Cluster-based Adaptive Charging Path Optimization Method

Abstract

The present invention discloses a cluster-based adaptive charging path optimization method. The wireless sensor network adopted by the present invention includes a plurality of rechargeable sensors randomly deployed in a two-dimensional plane area, a service base station, a mobile charger, and a warehouse, and the charger can charge multiple sensors simultaneously. First, obtain the remaining power information of the sensor nodes, and cluster the network by combining the spatial position and the remaining power information; then regard the problem of selecting the stop position of the cluster as a function optimization problem; optimize the stop position by the gradient descent method to determine the finally selected stop point of the charging vehicle; finally, solve the charging path according to the stop position and the corresponding stop time, and calculate the corresponding average charging delay of the cluster. The present invention uses the clustering method and the adaptive optimization method to reduce the charging waiting time to shorten the charging delay, and uses the greedy strategy to plan the charging path to reduce the moving distance of the charging vehicle, further reducing the charging delay.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless sensor networks, and particularly relates to a cluster-based adaptive charging path optimization method. Background Art

[0002] Wireless sensor nodes are widely used in the Internet of Things. One of the most critical problems that wireless sensor networks need to face is the limited network life due to their battery-powered sensors. Because once a node runs out of energy, its sensing quality and the connectivity of the entire network will decline. In rechargeable sensor networks, the mobile charging scheduling problem of scheduling charging vehicles to charge sensor nodes has become a popular research topic.

[0003] In the multi-node charging scheme of wireless energy transfer technology, the charger can charge multiple adjacent nodes simultaneously within its charging range, which greatly improves the charging efficiency. Some recent literature uses a charging vehicle with limited energy to charge sensor nodes to reduce the charging delay and extend the network operation life. For example, Han et al. proposed in "A Coverage-Aware Hierarchical Charging Algorithm in Wireless Rechargeable Sensor Networks" that when selecting the stop position, the energy consumption and sensor coverage need to be comprehensively considered. However, due to the limitations of the sensor coverage calculation method, different parameter values need to be set for different network parameters and sensor states. And the optimal parameter values need to be set by human experience or obtained through multiple experimental comparisons. Therefore, the universality of this scheme is weak. The literature "A Joint Energy Replenishment and Data Collection Algorithm in Wireless Rechargeable Sensor Networks" considered the energy consumption of sensors when selecting the stop position. The author transformed the determination of the stop position in each cluster into the problem of solving the centroid of a two-dimensional domain with multiple particles distributed with different densities. Then the path optimization problem was transformed into a TSP problem. However, this method determines the stop position through a fixed calculation formula, which makes the proposed algorithm still not flexible enough in the stop position selection problem. In the article "A Multi-node Renewable Algorithm Based on Charging Range in Large-Scale Wireless Sensor Network", Wu et al. abstracted the energy transfer model into a disk structure and placed this disk structure with the sensor as the center. Then the intersection between the structures was selected as the candidate stop position for the charging vehicle. Unfortunately, this method did not consider the change of sensor energy distribution. It can be seen that in the current research on mobile charging of charging vehicles, the change of sensor energy distribution is not fully considered when selecting the stop position, and the selection method of the stop position adopted is not flexible enough, which will increase the charging delay of the network. Summary of the Invention

[0004] The purpose of the present invention is to provide a cluster-based adaptive charging path optimization method aiming at the problems existing in the prior art, which can reduce the charging waiting time and effectively shorten the average charging delay of the network clusters on the premise of meeting the power constraint of the charging vehicle.

[0005] The method of the present invention first realizes clustering of network sensor nodes through a weighted clustering algorithm; secondly, regards the stop position selection problem as a function optimization problem and optimizes it through the gradient descent method; finally, plans a safe charging movement path for the charging vehicle. On the basis of determining the stop position, the algorithm determines the final charging path by considering the spatial constraints of the sensor nodes and the power constraints of the charging vehicle and solving the path planning problem through a greedy algorithm.

