A multi-resource collaborative scheduling optimization method in a cloud computing environment

Abstract

The application relates to the technical field of edge computing, and discloses a multi-resource cooperative scheduling optimization method in a cloud computing environment, which comprises the following steps: characterizing the resource state of a heterogeneous edge node as a representation point on a discrete state manifold, modeling a computing task as a cooperative hyperedge connected with all participating nodes, and using a potential function attached to the hyperedge to quantify a nonlinear coupling cost; a discrete state manifold and a cooperative hypergraph model are constructed, and discrete gradient optimization is performed on the manifold of each node in the discrete state manifold and the cooperative hypergraph model; the associated nodes in each hyperedge perform distributed potential game with the aim of minimizing the potential function; the optimization instructions of all nodes are harmonized by using discrete Hodge decomposition, and global consistent system state update instructions are generated; the instructions are analyzed into specific resource allocation and task offloading strategies, and are executed, effectively solving the problem that the nonlinear coupling cost is difficult to quantify and optimize in cross-domain edge cooperation, and improving the overall efficiency and decision feasibility of the system.

Description

Technical Field

[0001] This application relates to the technical field of edge computing and discloses a method for multi-resource collaborative scheduling optimization in a cloud computing environment. Background Technology

[0002] In edge computing scenarios, multiple edge nodes often need to work together to handle complex computing tasks. When nodes differ in hardware architecture, resource specifications, or management affiliation, there are still many shortcomings in achieving efficient joint resource allocation and task offloading. For example, existing solutions usually model the additional overhead brought by node collaboration as a simple linear or fixed cost. However, this cost is non-linear and highly dependent on which nodes are involved, what resource status they are in, and what tasks they are collaborating on. There is a lack of a unified model that can accurately characterize the heterogeneous state of nodes and the coupling relationship of multi-node tasks, resulting in optimization based on distortion and inefficient decision-making results in actual deployment. Common distributed optimization methods are difficult to guarantee optimal task-level collaboration and cannot adapt to dynamic environments. When a node participates in multiple collaborative tasks at the same time, the optimization instructions it receives from different task perspectives may conflict with each other. The lack of conflict reconciliation mechanisms means that the final instructions generated may not be able to satisfy the constraints of all tasks at the same time. Summary of the Invention

[0003] The purpose of this section is to outline some aspects of the embodiments of this application and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents, and such simplifications or omissions should not be construed as limiting the scope of this application.

[0004] To address the aforementioned technical issues, this application provides a method for optimizing multi-resource collaborative scheduling in a cloud computing environment.

[0005] On the one hand, this application provides a method for optimizing joint resource allocation and task unloading, including:

[0006] S1 represents the resource state of each heterogeneous edge node in the system as a representation point on a discrete state manifold, and models each computational task that requires collaboration as a collaborative hyperedge connecting all participating nodes. It defines a potential energy function for the collaborative hyperedge to quantify the cost of nonlinear coupling, and constructs a discrete state manifold and collaborative hypergraph model.

[0007] S2. Using the discrete state manifold and cooperative hypergraph model, each node performs independent discrete gradient optimization on its own discrete state manifold, and performs distributed potential game on the associated nodes of each cooperative hyperedge with the goal of minimizing the potential function. The optimization instructions of all nodes are harmonized in a holistic manner to generate globally compatible system state update instructions.

[0008] S3. Parse the globally compatible system state update instruction into specific resource allocation and task unloading strategies, and send them to the corresponding nodes for execution.

[0009] As a preferred embodiment of the joint resource allocation and task unloading optimization method of this application, wherein:

[0010] The method for representing the resource state as representation points on a discrete state manifold is as follows: S101, the continuous resource state vector collected by each node is discretized into a finite set of states by the feasible interval defined by hardware specifications and policy constraints through uniform quantization or non-uniform quantization of the operating point; S102, the finite set of states is used as a topological structure with adjacency relationships, and the topological structure is the discrete state manifold.

[0011] Each discrete state point in the finite set is a representation point, and each representation point uniquely corresponds to a feasible combination of resource usage for a node at a certain moment.

[0012] As a preferred embodiment of the joint resource allocation and task unloading optimization method of this application, wherein:

[0013] The method for modeling each collaborative computing task as a collaborative hyperedge is as follows: S111, parse the subtask division, data dependency relationship, and latency and reliability constraints in the task descriptor issued by the system to determine the set of candidate nodes that can meet some or all of its computing needs; S112, explicitly connect all nodes in the candidate node set with a hyperedge to form a task node binding relationship.

