Power utilization optimization scheduling method for port electric equipment cluster under limited data

By building a total power mapping model and voltage mapping model, and using the historical data of the measurement nodes for training, the power consumption optimization and scheduling problem of port electric equipment clusters under limited data conditions is solved, and high-precision power consumption optimization and energy efficiency improvement is achieved.

CN119994920AActive Publication Date: 2025-05-13SHANGHAI JIAOTONG UNIV
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Patent Information

Application Number
CN202510207684.0
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-02-25
Publication Date
2025-05-13
Estimated Expiration
2045-02-25

AI Technical Summary

Technical Problem

The prior art is difficult to achieve optimized power consumption scheduling of port electric equipment clusters under limited data conditions, resulting in problems such as high energy consumption and voltage instability in the power grid.

Method used

By constructing a total power mapping model and voltage mapping model, using the historical data of the measurement nodes for training, compensating the information of the measurement nodes without measurement nodes, and achieving accurate calculation of the optimization scheduling of the port electric equipment cluster power supply cluster.

Benefits of technology

With only 40% node measurements obtained, high-precision power consumption optimization of port electric equipment clusters is achieved, reducing data demand and improving energy efficiency.

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Abstract

A port electric equipment cluster power utilization optimization scheduling method under limited data comprises the following steps: respectively constructing a total power mapping model and a voltage mapping model, training based on historical measurement data with measurement nodes, and forming a measurement node data driven PEE scheduling optimization model by the trained total power mapping model and voltage mapping model, and solving to obtain the PEE configuration number corresponding to each logistics task. According to the method, the number of the PEEs allocated to the logistics task is calculated by using the available measurement values of a few nodes, and the information of the non-measurement nodes is compensated by using the data from the adjacent nodes with measurement, so that accurate active / reactive power and voltage mapping is realized.
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Description

Technical Field

[0001] The present invention relates to a technology in the field of port power control, in particular to a method for optimizing the power consumption of a port electric equipment cluster under limited data. Background Art

[0002] The scheduling of port electric equipment clusters (PEE) affects the temporal and spatial distribution of port power grid loads. Ignoring the optimization of PEE power consumption may lead to high power grid energy consumption and voltage instability. Existing technologies require a large amount of node operation data to establish a power grid flow model. It is difficult to make accurate state estimates when data is limited, and the resulting PEE allocation strategy may deviate from the optimal solution. Summary of the invention

[0003] In view of the above-mentioned shortcomings of the prior art, the present invention proposes a method for optimizing the electricity consumption of port electric equipment clusters under limited data. The available measurement values ​​of a few nodes are used to calculate the number of PEEs allocated to logistics tasks, and the data from measured adjacent nodes are used to compensate for the information of unmeasured nodes, so as to achieve accurate mapping of active / reactive power and voltage.

[0004] The present invention is achieved through the following technical solutions:

[0005] The present invention relates to a method for optimizing the electricity consumption of a port electric equipment cluster under limited data. A total power mapping model and a voltage mapping model are constructed respectively, and training is performed based on historical measurement data of measurement nodes. The trained total power mapping model and voltage mapping model are combined into a PEE scheduling optimization model driven by measurement node data. The number of PEE configurations corresponding to each logistics task is obtained by solving the model.

[0006] The total power mapping model includes: a fine-grained deep graph convolution module, a filtering connection module, and a power prediction module, wherein: the fine-grained deep graph convolution module performs information construction, fine-grained average information aggregation, and vertex feature update processing based on the active and reactive power data of the measured nodes, compensates the active and reactive power information of the unmeasured nodes, and obtains the total power characteristics of all nodes; the filtering connection module performs measured node screening processing based on the total power characteristics of all nodes to obtain the total power characteristics of the measured nodes; the power prediction module performs fitting learning of the total power characteristics of the measured nodes to the active power mapping of the first node based on the total power characteristics of the measured nodes, and obtains the total power consumption prediction value of the port power grid corresponding to the electric equipment cluster scheduling.

