. The method for site selection and electric vehicle path planning cooperation of a power swapping station as claimed in claim 1, wherein the iterative solution is performed on the optimization model to obtain an optimal site selection and electric vehicle path planning scheme for the power swapping station:
f1, initializing a power station changing address selection sequence and an electric vehicle path sequence;
step F2, judging whether a stagnation standard is met, if so, applying a local search strategy to the currently recorded optimal power conversion station site selection sequence, otherwise, updating the power conversion station site selection sequence by adopting a position updating mechanism to obtain a new power conversion station site selection sequence;
f3, adopting a destroy operator and an insert operator to destroy and repair the electric vehicle path sequence respectively and generating a new electric vehicle path sequence;
f4, judging whether the new electric vehicle path sequence is superior to the currently recorded optimal electric vehicle path sequence, if so, entering the step F5, otherwise, returning to the step F3;
f5, updating the weights and the fractions of the destroy operator and the insert operator;
step F6, taking the new electric vehicle path sequence as the currently recorded optimal electric vehicle path sequence, and taking the new power station address selection sequence as the currently recorded optimal power station address selection sequence;
and F7, judging whether the maximum iteration times are reached, if so, stopping iteration, and outputting an optimal power station location selection sequence and an electric vehicle path sequence, otherwise, returning to the step F2 and continuing to iterate.
5. The method for site selection of a power swapping station and electric vehicle path planning cooperation as claimed in claim 4, wherein the position updating mechanism updates the position of the site selection sequence of the power swapping station by adopting the following formula:
wherein,
represents the speed of the d element in the ith conversion station addressing sequence at the t +1 th iteration, and is/are selected>
Represents the position of the d-th element in the addressing sequence of the ith switching station in the t +1 th iteration, and/or is determined in advance>
Representing the position of the d element in the ith power station addressing sequence at the t iteration, and rand () is a random number subject to uniform distribution between 0 and 1.
6. The method of claim 4, wherein initializing the electric vehicle path sequence further comprises:
dividing the initial electric vehicle path sequence into sub-sequences corresponding to all warehouses according to the distance from the customer to each warehouse;
and selecting nodes from each subsequence or/and the power station address selecting sequence according to a preset rule, adding the nodes into the feasible solutions of the corresponding warehouse, obtaining the feasible solutions of each warehouse, and forming a final initial electric vehicle path sequence.
7. The method for site selection of a power conversion station and path planning of an electric vehicle according to claim 6, wherein the following formula is satisfied according to a preset rule:
wherein S is n Representing the nth warehouse D n Is feasible to solve the problem that the reaction solution is not stable,
the nearest neighbor client representing the jth client node as the (j + 1) th client node, B j+1 Represents the nearest power change station of the (j + 1) th client node, s (j+1)r Represents the (j + 1) th customer node to the nearest power change station B j+1 S, of jD Representing the jth client node to warehouse D n Distance of(s) j(j+1) Represents the distance between nodes j and j +1, q j Represents the electric vehicle electric quantity p at the node j j+1 Represents the demand of the (j + 1) th customer, w j Represents the electric vehicle load amount at node j>
Representing a binary variable, e representing the energy consumption rate. />
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