[0006] The wireless sensor network adopted by the method of the present invention includes: m sensor nodes O = {o o with a battery capacity of e 1 , o 2 ,..., o m} randomly deployed in a two-dimensional area Ω of interest. The sensor nodes can receive wireless energy transmission and maintain long-term operation; a charging vehicle with a capacity of IE, which is equipped with a wireless energy transmission device for charging multiple sensors simultaneously; a base station located at the center of the network, which is a convergence node for sensing data and is responsible for coordinating and scheduling the charging vehicle to achieve timely data collection and energy replenishment. The charging vehicle starts from the base station and charges the sensor nodes along the planned cruise route at a driving speed of ν. There is a stop position, i.e., an anchor point, in each cluster of the network. The charging vehicle charges the sensor nodes within its energy transmission range at this stop position and collects sensing data from the cluster head. The optimization method is as follows:

[0007] Step (1): Obtain the remaining power information of the sensor nodes, and cluster the network by combining the spatial positions and remaining power information of each sensor node.

[0008] Step (2): For each cluster, define the residence time of the charging vehicle at the corresponding stop position, and regard the stop position selection problem of this cluster as a function optimization problem.

[0009] Step (3): Optimize the stop position through the gradient descent method to determine the finally selected stop point of the charging vehicle.

[0010] Step (4): Solve the charging path according to the stop position and the corresponding stop time, and calculate the corresponding average charging delay of the cluster.

[0011] Furthermore, step (1) is specifically:

[0012] (1-1) Through the wireless communication transmission between the sensor nodes and the charging vehicle during the previous charging process, obtain the current remaining power information of node o j . When returning to the base station, the charging vehicle uploads the collected data to the base station and replaces its own battery; the base station calculates the stop position for the next round according to the collected energy data of the sensor nodes; if it is the first round of charging currently, it is default that the remaining power information of all nodes is e . o。

[0013] (1 - 2) Initialize the cluster centers. According to the ascending order of the remaining power, select the k nodes with the largest power consumption as the initial weighted mean vectors {u 1 , u 2 ,... u k}}.

[0014] (1 - 3) Calculate the cluster membership of each sensor node. Traverse each sensor node o j ;

[0015] Calculate the distance d j from node o i to each cluster center u ji = ||o j - u i || 2 , 1 ≤ i ≤ k;

[0016] Calculate the cluster center λ j nearest to node o j = argmin i∈{1,2,...,k} d ji ;

[0017] Assign o j to the corresponding λ j cluster, denoted as:

[0018] (1 - 4) Update the cluster centers. Traverse each cluster C i , calculate the new weighted mean vectors, and obtain the new cluster center The two components of the vector are: where E threshold represents the minimum threshold that needs to be satisfied during the sensor energy replenishment process, and x j and y j represent the position coordinate components of node o j respectively.

[0019] (1 - 5) If |u' i - u i | > η, it means that the cluster center has changed. Return to (1 - 3). Otherwise, the calculation of network clustering is completed, and step (1) ends. η is a set threshold, which is a relatively small number.

[0020] Furthermore, step (2) is specifically:

[0021] (2 - 1) The time j required for the charging vehicle to meet the energy replenishment requirements of any sensor node o where, is the sensor node o jReceived power α and β are parameters related to the physical configuration of the charger, and d j is the distance between the charger's transmitting antenna and node o j and the receiving antenna, and R c is the maximum charging coverage distance of the charger. When the distance between the charging vehicle and the sensor node exceeds R c , the charging vehicle cannot charge the sensor node.