[0007] The voltage mapping model includes: a fine-grained deep graph convolution module, a filtering connection module, and a voltage prediction module, wherein: the fine-grained deep graph convolution module performs information construction, fine-grained average information aggregation, and vertex feature update processing based on the active and reactive power data of the measured nodes, compensates for the active and reactive power information of the unmeasured nodes, and obtains the voltage characteristics of all nodes; the filtering connection module performs measured node screening processing based on the voltage characteristics of all nodes to obtain the voltage characteristics of the measured nodes; the power prediction module performs mapping fitting learning from the voltage characteristics of the measured nodes to the voltage of the measured nodes based on the voltage characteristics of the measured nodes to obtain the node voltage corresponding to the electric equipment cluster scheduling.

[0008] The training described above uses the loss function in: The total power consumption forecast value of the port power grid corresponding to the electric equipment cluster dispatch output by the total power mapping model, It is the actual value of the active power of the substation node obtained by the measuring unit.

[0009] The measurement node data-driven PEE scheduling optimization model includes: an initial PEE scheduling objective function, a reconstructed PEE scheduling objective function and a PEE scheduling optimization variable constraint, wherein: the initial PEE scheduling objective function is modeled according to the requirements of reducing the total electricity cost of port operations and preventing voltage over-limit, so as to obtain the optimization objective function of PEE scheduling; the reconstructed PEE scheduling objective function is based on the initial optimization objective, and the total power consumption of the port power grid and the node voltage in the optimization objective function are represented by a total power mapping model and a voltage mapping model, so as to obtain a PEE scheduling objective modeled as a convex function based on the mapping model; the PEE scheduling optimization variable constraint is processed by a formula that is convenient for solving the optimization model according to the logistics efficiency requirements that must be followed by the port electric equipment cluster scheduling, so as to obtain the optimization variable constraint modeled as a convex set. Technical Effects

[0010] The present invention performs intelligent flow perception by mining the limited available data, and optimizes the power consumption of the port electric equipment cluster scheduling by using only the measurement data of a small number of nodes, and can achieve the solution of the optimal logistics electric equipment cluster allocation strategy without relying on the accurate power grid model. The total power mapping model and voltage mapping model based on the fine-grained deep graph convolution online learning method collect, disseminate and aggregate the measured node data to compensate for the unmeasured node information, and on this basis, dynamically allocate PEE for logistics tasks with a small amount of node data to improve energy efficiency. Compared with the prior art, the present invention has the characteristics of low data demand and high-precision learning. It can perform accurate calculations with only the measurement values ​​of 40% of the nodes, without the need for measurement of all nodes. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a schematic diagram of the embodiment scenario;

[0012] Figure 2 It is a schematic diagram of the fine-grained depth map convolution block;

[0013] Figure 3 It is a schematic diagram of the total power mapping model and voltage mapping model for limited observable nodes;

[0014] Figure 4 It is a flow chart of the PEE power consumption optimization scheduling under limited information;

[0015] Figure 5 It is a schematic diagram of the port power grid based on the IEEE 33-node system;

[0016] Figure 6 It is a schematic diagram of the convergence behavior of the total power mapping network and other deep learning networks in the embodiment;

[0017] Figure 7 It is a schematic diagram of the convergence behavior of the voltage mapping network and other deep learning networks in the embodiment. Specific implementation manner

[0018] As Figure 1 shown, this is the application scenario of this embodiment, that is, the port power grid, whose topological structure is G = (Ν, E, R, X), where: the node set Ν = {1, 2,..., n} consists of substation nodes, ring main unit nodes, transformer nodes, etc., and n is the number of nodes; E is the edge set in the power grid; the resistance matrix R = [r ij and the reactance matrix X = [x ij in which r ij and x ij are the resistance and reactance between node i and node j respectively; there is a measurement node set Ν mear = {1, 2,..., m}, m << n, the nodes are numbered from 1 to m, and the nodes from m + 1 to n are non-measurement nodes.

[0019] In the described measurement node set Ν mear node 1 is a substation node, and nodes 2 to d are the nodes connected to the PEE. Nodes d + 1 to m refer to the points with large power and voltage changes, which can reflect the overall load fluctuation and power quality of the network to a certain extent although there is no PEE connection. p i 、q i and v i represent the active power, reactive power and voltage of the measurement node i at a certain moment. The active power, reactive power and voltage data vectors of the nodes obtained by the PEE power consumption optimization are respectively denoted as p mear = [p1, p2,..., p d ,pd+1 ,…,p m ] T ,q mear =[q1, q2, …, q d ,q d+1 , …, q m ] T , v mear =[v1, v2, …, v d , v d+1 , …, v m ] T .