[0014] The modeling of the cooperative hyperedge is used to define the scope and coordination objects of the hierarchical collaborative optimization computation:

[0015] Each collaborative hyperedge is used to define a set of associated nodes as a collaborative unit, which serves as the scope for task coupling optimization and conflict coordination. The set of all collaborative hyperedges and the intertwined node relationships constitute the coupled network structure in the overall optimization of the system.

[0016] As a preferred embodiment of the joint resource allocation and task unloading optimization method of this application, wherein:

[0017] A potential energy function is constructed for each collaborative hyperedge to quantify the cost of nonlinear coupling, including: inter-node data transmission overhead, which is related to the product of the state of the associated node and the state of the link between nodes; cross-domain compliance processing overhead, which is activated when the associated nodes belong to different management domains and has a nonlinear relationship with the data volume and security level; and additional latency caused by resource contention, which is reflected through the cross term of the resource utilization of the associated nodes.

[0018] As a preferred embodiment of the joint resource allocation and task unloading optimization method of this application, wherein:

[0019] The method for constructing the discrete-state manifold and cooperative hypergraph model is as follows:

[0020] S121. Gather the discrete state manifolds of all heterogeneous edge nodes to form the node state space of the system;

[0021] S122. Generate the corresponding set of cooperative hyperedges and their respective potential functions through the set of all tasks to be processed, forming a set of task coupling relationships;

[0022] S123. The node state space is taken as the node set of the hypergraph, and the task coupling relationship set is taken as the hyperedge set of the hypergraph. The discrete state manifold and cooperative hypergraph model are composed of the node set and the hyperedge set of the hypergraph.

[0023] As a preferred embodiment of the joint resource allocation and task unloading optimization method of this application, wherein:

[0024] The discrete gradient optimization is as follows: each node, based on the discrete state manifold model, takes the current state representation point as the starting point, calculates the discrete negative gradient direction based on the local cost function, and selects a pre-updated state point from the set of adjacent state points of its manifold that reduces the local cost estimate. This optimization process is executed in parallel and generates at least one pre-updated state point for each node.

[0025] As a preferred embodiment of the joint resource allocation and task unloading optimization method of this application, wherein:

[0026] The distributed potential game is as follows: through the cooperative hypergraph model, each cooperative hyperedge uses the pre-update state point generated by its associated nodes in the discrete gradient optimization as the initial strategy to initiate a finite number of iterative games with the goal of minimizing the hyperedge potential function.

[0027] In each iteration, each node calculates its potential energy based on the current strategy combination and adjusts its own strategy based on its discrete state manifold to reduce its potential energy until a Nash equilibrium state is reached where no one can unilaterally improve the potential energy. Finally, a set of coordinated states is output for each hyperedge.

[0028] As a preferred embodiment of the joint resource allocation and task unloading optimization method of this application, wherein:

[0029] The overall harmonization is as follows: for each node that obtains inconsistent harmonized states from its different cooperative hyperedges, the discrete Hodge decomposition is applied for global integration.

[0030] The Discrete Hodge decomposition decomposes the state update vector field of all nodes into globally coordinated gradient components and locally conflicting cyclic components. By synthesizing gradient components and eliminating cyclic components, a unique and globally compatible system state update instruction is generated, transforming the distributed local optimization and coupled coordination results into a joint decision that the system can execute.

[0031] As a preferred embodiment of the joint resource allocation and task unloading optimization method of this application, wherein:

[0032] The method for parsing globally compatible system state update instructions into specific resource allocation and task unloading strategies includes: based on the preset mapping relationship between each state representation point and the set of node physical resource parameters in the discrete state manifold model, decoding the target state representation point of each node in the instruction into specific allocation values ​​of the corresponding number of CPU cores, memory capacity, and bandwidth quota.

[0033] Based on the set of nodes associated with the collaborative hyperedge in the collaborative hypergraph model and their updated states, the subtask division ratio, data flow direction and computation order of each computation task among the participating nodes are determined, thus forming a task unloading path plan.