[0022] (2 - 2) For each cluster C i Given a stop position a i , the charging vehicle needs to perform energy transfer on all sensors of o i ∈N(a j ) at position a i . N(a i ) refers to the set of all sensors within the charging radius when the charging vehicle is at position a i ; ensuring that the charging requirements of sensors of o j ∈N(a i ) can be met, then the time the charging vehicle stays at a i

[0023] (2 - 3) For each cluster C i Given a stop position a i , regarding the selection problem of the stop position a i of each cluster C i as a function optimization problem: Represent the stop position a i as a position coordinate obtained by weighted calculation of the sensor node positions within the cluster range, that is: a i =(x i , y i ) = W iter ·loc i ; W iter =(W x , W y ) represents the weight vector in the iter-th round, is the set of sensor node position vectors within the cluster N(a i ), is the position information of each node o j ∈N(a i ), that is

[0024] (2 - 4) The weight matrix W 0 is initialized as a matrix of all 1s, that is, all points within the cluster have equal weights.

[0025] Furthermore, step (3) is specifically: ​

[0026] (3-1) Calculate each stop position a i 's residence time to obtain an expression regarding a i :

[0027]

[0028] (3-2) Regard the stop position optimization problem as a parameter optimization problem of a function regarding T i , and this problem is solved by the gradient descent method: Assume that the sensor node with the maximum charging time is o max , and its corresponding remaining energy is According to the gradient descent method, the partial derivative of the max function is non-zero only at the o max node. At the node position loc max =(x max , y max ), calculate the partial derivative with respect to W=(W max ), W x , W y ), that is: After calculation and simplification, obtain the partial derivatives Δ x and Δ y : where d max represents the distance between o max and a i , X and Y respectively represent the vectors of the cluster nodes in the x-axis and y-axis directions, and W x and W y respectively represent the components of W in the x-axis and y-axis directions.

[0029] (3-3) Update the weight W k+1 according to the partial derivative, expressed as: learningrate is the defined hyperparameter, representing the degree of weight update in each round of iteration. The larger the learningrate, the greater the amplitude of weight update.

[0030] (3-4) Repeat (3-1) to (3-3) until iterating for iteration rounds, where iteration is the defined hyperparameter.

[0031] (3-5) Obtain the set of stop positions A={a i} and calculate the corresponding T i .

[0032] Furthermore, step (4) is specifically:

[0033] (4-1) Initialization process, set the current position as the base station O cur =BS, and the power of the charging vehicle is Emc = IE, candidate time set The charging task sequence is empty, that is

[0034] (4-2) Traverse the stop position a i , and determine whether it satisfies and a i The addition of will not cause E mc Does not meet the power limit, expressed as: P charge and P move are the power during the charging process and the traveling process of the charging vehicle respectively, and the stop position a i and the current position O cur The distance D i = ||O cur - a i || 2 .

[0035] If both are satisfied, then calculate D i ;

[0036] Calculate the time required to complete the charging task from the current position O cur to a i

[0037] Store in the candidate time set T set as: T set = T set ∪{t i}.

[0038] (4-3) If the candidate time set T set is empty, the charging vehicle returns to the base station for charging, that is, set the current position to the base station O cur = BS, the power of the charging vehicle E mc = IE; otherwise, stop the position algorithm, and each time select the point with the least time consumption from the candidate time set T set as the next stop position to be visited, expressed as: A finish = A finish + O cur , and at the same time make

[0039] (4-4) Repeat (4-2) and (4-3) until all stop positions are visited to obtain the final charging path A finish .

[0040] The beneficial effects of the present invention include:

[0041] ​1. For the two-dimensional planar application scenario of the actual deployment area, the present invention proposes an adaptive optimization method based on clustering to minimize the average charging delay of clusters. Compared with traditional methods, it can optimize the stopping position without presetting parameters and satisfying the power constraint of the charging vehicle, reduce the charging waiting time, and shorten the average charging delay of the clusters.