[0020] like Figure 4 As shown, this embodiment involves a method for optimizing the scheduling of electricity consumption of a port electric equipment cluster under limited data. A total power mapping model and a voltage mapping model are constructed respectively, and are trained using historical measurement data based on measurement nodes. The trained total power mapping model and voltage mapping model are combined into a PEE scheduling optimization model driven by measurement node data, and the number of PEE configurations corresponding to each logistics task is obtained by solving the model.

[0021] In this embodiment, the total power mapping model and the voltage mapping model are both implemented by a neural network including a plurality of graph convolution layers, a filter connection layer and a prediction layer connected by residuals, wherein: each graph convolution layer transmits messages by using the feature data of itself and neighboring nodes to compensate for the information of the unmeasured nodes, and converts the transformed vertex features into As the residual output of layer l, After addition, a new input of the l+1 layer is formed; the filter connection layer traverses the vertex features of all nodes and extracts the vertex features of the measurement nodes from them; the prediction layer of the total power mapping model is implemented using a multilayer perceptron, and the prediction layer of the voltage mapping model is implemented using a multilayer perceptron.

[0022] The graph convolution layer enables nodes to collect feature data from L-layer neighborhoods through stacked L-layer graph convolution layers. Specifically, the message passing rule of the L-layer fine-grained deep graph convolution online learning method is: in: p i and q i are the active power and reactive power of the measured node i, respectively. is the vertex feature of node i in the lth layer, Ψ (l) is the function used to update the features of the vertices in the lth layer, ReLU(·) is the activation function, and GraphConv(·) is the generalized graph convolution function, which passes to the current node the aggregate information of the features from all neighboring nodes. and n i Represent the neighbor node set and the number of neighbor nodes of node i respectively. For each neighbor j∈υ(i), the information constructor γ is constructed by (l) Applied to Vertex Features Neighborhood characteristics and edge features Constructing aggregate information p j and q j are the active power and reactive power of the measured node j, respectively. MLP(·) is a multi-layer perceptron.

[0023] like Figure 2 As shown, the filter connection layer is located between the L layer output and the model prediction layer, and its output is Among them: concat(·) refers to traversing the vertex features of all nodes, and then extracting the vertex features of the measurement node from them through the pick(·) function, L-layer fine-grained deep graph convolution block and its message passing process The vertex feature of node i after L-layer transformation is expressed as

[0024] like Figure 3 As shown, the prediction layer of the total power mapping model is implemented using a multilayer perceptron, and its loss function Among them: The actual value of the active power of the substation node obtained by the measurement unit F p (·) is the functional relationship between the power of the substation node and the power of other measured nodes, p1 is the active power of the substation node, is the predicted value of the total power mapping model.

[0025] The prediction layer of the voltage mapping model adopts a multilayer perceptron, and its loss function is: Where: The actual voltage value of the measurement node F v (·) is the voltage mapping model that fits the functional relationship between the measurement node power and the measurement node voltage is the predicted value of the voltage mapping model. The substation node is designated as a balancing node, and its voltage v1 is given as a reference voltage and does not participate in the model training.

[0026] The PEE scheduling optimization model is established based on the trained total power mapping model and voltage mapping model to determine the optimal number of electric logistics equipment assigned to the operation task. The specific implementation process includes:

[0027] 1) Initial PEE scheduling objective function: The goal is to minimize the total electricity cost of port operations, and the voltage constraint is used as a penalty term to facilitate the solution. Specifically: Where: T is the scheduling period, t∈{1, 2,…, T}. t is the electricity price in period t. σ is the penalty factor for controlling the voltage not to exceed the lower limit of 0.95pu.