[0034] As a preferred embodiment of the joint resource allocation and task unloading optimization method of this application, wherein:

[0035] The parsed resource allocation values ​​and task unloading paths are encapsulated into control commands that can be recognized by the nodes, and sent to each target node through the system communication link. After receiving the command, each node dynamically configures its resource manager according to its content and starts the corresponding subtask executor, and sends a status confirmation message back to the coordinator after the execution is completed.

[0036] The beneficial effects of this application are as follows:

[0037] This application constructs a joint model of discrete state manifold and cooperative hypergraph to describe the resource constraint state of heterogeneous nodes and the nonlinear coupling relationship of multiple nodes caused by tasks, thus solving the problem of distortion in the description of cooperative costs caused by the simplification of existing models.

[0038] This application employs a hierarchical collaborative optimization mechanism that combines discrete gradient optimization, hyperedge potential game theory, and Hodge global reconciliation to achieve task-level collaborative optimization and resolve decision conflicts among multiple tasks while ensuring the local autonomy of nodes. This addresses the problem of difficulty in balancing local optimization and global cooperation, as well as the lack of conflict reconciliation mechanisms, thereby generating globally compatible optimization instructions. Attached Figure Description

[0039] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained through these drawings without creative effort. Wherein:

[0040] Figure 1 The overall method flowchart of the joint resource allocation and task unloading optimization method provided in this application;

[0041] Figure 2 A flowchart illustrating the global resource view construction process in a joint resource allocation and task unloading optimization method provided in this application;

[0042] Figure 3 The optimization process diagram provided in this application is for a joint resource allocation and task unloading optimization method.

[0043] Figure 4 This application provides a flowchart of task unloading path planning and execution in a joint resource allocation and task unloading optimization method. Detailed Implementation

[0044] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the specific embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0045] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0046] Secondly, the term "an embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of this application. The phrase "in one embodiment" appearing in different ways in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that excludes other embodiments.

[0047] Example 1

[0048] like Figure 1 As shown, a joint resource allocation and task offloading optimization method includes:

[0049] S1. Represent the resource state of each heterogeneous edge node in the system as a representation point on a discrete state manifold, and model each computational task that requires collaboration as a collaborative hyperedge connecting all participating nodes. Define a potential energy function for the collaborative hyperedge to quantify the cost of nonlinear coupling, and construct a discrete state manifold and collaborative hypergraph model.

[0050] In a preferred example, the heterogeneous edge node refers to a computing node with differences in architecture, computing power, storage, network interface, or management domain; the resource status is a multi-dimensional vector characterizing the real-time load and capabilities of the node. The dimensions of this multi-dimensional vector may include: the number of available computing cores for CPU, GPU, and FPGA and their current utilization rate, free memory capacity, storage I / O throughput, remaining uplink and downlink network bandwidth, and the security and billing policy identifier of the management domain to which the node belongs; the value of the resource status is periodically collected by resource probes deployed on each node and aggregated to the coordinator via a lightweight communication protocol, such as... Figure 2 As shown, the complete process from node resource acquisition and quantization to constructing a discrete state manifold is illustrated, with a focus on two methods: uniform quantization and non-uniform quantization.

[0051] Specifically, by deploying local resource monitoring probes on each heterogeneous edge node, a multi-dimensional resource status vector reflecting the real-time load and capabilities of the node is periodically collected. The dimensions of the multi-dimensional resource status vector include key resource types, such as the available computing power and utilization rate of various processing units (CPU, GPU, FPGA), memory capacity, storage I / O rate, network bandwidth, etc. The maximum memory capacity of each node, resource reservation policy, service level agreement requirements, security domain isolation rules, etc., jointly define the feasible interval. The feasible interval is used to construct the value space of the resource status vector.

[0052] The method for representing the resource state as a representation point on a discrete state manifold is as follows: S101, the continuous resource state vector collected by each node is discretized into a finite set of states by the feasible interval defined by hardware specifications and policy constraints through uniform quantization or non-uniform quantization of the operating point.

[0053] The continuous resource state vector is mapped to a finite, discrete set of states. The mapping process preferably employs uniform quantization and non-uniform quantization.

[0054] Specifically, the uniform quantization divides the feasible interval of each resource dimension into several smaller intervals, each of which is represented by a representative value. The representative values ​​of all dimensions are combined to generate multidimensional discrete state points for scenarios with relatively uniform resource constraints.

