Microcell architecture-based edge computing microservice deployment and task scheduling method
By using the L2Box-ADMM algorithm for microservice deployment and task scheduling in 5G and vehicle-to-everything (V2X) scenarios and based on a microcell architecture edge computing network, the problem of insufficient resource utilization in existing technologies is solved, resulting in lower user latency and higher quality service.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-03-03
- Publication Date
- 2026-04-10
AI Technical Summary
Existing microservice deployment strategies fail to fully utilize the shared characteristics of microservice image layers in edge computing, resulting in insufficient resource utilization, inability to effectively reduce user latency, and overly simplistic assumptions about existing edge network structures that do not reflect reality.
This paper proposes a microservice deployment and task scheduling method based on the L2Box-ADMM algorithm. By describing and modeling the edge computing network under the microcell structure of 5G and vehicle-to-everything (V2X) networks, the problem is transformed into a linear integer programming problem, which is then solved using the L2Box-ADMM algorithm to optimize microservice deployment and task scheduling and reduce total user latency.
Compared to other algorithms, it reduces the total latency for users by 35%, provides better service, and makes full use of the cooperation between edge computing nodes and the sharing of mirror layers.
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Figure CN116347473B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of mobile edge computing microservice, and particularly relates to an edge computing microservice deployment and task scheduling method based on a microcell architecture. BACKGROUND
[0002] Container technology is an emerging virtualization technology. Compared with a traditional virtual machine, container technology has advantages such as lightweight, easy deployment, and high isolation degree [1]. Compared with a traditional development structure, a microservice architecture based on container technology splits a service into a plurality of modules for separate development, so that development is more flexible [2]. Currently, companies such as Google and Facebook have begun to use a microservice architecture to replace a traditional architecture.
[0003] With unprecedented development of mobile networks, intelligent devices have become an indispensable part of people's lives. The emergence of a large number of complex applications (e.g., VR, mobile video, and intelligent medical devices) leads to a large amount of data that needs to be processed in the future and puts forward a lower delay and more stable requirement for networks [3]. Traditional cloud computing centrally processes data to be processed in a central cloud, and this mode cannot meet the requirements of mobile intelligent devices for networks in the big data era. Therefore, deploying computing resources and storage resources to the network edge closer to users has become a promising mode to supplement the central cloud mode.
[0004] Limited by the limited coverage range of an edge network, a microcell is introduced into a 5G edge network as a basic element of the edge network.
[0005] A microservice relying on container technology has a lightweight feature that meets the concept of providing a low-delay service with limited resources by edge computing, and the combination of the two can provide users with better services.
[0006] Microservice deployment is a key problem for providing low-delay services for mobile users in edge computing. The layer structure of a microservice image enables different microservices to share the same image layer, and reasonable image deployment can fully utilize the characteristics of image layer sharing and thus maximize the use of limited computing resources of edge computing nodes. Existing papers mostly treat microservices as a lightweight virtual machine, do not fully utilize the inherent characteristics of microservices, and have a considerable gap between the proposed deployment strategy and the optimal strategy [4][5]. Although [6][7] consider the characteristics of microservices, the edge network structure considered is very simple, and the assumption that only one type of microservice image is deployed on one edge server does not conform to reality.
[0007] The application considers micro-service deployment and task scheduling problems in edge resource constrained scenarios under 5G and vehicle networking microcell structure, fully utilizes cooperation between 5G edge computing nodes and micro-service mirror layer sharing characteristics to consider problems, and proposes a solving method with L2Box-ADMM algorithm as the core. Simulation experiments based on real data show that the deployment and scheduling strategy given by the algorithm has more excellent performance than other algorithms. SUMMARY
[0008] The application aims to propose an edge computing micro-service deployment and task scheduling method based on microcell architecture in 5G and vehicle networking scenarios to obtain a strategy for reducing the total delay of all users in the scenario.
[0009] The edge computing micro-service deployment and task scheduling method based on microcell architecture proposed by the application first describes the microcell-based edge computing network structure in the 5G scenario; then, on this basis, the micro-service deployment and task scheduling problem is systematically modeled, and the optimization target is to minimize the delay of all users, which mainly manifests as processing data upload delay; subsequently, the problem is transformed into a linear integer programming problem by decomposing and completely solving the sub-problems; finally, the L2Box-ADMM algorithm is used to solve the linear integer programming problem. Test results show that, compared with other micro-service deployment and task scheduling algorithms, the method of the application can find a micro-service deployment and task scheduling strategy that satisfies the resource constraint condition and has smaller total delay, and can reduce the gap from the optimal solution by 35%.