[0042] 2. The present invention realizes clustering through a weighted clustering algorithm, regards the stopping position selection problem as a function optimization problem, and then optimizes it through the gradient descent method. Through a certain number of rounds of iteration, the theoretically optimal stopping position can be gradually approximated. Finally, through a greedy path planning strategy, this strategy ensures that the charging delay is further reduced under the capacity constraint of the charging vehicle's energy. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic diagram of the wireless sensor network adopted by the present invention;

[0044] Figure 2 It is a schematic diagram of the charger model adopted by the present invention;

[0045] Figure 3 It is a specific flowchart of the present invention;

[0046] Figure 4 It is a schematic diagram for the implementation of step 4. DETAILED DESCRIPTION OF THE INVENTION

[0047] The method of the present invention will be further described in detail below with reference to the drawings and embodiments.

[0048] An adaptive charging path optimization method based on clusters, Figure 1 The schematic diagram of the network shows the basic composition of the wireless sensor network model adopted by this method. In a large wireless sensor network, m rechargeable sensor nodes are randomly distributed, and the sensors in the sensor set O are all equipped with rechargeable batteries with a capacity of e o . i Each sensor o sense performs data aggregation on the data stream and self-sensed data. Calculate the energy consumption of the sensor under the real sensor energy consumption model. The energy consumptions during data sensing, receiving, and transmitting are P Rx , P Tx , and P sense = λ × b v , where b v (in bps) is the data monitoring rate of sensor o i , and are its data receiving and transmitting rates respectively, and d uvis the Euclidean distance between sensors u and v, and α is equal to 2. Sensor nodes are organized into clusters C = {C 1 , C 2 ,..., C i}, where data is transmitted to the cluster head through multi-hop transmission. The base station is located at the center of the network and is the convergence node of sensing data. It is also responsible for coordinating and scheduling the charging vehicle to achieve timely data collection and energy replenishment. The charging vehicle starts from the base station and travels along the planned tour route to charge the sensors at a speed of ν. There is a stop position (or called an anchor point) in each cluster of the network. The charging vehicle charges the sensor nodes within its energy transmission range at this stop position and collects the sensed data from the cluster head. Before each round of charging, the base station calculates the optimal stop position for the charging vehicle according to the energy consumption of the sensor nodes, which is used to replenish the energy of the sensors and collect the sensed data in each cluster. At the same time, the base station also synchronizes the position information of the sensors to the charging vehicle. After determining the stop positions in each cluster, the base station plans the tour path of the charging vehicle. Then, the charging vehicle travels along the planned trajectory and visits the stop positions calculated in the previous step in sequence. When returning to the base station, the charging vehicle uploads the collected data to the base station and replaces its own battery. The base station calculates the stop positions for the new round according to the energy data of the sensor nodes collected. The present invention reduces the charging waiting time under the premise of meeting the power constraint of the charging vehicle and effectively shortens the average charging delay of the network clusters.

[0049] As Figure 2 shown, the method adopts an omnidirectional charging model, where the charging vehicle is the transmitting party and the sensor nodes are the receiving parties. In this model, the receiving power of the receiving node is inversely proportional to the square of the distance between it and the charging vehicle. As the distance increases, the receiving power will drop sharply.

[0050] As Figure 3 shown, the method is as follows:

[0051] Step (1) Obtain the remaining power information of the sensor nodes, and divide the network into clusters by combining the spatial positions and remaining power information of each sensor node; specifically:

[0052] (1-1) Through the wireless communication transmission between the sensor nodes and the charging vehicle during the previous round of charging, obtain the current remaining power information of node o j When returning to the base station, the charging vehicle uploads the collected data to the base station and replaces its own battery. The base station calculates the stop positions for the next round according to the energy data of the sensor nodes collected; if it is the first round of charging currently, the remaining power information of all nodes is defaulted to e o .

[0053] (1-2) Initialize the cluster center, and select the power consumption in ascending order according to the remaining power​ The largest k nodes are used as the initial weighted mean vectors {u 1 , u 2 ,... u k}}.