[0055] The non-uniform quantization identifies typical patterns or efficient working points of node resource usage based on historical data or domain knowledge. These working points can correspond to the optimal resource configuration for certain common task types. During specific quantization, the system is divided around these preset working points, with a coarser division in resource areas that are not frequently used or have low efficiency.

[0056] Through quantization, the infinite number of possible continuous states of each node are reduced to a finite set of discrete states. Each state point in the discrete state set represents a feasible combination of resource usage under hardware and policy constraints.

[0057] S102. The finite set of states is taken as a topological structure with adjacency relationships, and the topological structure is the discrete state manifold.

[0058] The specific definition of the adjacency relationship is as follows: For any two state points in the discrete state set, if there exists a minimum feasible adjustment operation that satisfies the node's hardware and management strategy, such as adding or releasing a CPU core allocation, or adjusting memory capacity with a fixed step size, that can directly transform the node's resource state from the first state point to the second state point, then the first state point and the second state point are defined as adjacent state points. All state points and their adjacency relationships together constitute the discrete state manifold of the node. Mathematically, this manifold can be represented as a graph Gi=(Vi,Ei), where the vertex set Vi is all discrete state points, and the edge set Ei is all pairs of state points that satisfy the above adjacency relationship.

[0059] Each discrete state point in the finite set is a representation point, and each representation point uniquely corresponds to a feasible combination of resource usage for a node at a certain moment.

[0060] The adjacency relationship is defined as follows: if two discrete state points are considered adjacent, then their transition corresponds to the smallest and most direct adjustment operation on the node resources. For example, a new state point achieved by adding one CPU core or reducing memory reservation by 10% from the current state point can be defined as a neighbor of the original state point.

[0061] The manifold is formed by combining all discrete state points and their adjacency relationships to create a graph-like or grid-like topological structure, which is the discrete state manifold of the current node.

[0062] In the manifold, each state point not only represents a specific combination of resources, but also clearly indicates that it can be adjusted to other feasible states in one step from the current node through adjacency relationships. The discrete gradient optimization described in S2 can explore from a state point to its neighboring state points along the edges of the manifold, and perform efficient local search in the discrete space.

[0063] Resource states are represented as points on a discrete state manifold. Quantization discretizes the continuous constraint problem to reduce complexity, and adjacency topology is introduced to structure the discrete points. Each point is represented as a basic computational unit of the node's resource state in the optimization model, improving the computational accuracy of each point and reducing computational errors. Figure 3 As shown.

[0064] The method for modeling each collaborative computing task as a collaborative hyperedge is as follows: S111, analyze the subtask division, data dependency relationship, and latency and reliability constraints in the task descriptor issued by the system, and determine the set of candidate nodes that can meet some or all of its computing needs.

[0065] Specifically, the task descriptor includes the task's metadata and requirement constraints. S111, the task's metadata and requirement constraints are parsed, and the parsing includes structure parsing and constraint parsing.

[0066] The structure parsing is used to identify the internal structure of a task, including its task descriptor being divided into logical subtasks, and the data dependencies between subtasks, such as the output of one subtask being the input of another subtask.

[0067] The constraint parsing is used to extract non-functional constraints of the task symbol, such as the total completion delay limit and reliability requirements.

[0068] The candidate node matching process uses structural analysis and constraint analysis, combined with the discrete state manifolds of each node in the current system, to filter out nodes that meet some or all of the computational requirements of the current task, thus forming a candidate node set.

[0069] A preferred matching criterion includes: whether the node has the computing units required to execute a specific subtask, whether it has sufficient idle resources, and whether its network location can meet the latency requirements of data dependencies.

[0070] S112. Connect all nodes in the candidate node set with a superedge to form a task node binding relationship;

[0071] After determining the set of candidate nodes, modeling is performed using a hypergraph.

[0072] Specifically, the hyperedge is created for the computing task that needs to collaborate. A hyperedge can directly connect any number of nodes, that is, the entire set of candidate nodes.

[0073] Furthermore, the collaborative hyperedge explicitly associates all nodes in the candidate node set together, forming a binding relationship between tasks and nodes, and the hyperedge serves as the unique representative of the current collaborative task in the optimization model.

[0074] The modeling of the collaborative hyperedge is used to limit the scope of the hierarchical collaborative optimization computation and the coordination objects.