[0010] (I) Description of the microcell-based edge computing network structure in the 5G scenario
[0011] Consider a region centered on a macrocell, and there are some microcells and users in the region. The macrocell covers the entire region and can directly provide services to all users, and the microcell covers a part of the region and can directly provide services to a part of the users. Let the microcell node set be N={1,2,…,N,N+1}, where the serial number N+1 represents the macrocell. Use C n and S n to represent the computing resources and storage resources of node n, respectively.
[0012] Use a binary matrix D to represent whether there is an optical fiber for direct communication between microcells. D n,n′ =1 indicates that there is an optical fiber connection between microcell-n and microcell-n'. Microcells with optical fiber connection can cooperate with each other and transmit data to each other. The macrocell and all microcells in the region have optical fiber communication. Use I n,n′This represents the bandwidth of wired communication between microcell-n and microcell-n'. This value is 0 when there is no fiber optic connection between them. A service requested by a user from a microcell can be delivered to an adjacent microcell for processing. Only macrocells and the central cloud are connected via the backbone network within a microcell. Tasks requested by a user from a macrocell can be directly uploaded to the central cloud for processing. Services requested by a user from other microcells need to be first transferred to a macrocell before being uploaded to the central cloud for processing. (Using I...) N+1,N+2 This indicates the communication bandwidth between the macrocell and the central cloud.
[0013] The set of users is U = {1, 2, ..., U}, and the size of the data that each user needs to process is R. u Let M = {1, 2, ..., M} denote the set of all microservices, and G... m This represents the computing resources required by microservice m. L = {1, 2, 3, ..., L} represents the mirror layer of all microservices. Indicates whether microservice m contains a mirror layer l, K l M represents the storage space required for mirror layer l. u This indicates the type of microservice requested by user u.
[0014] Users select a directly connectable node to establish a connection and access the edge network, uploading data that needs processing and requesting microservices. The requested services can be provided directly by the accessed node, by adjacent nodes, or by the central cloud. For edge nodes to provide services to users, they need to store all the required image layers of the microservices locally and have sufficient computing resources to perform the computation.
[0015] (II) System Modeling of Microservice Deployment and Task Scheduling Issues
[0016] To systematically model the microservice deployment and task scheduling problem, factors such as system decisions, communication latency, and constraints need to be considered before a model is finally built.
[0017] (1) System decision
[0018] The system makes decisions in four parts, and all decision variables are 0-1 variables.
[0019] The first part is the decision to deploy microservices on micro-regions, x n,m =1 indicates that microservice m is deployed on micro-region-n; otherwise, it indicates that no such microservice is deployed.
[0020] The second part is the deployment of the mirror layer on top of the microcell, y n,l =1 indicates that the mirror layer l is deployed on the microcell-n; otherwise, it indicates that the mirror layer is not deployed.
[0021] The third part, the decision is to let the user select a microcell to establish a connection to access the edge network and transmit the data that needs to be processed through this microcell, z u,n =1 indicates that user u accesses microcell-n, otherwise it indicates that user u does not access microcell-n.
[0022] The fourth part is which edge node or central cloud delivers the service requested by the user w u,n =1 indicates that the task of user u is delivered to microcell-n to execute, in particular, when n=N+2, it indicates that the task of user u is completed by the central cloud.
[0023] (2) Communication delay
[0024] For user u and microcell-n, assume that the positions of the two are UP u and NP n , respectively. The channel bandwidth allocated to a user by a microcell is W, the signal fading obeys the exponential α, the transmit power of the user mobile device is δ u , the channel gain is H, and the channel noise is σ 2 . If user u is within the coverage of microcell-n, the bandwidth E u,n of wireless communication between the two is given by the Shannon theorem, which is:
[0025]
[0026] Otherwise, the bandwidth E u,n of wireless communication between the two is 0.