[0054] (1 - 3) Calculate the cluster membership of each sensor node. Traverse each sensor node o j ;

[0055] Calculate the distance d j from node o i to each cluster center u ji = ||o j - u i || 2 , 1 ≤ i ≤ k;

[0056] Calculate the cluster center λ j nearest to node o j = argmin i∈{1,2,...,k} d ji ;

[0057] Assign o j to the corresponding λ j cluster, denoted as:

[0058] (1 - 4) Update the cluster centers. Traverse each cluster C i , calculate the new weighted mean vector to obtain the new cluster center The two components of the vector are: where E threshold represents the minimum threshold that needs to be satisfied during the sensor energy replenishment process, and x j and y j respectively represent the position coordinate components of node o j .

[0059] (1 - 5) If |u' i - u i | > η, it means the cluster centers have changed. Return to (1 - 3). Otherwise, the calculation of network clustering is completed, and step (1) ends. η is a set threshold and is a relatively small number.

[0060] Step (2) For each cluster, define the residence time of the charging vehicle at the corresponding stop position, and regard the stop position selection problem of this cluster as a function optimization problem; specifically:

[0061] (2 - 1) The time j required for the charging vehicle to meet the energy replenishment requirements of any sensor node o where is the receiving power of sensor node o j . α and β are parameters related to the physical configuration of the charger, d j It is the charger transmitting antenna and node o j Distance between receiving antennas, R c is the maximum charging coverage distance of the charger. When the distance between the charging vehicle and the sensor node exceeds R c When the charging vehicle is not able to charge the sensor nodes.

[0062] (2-2) For each cluster C i Given a stop position a i , the charging car is at position a i Need to o j ∈N(a i ) of all sensors to transmit energy, N(a i ) means when the charging vehicle is in position a i The collection of all sensors within its charging radius; ensure o j ∈N(a i ) can meet the charging requirements of the sensors, then the charging vehicle is i Time of stay

[0063] (2-3) For each cluster C i Given a stop position a i , each cluster C i Stop position a i The selection problem is considered as a function optimization problem: the stopping position a i It is represented as a position coordinate obtained by weighted calculation of the sensor node position within the cluster, that is: i =(x i ,y i )=W iter ·loc i ; W iter =(W x ,W y ) represents the weight vector of the iter round, is a cluster N(a i ), For each node o j ∈N(a i ), that is,

[0064] (2-4) Weight matrix W 0 Initialized as a full 1 matrix, that is, all points in the cluster have equal weights.

[0065] Step (3) optimizes the stopping position by using a gradient descent method to determine the final selected stopping point of the charging vehicle; specifically:

[0066] (3-1) Calculate the residence time of each stop position a i to obtain an expression regarding a i as follows:

[0067]

[0068] (3-2) Regard the stop position optimization problem as a parameter optimization problem of a function regarding T i , and solve this problem through the gradient descent method: Assume that the sensor node with the maximum charging time is o max , and its corresponding remaining energy is According to the gradient descent method, the partial derivative of the max function is non-zero only at the o max node. At the location loc max =(x max , y max ) of the o max node, calculate the partial derivatives with respect to W=(W x , W y ), that is: After calculation and simplification, obtain the partial derivatives Δ x and Δ y : where d max represents the distance between o max and a i , X and Y respectively represent the vectors of the cluster nodes in the x-axis and y-axis directions, and W x and W y respectively represent the components of W in the x-axis and y-axis directions.

[0069] (3-3) Update the weight W k+1 according to the partial derivatives, expressed as: learningrate is a defined hyperparameter, representing the degree of weight update in each round of iteration. The larger the learningrate, the greater the amplitude of weight update.

[0070] (3-4) Repeat steps (3-1) to (3-3) until iteration rounds, where iteration is a defined hyperparameter.

[0071] (3-5) Obtain the stop position set A={a i} and calculate the corresponding T i .