[0028] 2) Reconstruct the PEE scheduling objective function: Based on the trained model, we get: in: F v (e t +ε t ) j Represents the jth element in the prediction result set of the voltage mapping model. The input increment matrix ε consisting of the optimization variables t Represents the total active power of the electric logistics equipment at node k in time period t, k∈{2, 3,…, d}. The meaning is the reactive power of the equipment. In this paper, the power factor is 0.9, that is,

[0029] 3) PEE scheduling optimization variable constraints: Where: P LE is the rated power of a single logistics device. When there are f logistics tasks to be processed in a scheduling cycle, skt represents the sequence number of the task that receives the service of the logistics device at node k in period t, skt∈{1, 2, …, f}. and are the start and end time of task skt respectively. When node k is not in the task processing period, the logistics equipment load If is 0, the constraints are: Where: C skt is the number of devices, is the latest completion time of the task skt to ensure logistics efficiency, H skt is the number of containers, and η is the handling efficiency of a single device. and are the maximum and minimum equipment requirements for task skt, and then we get: in:

[0030] 4) Based on the multi-population genetic method, the PEE scheduling optimization model is solved. The optimized variables are converted and rounded to obtain the number of PEEs assigned to logistics tasks at each node. The PEE power consumption optimization scheduling process under limited information is as follows: Figure 4 shown.

[0031] After specific practical experiments, the performance of the method is tested on a port power grid based on the IEEE 33-node system. Nodes 1 to 13 are measurement nodes, among which nodes 2 to 4 are nodes connected to PEE, such as Figure 5 As shown. The data set contains 30,000 active power, reactive power and voltage data, of which: 80% are training sets and 20% are test sets. In this embodiment, the total power mapping model and the voltage mapping model both contain 5 convolutional layers, each convolutional layer has 3 MLP layers, and each hidden layer has 20 neurons. A port scheduling cycle is set to 24 hours. The peak, flat and valley electricity prices λ t They are 1.094, 0.875 and 0.471 yuan / kWh respectively. The rated power of a single PEE is 320kW, and the processing efficiency η is 35TEU / h. The penalty coefficient σ is 0.3. The minimum and maximum equipment requirements are 2 and 5 respectively, and other parameters are shown in Table 1.

[0032] Table 1 Logistics operation task parameters

[0033] In order to evaluate the effectiveness of the model with limited observable nodes, the average relative error is introduced to describe the accuracy of the results, including the average relative error of the power mapping module. The average relative error of the voltage mapping model in: is the ith element of the actual voltage sequence obtained by the measurement unit, F v,i (·) is the i-th element of the output vector of the voltage mapping model. The smaller the average relative error, the more accurate the learning effect.

[0034] like Figure 6 As shown, the total power mapping model based on the fine-grained deep graph convolution online learning method is significantly better than the deep neural network. The average relative error of the latter is about 35%, because simple data-to-data training makes it difficult to learn complex nonlinear relationships with only limited measurement node data. In the field of graph learning, the fine-grained mapping model of the present invention is compared with the existing graph convolution network using mean aggregation. The average relative error of the present invention is 0.628%, which is 0.96% higher than the 1.583% of the convolution network. This proves that the fine-grained deep graph convolution online learning method can make full use of known data and adapt to the uneven distribution and sparse characteristics of port data sets.

[0035] like Figure 7 As shown, the convergence behaviors of the voltage mapping model, graph convolution network and deep neural network based on the fine-grained deep graph convolution online learning method are shown. The average relative errors of the three are 0.362%, 0.967% and 11.294% respectively, which once again proves the superiority of the present invention.

[0036] Based on the trained total power mapping model and voltage mapping model, a PEE scheduling optimization model driven by measurement node data is established and solved. The corresponding logistics equipment optimization configuration scheme is shown in Table 2. To prove the effectiveness of the present invention, it is compared with the standard method. The latter is based on the power flow analysis method, in which: the measurement data and topology information of all nodes are known. As shown in Table 3, the results obtained by the two methods are relatively close, which confirms the reliability of the proposed method. Moreover, the present invention only requires measurements from a small number of nodes and can be applied to situations where measurements are insufficient.

[0037] Table 2 PEE configuration optimization results

[0038] Table 3 Comparison between the present invention and the standard method

[0039] To verify the robustness of the present invention to the load fluctuation of the unmeasured nodes, the unmeasured nodes are randomly selected to add disturbances to generate data sets with different load fluctuations. On this basis, the power flow mapping model is trained and used for PEE allocation. The accuracy of the mapping model and the related scheduling results are shown in Table 4. Despite the different load fluctuations, the results are basically consistent. The slight differences can be attributed to the slight differences in the convergence of the mapping model training, which is allowed in the machine learning model training, proving the robustness of the present invention.