[0027] The service is provided by the microcell-n directly accessed by the user, and the communication delay t u,n,n only has the part of wireless transmission:
[0028]
[0029] The service is provided by the adjacent microcell-n' of the microcell-n directly accessed by the user, and the communication delay t u,n,n′ includes the part of wireless transmission and the limited transmission between nodes:
[0030]
[0031] The service requested by the user is completed by the central cloud, if the user directly connects to a normal microcell, the data that needs to be processed needs to be transmitted to the macrocell first, and then handed over to the central cloud, and the communication delay t u,n,N+2 is:
[0032]
[0033] If the user is directly connected to a macro cell, then the data can be handed over directly to the central cloud, with a communication delay t u,N+1,N+2 For:
[0034]
[0035] (3) Constraint restrictions
[0036] The storage space occupied by the mirror layer stored on the micro cell cannot exceed its own storage capacity:
[0037]
[0038] If it is decided to deploy a certain microservice mirror on the micro cell, all the mirror layers required by the microservice need to be stored:
[0039]
[0040] Use θ u,n =1 to represent whether the user is within the signal coverage range of a certain micro cell, and the user must access the edge network through a micro cell that can establish a connection:
[0041]
[0042]
[0043] The user's task must be executed by a certain edge node or central cloud:
[0044]
[0045] The micro cell that executes the service for the user needs to deploy the corresponding microservice:
[0046]
[0047] The computing resources required by the task executed on the micro cell-n cannot exceed the computing capacity of the micro cell itself:
[0048]
[0049] Expand a column for matrix D to represent whether each micro cell can upload data to the central cloud through a certain path, according to the above description of network functions, this column should be all 1. For users, the node that executes the computing task should be able to transmit data between the node that accesses the network in some way:
[0050]
[0051] (4) Model establishment
[0052] Based on the above factors, the problem model to be solved by the present application is expressed in the following form:
[0053]
[0054] s.t.: formula (7)-(13)
[0055] This is a 0-1 programming problem with quadratic constraints and a quadratic objective function.
[0056] (Three) Decompose the problem model and convert it into a linear integer programming problem
[0057] Consider the sub-problem about variable z under the condition that variables x, y, and w are fixed. At this time, the problem is to let each user select a micro cell that can be connected to access the edge network, so that the communication delay of uploading data to the micro cell performing the task is the shortest. At this time, the decisions of different users are not coupled, so the global delay is the lowest when each user's delay is the lowest.
[0058] Let ξ u,n′ represent the minimum delay of user u uploading data to all paths of micro cell-n', and when n' = N+2, it represents uploading the task to the center cloud for processing. Let ζ u,n′ represent the serial number of the micro cell connected wirelessly when the delay of user u uploading data reaches ξ u,n′ . Then z u,n =1 if w u,n′ =1 and n=ζ u,n′ .
[0059] At this point, the problem is converted into a linear integer programming problem:
[0060]
[0061] s.t. formula (6), (7), (10), (11), (12)
[0062] Since there is an overlapping constraint between the micro service deployment and the image layer deployment decision in the problem, and the computing resource constraint and the storage resource constraint have a constraint feature similar to the knapsack problem, this problem is still an NP-hard problem.
[0063] (Four) Solve by using L2Box-ADMM
[0064] First, the alternative method is to represent the integer space {0,1} p of dimension p by the intersection of the box space S b =[0,1] p of the same dimension and the ellipsoid space S2, where the ellipsoid space S2 is an ellipsoid with each dimension being a sphere with center at the point and radius On the one hand, {0, 1} p The variable in the space is obviously in the box space and ellipsoid space. On the other hand, the distance of any dimension of the variable in any box space to is not greater than Therefore, in order to also be on the ellipsoid space, each variable must be 0 or 1.
[0065] Then the iterative solution of ADMM. The vector v = [x; y; w] represents the concatenation of the decision variables. The problem to be solved now is a linear programming problem, so it can be written in a compact matrix and vector form, and for convenience, introduce auxiliary variables h, each element of which is non-negative, to change the inequality constraints into equality constraints:
[0066]
[0067] A1v = g1,
[0068] A2v + h = g2,
[0069] v = e1 = e2, e1∈S b , e2∈S2; (16)
[0070] A1 describes the equality constraint (10), A2 describes the inequality constraints (6), (7), (11), (12). e1 and e2 are auxiliary variables, respectively belonging to the box space S b and the ellipsoid space S2.