[0072] Step (4) Solve the charging path according to the stop position and the corresponding stop time, and calculate the corresponding average cluster charging delay; specifically:

[0073] (4-1) Initialization process, set the current position as base station O cur = BS, the battery level E of the charging vehicle mc = IE, the candidate time set The charging task sequence is empty, that is

[0074] (4-2) Traverse the stop position a i , and judge whether it satisfies and a i The addition of which will not cause E mc to not meet the battery level limit, expressed as: P charge and P move are the power during the charging process and the traveling process of the charging vehicle respectively, and the stop position a i and the current position O cur The distance D i = ||O cur - a i || 2 .

[0075] If both are satisfied, then calculate D i ;

[0076] Calculate the time required to complete the charging task from the current position O cur to a i

[0077] Store it in the candidate time set T set as: T set = T set ∪ {t i}.

[0078] (4-3) If the candidate time set T set is empty, the charging vehicle returns to the base station for charging (as Figure 4 shown), that is, set the current position as base station O cur = BS, the battery level E of the charging vehicle mc = IE; otherwise, the stop position algorithm, each time select the point with the least time consumption from the candidate time set T set as the next stop position to be visited, expressed as: A finish = A finish + O cur , and at the same time make

[0079] (4-4) Repeat (4-2) and (4-3) until all stop positions are visited, and obtain the final charging path A finish .