[0040] Table 4 Results of the present invention under different load fluctuations

[0041] In terms of power flow variable mapping, the learning accuracy of the total power mapping model of this method is greatly improved, with an average relative error of 0.628%, which is significantly better than the 35% error of the deep neural network and 0.96% higher than the 1.583% of the convolutional network. The voltage mapping model of this method has an average relative error of 0.362%, which is better than the 11.294% error of the deep neural network and the 0.967% error of the graph convolutional network. In solving the optimal scheduling strategy for power consumption of port electric equipment clusters, compared with the existing technology that requires measurement data of all nodes, this method can perform accurate calculations with only 40% of the nodes' measurement values.

[0042] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principle and purpose of the present invention. The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. Each implementation scheme within its scope shall be subject to the constraints of the present invention.

Claims

1. A method for optimizing the power consumption of a port electric equipment cluster under limited data, characterized in that: The total power mapping model and voltage mapping model are constructed respectively, and are trained based on the historical measurement data of the measurement nodes. The trained total power mapping model and voltage mapping model are combined into a PEE scheduling optimization model driven by the measurement node data. The number of PEE configurations corresponding to each logistics task is obtained by solving the model. The total power mapping model includes: a fine-grained deep graph convolution module, a filtering connection module, and a power prediction module, wherein: the fine-grained deep graph convolution module performs information construction, fine-grained average information aggregation, and vertex feature update processing based on the active and reactive power data of the measured nodes, compensates the active and reactive power information of the unmeasured nodes, and obtains the total power characteristics of all nodes; the filtering connection module performs measured node screening processing based on the total power characteristics of all nodes to obtain the total power characteristics of the measured nodes; the power prediction module performs fitting learning of the total power characteristics of the measured nodes to the active power mapping of the first node based on the total power characteristics of the measured nodes, and obtains the total power consumption prediction value of the port power grid corresponding to the electric equipment cluster scheduling; The voltage mapping model includes: a fine-grained deep graph convolution module, a filtering connection module, and a voltage prediction module, wherein: the fine-grained deep graph convolution module performs information construction, fine-grained average information aggregation, and vertex feature update processing based on the active and reactive power data of the measured nodes, compensates for the active and reactive power information of the unmeasured nodes, and obtains the voltage characteristics of all nodes; the filtering connection module performs measured node screening processing based on the voltage characteristics of all nodes to obtain the voltage characteristics of the measured nodes; the power prediction module performs mapping fitting learning from the voltage characteristics of the measured nodes to the voltage of the measured nodes based on the voltage characteristics of the measured nodes to obtain the node voltage corresponding to the electric equipment cluster scheduling.

2. The method for optimizing the power consumption of a port electric equipment cluster under limited data according to claim 1 is characterized in that: The training described above uses the loss function in: The total power consumption forecast value of the port power grid corresponding to the electric equipment cluster dispatch output by the total power mapping model, It is the actual value of the active power of the substation node obtained by the measuring unit.

3. The method for optimizing the power consumption of a port electric equipment cluster under limited data according to claim 1 is characterized in that: The measurement node data-driven PEE scheduling optimization model includes: an initial PEE scheduling objective function, a reconstructed PEE scheduling objective function and a PEE scheduling optimization variable constraint, wherein: the initial PEE scheduling objective function is modeled according to the requirements of reducing the total electricity cost of port operations and preventing voltage over-limit, so as to obtain the optimization objective function of PEE scheduling; the reconstructed PEE scheduling objective function is based on the initial optimization objective, and the total power consumption of the port power grid and the node voltage in the optimization objective function are represented by a total power mapping model and a voltage mapping model, so as to obtain a PEE scheduling objective modeled as a convex function based on the mapping model; the PEE scheduling optimization variable constraint is processed by a formula that is convenient for solving the optimization model according to the logistics efficiency requirements that must be followed by the port electric equipment cluster scheduling, so as to obtain the optimization variable constraint modeled as a convex set.

4. The method for optimizing the power consumption of a port electric equipment cluster under limited data according to claim 1 is characterized in that: The total power mapping model and the voltage mapping model are both implemented by a neural network including a plurality of graph convolution layers, a filter connection layer and a prediction layer connected by residuals, wherein: each graph convolution layer transmits messages by using the feature data of itself and neighboring nodes to compensate for the information of the unmeasured nodes, and transforms the transformed vertex features into As the residual output of layer l, After addition, a new input of the l+1 layer is formed; the filter connection layer traverses the vertex features of all nodes and extracts the vertex features of the measurement nodes from them; the prediction layer of the total power mapping model is implemented using a multilayer perceptron, and the prediction layer of the voltage mapping model is implemented using a multilayer perceptron.