[0071] We introduce the dual multipliers k1, k2, k3, k4, the penalty factors ρ1, ρ2, ρ3, ρ4, the iterative update step size γ, and the ADMM iterative solution follows the flow:
[0072] (1) Update the auxiliary variables:
[0073]
[0074] where, represents the projection into the box space, which means
[0075]
[0076] where, represents the projection into the sphere space, which is
[0077]
[0078] h t+1= max(0, g2- y2v t ), (19)
[0079] (2) Update the variable v
[0080] To update the variable v, we need to solve the following linear system:
[0081]
[0082] For this linear system, we can use the existing preconditioned conjugate gradient method to solve it. And since the matrix is very sparse, we can solve it very quickly.
[0083] (3) Update the dual multiplier:
[0084] The update of the dual variable follows the formula:
[0085]
[0086]
[0087]
[0088]
[0089] The L2Box-ADMM algorithm can provide a solution in which each variable is very close to 0-1. After a simple rounding of this solution, we can obtain a high-quality feasible solution.
[0090] The pseudo code of the L2Box-ADMM algorithm is shown in Appendix 1.
[0091] The subsequent rounding algorithm first places the mirror layer according to the solution obtained by the L2Box-ADMM until the storage space of the micro cell cannot continue to place the mirror layer. According to the mirror layer deployed on the micro cell, we can determine what micro service each micro cell is deployed. Then, according to the solution obtained by the L2Box-ADMM, we assign each user's request task to the corresponding micro cell for execution. However, due to the actual micro service deployment and the deployment in the L2Box-ADMM solution, there is a part of the user's request that cannot be assigned to the corresponding micro cell for execution. For this part of the user, the present application uses a heuristic method to assign their tasks. Calculate the second shortest allocation path and the time difference of the shortest allocation path of these tasks that have not been allocated to the user. The larger this difference is, the greater the overall delay increase will be if the user cannot enjoy the shortest delay allocation path. Therefore, the tasks of these users are preferentially allocated to the micro cell with the smallest delay for execution. The pseudo code of the rounding algorithm is shown in Appendix 2. Attached Figure Description
[0092] Figure 1 This is a schematic diagram of the microcell-based edge computing network structure in a 5G edge computing network.
[0093] Figure 2 This is a performance comparison between our algorithm and the comparison algorithm under different workloads.
[0094] Figure 3 This is a performance comparison between our algorithm and the comparison algorithm under different storage resources.
[0095] Figure 4 This is a performance comparison between our algorithm and the comparison algorithm under different computing resources. Detailed Implementation
[0096] System environment: Python;
[0097] Number of users: 100;
[0098] Number of microservices: 20;
[0099] Number of image layers for a single microservice: 4-8 layers;
[0100] Total number of mirrored layers: 116;
[0101] Number of micro-cells: 15;
[0102] Number of macrocells: 1;
[0103] Mirror layer size: 10MB-400MB;
[0104] Microservices require computing resources of 0.15GHz-0.45GHz;
[0105] The user needs to process data of 5MB-20MB;
[0106] Inter-cell communication bandwidth: 30-45Mbps;
[0107] Communication bandwidth between microcells and macrocells: 8-12 Mbps;
[0108] Communication bandwidth between macrocells and the central cloud: 20Mbps;
[0109] In addition to the parameter settings mentioned above, this invention also sets the probability of each microservice being requested based on the statistics of the number of microservice requests on the Fuxi Cloud Platform, so that the distribution of microservices requested by users in the scenario conforms to the actual distribution characteristics.
[0110] The comparative algorithm is an algorithm that greedily selects the microcell with the lowest delay to serve each user (LDG) and an algorithm that prioritizes the microcell with the most requests from users in the coverage range (MDG), and an algorithm that rounds based on a linear relaxation solution (GR).
[0111] The experimental results show that the algorithm of the present application can perform better than the comparative algorithm in most scenarios, and can obtain a strategy very close to the optimal solution. Compared with the best algorithm in other algorithms, the gap between the average and the optimal solution can be reduced by 35%.
[0112] Appendix 1: Pseudocode of L2Box-ADMM algorithm
[0113]
[0114] Appendix 2: Pseudocode of rounding the solution of L2Box-ADMM algorithm
[0115]
[0116] Reference:
[0117] [1] Ma L, Yi S, Carter N, et al. Efficient live migration of edge services leveraging container layered storage. IEEE Transactions on Mobile Computing, 2018, 18(9): 2020-2033.