Claims

1. Cluster-based Adaptive Charging Path Optimization Method, and the wireless sensor network adopted by this method includes: The capacity of m batteries is e o The sensor node O = {o 1 ,o 2 ,...,o m } Randomly deployed in the two-dimensional area of ​​interest Ω, the sensor nodes can receive wireless energy transmission and maintain long-term operation; the charging vehicle with a capacity of IE, the charging vehicle is equipped with wireless energy transmission equipment that can charge multiple sensors at the same time; A base station located at the center of the network, which is the aggregation node of sensing data, responsible for coordinating and scheduling charging vehicles to achieve timely data collection and energy replenishment; The charging vehicle starts from the base station and charges the sensor nodes along the planned cruise route at a speed of ν. There is a stop position in each cluster of the network. The charging vehicle charges the sensor nodes within its energy transmission range at this stop position and collects sensing data from the cluster head. The specific method is as follows: Step (1) Obtain the remaining battery information of the sensor nodes, and divide the network into clusters by combining the spatial positions and remaining battery information of each sensor node. Specifically: (1-1) Obtain the current remaining battery level information of node o through wireless communication transmission between the sensor node and the charging vehicle during the previous charging process j When returning to the base station, the charging vehicle uploads the collected data to the base station and replaces its own battery; the base station calculates the stop position for the next round based on the collected energy data of the sensor nodes; if it is the first round of charging, the remaining battery level information of all nodes is defaulted to e o ; (1-2) Initialize the cluster centers. Select the k nodes with the highest power consumption in ascending order according to the remaining power as the initial weighted mean vectors {u , u 1 , u 2 ,... u k}; (1-3) Calculate the cluster membership of each sensor node and traverse each sensor node o j ; Computing node o j to each cluster center u i the distance d ji = ||o j - u i || 2 , 1 ≤ i ≤ k; Calculate the cluster center λ closest to node o j j = argmin i∈{1,2,...,k} d ji ;​ Assign o j to the corresponding λ j cluster, expressed as: (1 - 4) Update the cluster center, traverse each cluster C i , calculate the new weighted mean vector to obtain the new cluster center The two components of the vector are: Among them, E threshold represents the minimum threshold that needs to be satisfied during the sensor energy replenishment process, x j and y j respectively represent the position coordinate components of node o j ; (1 - 5) If |u i ′ - u i | > η, it means that the cluster center has changed, return to (1 - 3), otherwise the calculation of network clustering is completed, end step (1), where η is a set threshold value; Step (2) For each cluster, define the residence time of the charging vehicle at the corresponding stop position, and regard the stop position selection problem of this cluster as a function optimization problem. Specifically: (2-1) The charging vehicle meets the energy replenishment requirements of any sensor node o j The duration required for energy replenishment wherein, is the receiving power of sensor node o j ; α and β are parameters related to the physical configuration of the charger, and d j is the distance between the transmitting antenna of the charger and the receiving antenna of node o j ; R c is the maximum charging coverage distance of the charger. When the distance between the charging vehicle and the sensor node exceeds R c , the charging vehicle cannot charge the sensor node; (2-2) For each cluster C i Given a stop position a i , the charging vehicle needs to transfer energy to all sensors of o i ∈N(a j ) at position a. N(a i ) refers to the set of all sensors within the charging radius of the charging vehicle when it is at position a i ; ensure that the energy charging requirements of sensors o i ∈N(a j ) can all be met, then the residence time of the charging vehicle at a i i ​​ (2 - 3) For each cluster C i Given a stop position a i , for each cluster C i the problem of selecting the stop position a i is regarded as a function optimization problem: represent the stop position a i as a position coordinate obtained by weighted calculation of the positions of sensor nodes within the range of this cluster, that is: a i =(x i , y i ) = W iter ·loc i ; W iter =(W x , W y ) represents the weight vector in the iter-th round, is the set of position vectors of sensor nodes within the cluster N(a i ), is the position information of each node o j ∈N(a i ), that is (2-4) Weight matrix W 0 Initialized as a matrix of all 1s, that is, all points within the cluster have equal weights; Step (3) Optimize the stop position by the gradient descent method to determine the finally selected stop point of the charging vehicle. Specifically: (3-1) Calculate the residence time at each stop position a i to obtain an expression for a i as follows:​ (3-2) Consider the problem of optimizing the stop position as a problem of optimizing the parameters of a function with respect to T i This problem is solved by the gradient descent method: Assume that the sensor node that requires the maximum charging time is o max , and its corresponding remaining energy is According to the gradient descent method, the partial derivative of the max function is non-zero only at the o max node. At the position loc max of the o max node = (x max , y max ), calculate the partial derivative of W = (W x , W y ) as follows: After calculation and simplification, the partial derivatives Δ x and Δ y are obtained: where d max represents the distance between o max and a i , X and Y respectively represent the vectors of the cluster nodes in the x-axis and y-axis directions, and W x and W y respectively represent the components of W in the x-axis and y-axis directions; (3-3) Update the weight W according to the partial derivative k+1 , expressed as: learningrate is a defined hyperparameter, representing the degree of weight update in each iteration. The larger the learningrate, the greater the amplitude of weight update; (3-4) Repeat (3-1) to (3-3) until iteration rounds, where iteration is the defined hyperparameter; (3 - 5) Obtain the set of stop positions \(A=\{a i \}\) and calculate the corresponding \(T i ;\ Step (4) Solve the charging path according to the stop position and the corresponding stop time, and calculate the corresponding average charging delay of the cluster. Specifically: (4-1) Initialization process, set the current position as base station O cur = BS, the power of the charging vehicle E mc = IE, the candidate time set The charging task sequence is empty, that is (4-2) Traversal stop position a i , determine whether it satisfies and the addition of a i will not cause E mc to not satisfy the power limit, expressed as: P charge and P move are the power during the charging process and the traveling process of the charging vehicle respectively, and the stop position a i and the current position O cur the distance D i = ||O cur - a i || 2 ; If both are satisfied, calculate D i ; Calculate the time required from the current position O cur to a i to complete the charging task In the candidate time set T set is stored as: T set = T set ∪{t i}; (4-3) If the candidate time set T set is empty, the charging vehicle returns to the base station for charging, that is, set the current position as the base station O cur = BS, and the battery level E of the charging vehicle mc = IE; otherwise, stop the location algorithm, and each time select the point with the least time consumption from the candidate time set T set as the next stop position to be visited, which is expressed as: A finish = A finish + O cur , and at the same time make (4-4) Repeat (4-2) and (4-3) until all stop positions have been visited to obtain the final charging path A finish .

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