5. The method for optimizing the power consumption of a port electric equipment cluster under limited data according to claim 4 is characterized in that: The graph convolution layer enables nodes to collect feature data from L-layer neighborhoods through stacked L-layer graph convolution layers. Specifically, the message passing rule of the L-layer fine-grained deep graph convolution online learning method is: in: p i and q i are the active power and reactive power of the measured node i, respectively. is the vertex feature of node i in the lth layer, Ψ (l) is the function used to update the features of the vertices in the lth layer, ReLU(·) is the activation function, and GraphConv(·) is the generalized graph convolution function, which passes to the current node the aggregate information of the features from all neighboring nodes. υ(i) and n i Represent the neighbor node set and the number of neighbor nodes of node i respectively. For each neighbor j∈υ(i), the information constructor γ is constructed by (l) Applied to Vertex Features Neighborhood characteristics and edge features Constructing aggregate information p j and q j are the active power and reactive power of the measured node j, respectively. MLP(·) is a multi-layer perceptron.

6. The method for optimizing the power consumption of a port electric equipment cluster under limited data according to claim 4 is characterized in that: The filter connection layer is located between the L layer output and the model prediction layer, and its output is Among them: concat(·) refers to traversing the vertex features of all nodes, and then extracting the vertex features of the measurement node from them through the pick(·) function, L-layer fine-grained deep graph convolution block and its message passing process The vertex feature of node i after L-layer transformation is expressed as 7. The method for optimizing the power consumption of a port electric equipment cluster under limited data according to claim 4 is characterized in that: The prediction layer of the total power mapping model is implemented using a multilayer perceptron, and its loss function is Among them: The actual value of the active power of the substation node obtained by the measurement unit F p (·) is the functional relationship between the substation node power and other measured node power, p1 is the active power of the substation node, is the predicted value of the total power mapping model.

8. The method for optimizing the power consumption of a port electric equipment cluster under limited data according to claim 4 is characterized in that: The prediction layer of the voltage mapping model adopts a multilayer perceptron, and its loss function is: Where: The actual voltage value of the measurement node F v (·) is the voltage mapping model that fits the functional relationship between the measurement node power and the measurement node voltage is the predicted value of the voltage mapping model. The substation node is designated as a balancing node, and its voltage v1 is given as a reference voltage and does not participate in the model training.

9. The method for optimizing the power consumption of a port electric equipment cluster under limited data according to claim 4 is characterized in that: The PEE scheduling optimization model is established based on the trained total power mapping model and voltage mapping model to determine the optimal number of electric logistics equipment assigned to the operation task. The specific implementation process includes: 1) Initial PEE scheduling objective function: The goal is to minimize the total electricity cost of port operations, and the voltage constraint is used as a penalty term to facilitate the solution. Specifically: Where: T is the scheduling period, t∈{1, 2, …, T}, λ t is the electricity price during period t, σ is the penalty factor for controlling the voltage not to exceed the lower limit of 0.95 pu; 2) Reconstruct the PEE scheduling objective function: Based on the trained model, we get: in: represents the jth element in the prediction result set of the voltage mapping model, and the input increment matrix ε consisting of the optimization variables t represents the total active power of the electric logistics equipment at node k in time period t, k∈{2, 3, …, d}, The meaning of is the reactive power of the equipment; 3) PEE scheduling optimization variable constraints: Where: P LE is the rated power of a single logistics device. When there are f logistics tasks to be processed in a scheduling cycle, skt represents the sequence number of the task that receives the service of the logistics device at node k in period t, skt∈{1, 2, …, f}, and are the start and end time of task skt, respectively. When node k is not in the task processing period, the logistics equipment load If is 0, the constraints are: Where: C skt is the number of devices, is the latest completion time of the task skt to ensure logistics efficiency, H skt is the number of containers, η is the processing efficiency of a single device, and are the maximum and minimum equipment requirements for task skt, and then we get: in: 4) The PEE scheduling optimization model is solved based on a multi-population genetic method. The optimized variables are converted and rounded to obtain the number of PEEs assigned to logistics tasks at each node.

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