[0118] [2] Kang H, Le M, Tao S. Container and microservice driven design for cloud infrastructure devops. IEEE International Conference on Cloud Engineering (IC2E). 2016, pp. 202-211.
[0119] [3] Cisco Mobile Visual Networking Index, Feb. 2017. [On-line]. Available: https: / / newsroom.cisco.com / pressreleasecontent?articleId=1819296. Last Accessed on: Jun. 2018
[0120] [4]. Li, B. An, J. Ma, and D. Cao, “Comparison between chunk-based and layer-based container image storage approaches: an empirical study,” in 2019 IEEE International Conference on Service-Oriented System Engineering (SOSE). IEEE, 2019, pp. 197-1975.[5]A. Samanta, L. Jiao, M. M and L. Wang, “Incen-tivizing microservices for online resource sharing in edge clouds,” in 2019 IEEE 39th International Conference on Distributed Computing Systems (ICDCS). IEEE, 2019, pp. 420-430.
[0121] [6] L. Gu, D. Zeng, J. Hu, B. Li, and H. Jin, “Layer aware microservice placement and request scheduling at the edge,” in IEEE INFOCOM 2021 - IEEE Conference on Computer Communications. IEEE, 2021, pp. 1-9.
[0122] [7] L. Gu, D. Zeng, J. Hu, H. Jin, S. Guo, and A. Y. Zomaya, “Exploring layered container structure for cost efficient microservice deployment,” in IEEE INFOCOM 2021 - IEEE Conference on Computer Communications. IEEE, 2021, pp. 1-9.
Claims
1.A method for edge computing micro-service deployment and task scheduling based on micro-cell architecture in 5G and vehicle-to-everything scenarios, characterized in that, The specific steps are: (1) The system decision includes four parts, all decision variables are 0-1 variables. (2) Communication delay (3) Constraint limitation (3.1) The storage space occupied by the mirror layer stored on the micro cell cannot exceed its own storage capacity: (3.2) If it is decided to deploy a certain micro service mirror on the micro cell, all mirror layers required by the micro service need to be stored: (3.4) The user's task must be executed by a certain edge node or central cloud: (3.5) The micro cell that provides services for the user needs to deploy the corresponding micro service: The first part is the decision to deploy microservices on the microcell, denotes that the microservice m is deployed on the microcell -n, otherwise it denotes that no such microservice is deployed; The second part is the deployment of the mirror layer on the micro cell, represents that the mirror layer l is deployed on the micro cell-n, otherwise it represents that this mirror layer is not deployed; The third part, the decision is to let the user select a microcell to establish a connection to access the edge network and transmit the data that needs to be processed through the microcell, represents that the user u accesses the microcell-n, otherwise it represents that the user does not access the microcell-n; The fourth part is which edge node or central cloud delivers the user's requested service The task of user u is delivered to microcell-n to execute, and when The task of user u is delivered to microcell-n to execute, and when (3.6) The computing resources required by the task executed on micro cell-n cannot exceed the computing capacity of the micro cell itself: For user u and microcell-n, assume that the positions of the two are respectively and ; the channel bandwidth assigned to a user by the microcell is , the signal fading obeys exponential , the transmitting power of the user mobile device is , the channel gain is H, and the channel noise is ; if user u is within the coverage of microcell-n, the bandwidth of the wireless communication between the two is given by the Shannon theorem, specifically: , (1) Otherwise the bandwidth of the wireless communication between the two is 0; Service provided by microcell-n directly accessed by user, communication delay Only this part of wireless transmission: , (2) The service is provided by a neighbouring microcell-n' to which the user has direct access, the communication delay comprises a wireless transmission and a limited transmission section between nodes: , (3) The service requested by the user is completed by the central cloud, and if the user is directly connected to a normal microcell, the data to be processed is first transmitted to the macrocell and then handed over to the central cloud, and the communication delay is: , (4) If the user is directly connected to a macrocell, then the data is handed directly to the central cloud, with the communication delay is: , (5) (3.7) Expand a column for matrix D to represent whether each micro cell can upload data to the central cloud through a certain path according to the above description of network function, this column is all 1; for users, the node that executes the computing task and the node that accesses the network transmit data in a certain way: (4) Model establishment ; Based on the above factors, the problem model to be solved is expressed as follows: ; (3.3) with denotes whether a user is within the signal coverage of a certain microcell and the user must access the edge network through a microcell that can establish a connection: ; ; This is a 0-1 programming problem with quadratic constraints and quadratic objective functions; ; Step (three) decomposes the problem model and converts it into a linear integer programming problem, which includes: ; Consider the sub-problem about variable z under the condition of fixed variables x, y, w, at this time the problem is to let each user choose a micro cell that can be connected to access the edge network, so as to make the communication delay of data uploading to the micro cell that executes the task shortest; ; At this point the problem is transformed into a linear integer programming problem: ; Step (one) describes the micro cell-based edge computing network structure under the 5G scenario, which includes: Consider a region centered on a macro cell, there are some micro cells and users in the region; the macro cell covers the entire range of the region and can directly provide services for all users, the micro cell covers a part of the range and can directly provide services for a part of the users; , (14); ; Users choose a node that can be directly connected to establish a connection to access the edge network, upload data that needs to be processed and request micro services; the services requested by the user are provided by the accessed node directly, or by the adjacent node of the accessed node, or by the central cloud; the edge node needs to save all mirror layers required by the micro service locally and has enough computing resources to provide computing to provide services for the user. Step (four) uses L2Box-ADMM to solve; specifically: with denotes that the user u uploads data to the microcell -n' with the smallest delay among all paths, when denotes that the task is uploaded to the central cloud for processing; with denotes that the user u uploads data with a delay that reaches when the wireless connection is to the microcell of order n; then if and ; , (15 ); 。 2. The method of claim 1, wherein, Let the set of microcell nodes be N = {1, 2, …, N, N+1}, where the serial number N+1 represents the macrocell; use and respectively represent the computing resources and storage resources of node n; use a binary matrix D to represent whether there is a fiber that can directly communicate between microcells; represent that there is a fiber connection between microcell-n and microcell-n'; microcells with fiber connections can cooperate with each other and transmit data to each other; where the macrocell and all microcells in the area have fiber communication; use to represent the bandwidth of wired communication between microcell-n and microcell-n', when there is no fiber connection between them, this value is 0; the service requested by a user to a microcell can be delivered to an adjacent microcell for processing; only the macrocell and the central cloud in the microcell are connected through the backbone network, and the task requested by the user to the macrocell can be directly uploaded to the central cloud for processing, and the service requested by the user to other microcells needs to be first transferred to the macrocell and then uploaded to the central cloud for processing; use to represent the communication bandwidth between the macrocell and the central cloud; Let the set of users be U = {1, 2, …, U}, and the size of data that a user needs to process be Let M = {1, 2, …, M} represent the set of all microservices, represent the computing resources required by microservice m; L = {1, 2, 3, …, L} represents the image layers of all microservices, represent whether microservice m contains image layer l, represent the storage space required by image layer l, represent the microservice type requested by user u; 3. The method of claim 1, wherein, First, by the substitution method, let the integer space of dimension p be represented by the intersection of the box space of the same dimension and the ellipsoid space where the ellipsoid space is a sphere with radius centered at the point with each coordinate equal to ; Then solve the iteration of ADMM; vector Indicates the connection of the decision variable; Write the linear programming problem in compact matrix and vector form, and for convenience, introduce auxiliary variables that are all nonnegative Convert inequality constraints to equality constraints: , , , , , ; (16) Described are equality constraints (10), Described are inequality constraints (6), (7), (11), (12); and are auxiliary variables, belonging to the box space and the ellipsoid space respectively; introducing dual multipliers , penalty factor , iterative update step size ; The ADMM iteration solving process is as follows: (1) updating the auxiliary variable: ; wherein represents a projection into the box space, which means that ; ; wherein represents a projection into a spherical space, in particular: ; ; (2) updating the variable updating variables The following system of linear equations needs to be solved: ; ; , (20) The pre-conjugate gradient descent method is used to solve the above linear equation set; (3) updating the dual multiplier: The formula for updating the dual variable is: ; ; ; ; The L2Box-ADMM algorithm obtains a solution very close to 0-1 for each variable, and after rounding, a high-quality feasible solution is obtained.
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