[0075] Each collaborative hyperedge is used to define a set of associated nodes as a collaborative unit, which serves as the scope for task coupling optimization and conflict coordination. The set of all collaborative hyperedges and the intertwined node relationships constitute the coupled network structure in the overall optimization of the system.

[0076] By using hypergraphs, task collaboration requirements are quantified into higher-order relationships, thereby limiting the scope and objects of optimization and coordination. This overcomes the shortcomings of traditional pairwise association models that cannot express group collaboration effects. The combination of collaborative hyperedges and discrete state manifolds constitutes a discrete state manifold and collaborative hypergraph model: nodes carry their own resource state information on the discrete manifold, while tasks act as hyperedges to weave related nodes into a collaborative network.

[0077] Each collaborative hyperedge defines a collaborative unit, whose members are the set of nodes associated with the current hyperedge. The calculation cost of the potential energy function for the current task and the coordination between nodes in the distributed potential game are all restricted to this unit, realizing fine-grained management of tasks and decomposing the globally complex optimization problem into multiple sub-problems with clear scopes of action and based on tasks.

[0078] All tasks in the system correspond to all cooperative hyperedges and their associated nodes, forming a cooperative hypergraph. In this cooperative hypergraph, a node can be connected by multiple different hyperedges simultaneously, meaning a node participates in multiple tasks. The set of all hyperedges and their intertwined node relationships represent the coupling and competition network between tasks and between tasks and resources in the system. The set of all hyperedges and their intertwined node relationships serve as the computational skeleton for hierarchical cooperative optimization. That is, discrete gradient optimization occurs at the node level, distributed potential game occurs at the hyperedge level, and global reconciliation handles conflicts between different hyperedges' instructions to the same node.

[0079] When multiple heterogeneous edge nodes collaboratively process a computing task, in addition to the computational overhead of each node, additional costs arise from the collaborative behavior. These additional costs are not a simple linear sum of the costs of each node, but rather exhibit complex nonlinear coupling characteristics. For example, the data exchange overhead between nodes depends not only on the amount of data, but also on the current network load of the two endpoints, the processing of security protocols across management domains, and the competition for shared resources. Moreover, these factors are interconnected and amplify each other.

[0080] The potential energy function defined for each cooperative hyperedge e is used to map all nonlinear coupling costs caused by the computational task represented by the hyperedge to continuous, differentiable scalar values, where the independent variable X is a vector whose components consist of the current resource state representations of all nodes associated with the hyperedge e.

[0081] A preferred setting rule for the potential function may include: covering the main nonlinear coupling factors affecting the efficiency of task collaboration, facilitating efficient minimization in subsequent distributed potential games; the parameters in the potential function should be configurable according to specific task characteristics and real-time network conditions to reflect cost sensitivity under different scenarios.

[0082] A potential energy function is constructed for each collaborative hyperedge. The independent variable of the potential energy function is a vector composed of the resource state representation points of all nodes associated with the current hyperedge. This function is used to quantify the nonlinear coupling cost, which includes: inter-node data transmission overhead, which is related to the product of the state of the associated nodes and the link state between the nodes; cross-domain compliance processing overhead, which is activated when the associated nodes belong to different management domains and has a nonlinear relationship with the data volume and security level; and additional latency caused by resource contention, which is reflected through the cross term of the resource utilization rate of the associated nodes.

[0083] A specific form of the potential energy function is a composite function containing logarithmic and polynomial cross terms, for example:

[0084]

[0085] in, It is the potential energy function value of the hyperedge e. Here are the global weight coefficients for the logarithmic terms, log(·) is the natural logarithm function, and ∑ is the summation operation. The interaction weight coefficient between nodes i and j Let i be the key state component of node i. Let J be the key state component of node j. Let be the interaction weight coefficient between nodes i, j, and k. These are the key state components of node k.

[0086] (i,j)∈ This represents the summation of all unordered node pairs (i,j) in the nodes associated with the superedge e.

[0087] (i,j,k)∈ This represents the summation of all unordered triples (i,j,k) in the nodes associated with the superedge e.

[0088] It should be noted that: in middle

[0089] It is used to calculate the weighted sum of all pairwise interactions of all nodes, log(1+...) is used to add 1 and take the natural logarithm, and finally multiply by the global weight α for scaling.

[0090] Used to calculate the weighted sum of triple interactions across all nodes.

[0091] Capture the pairwise coupling effects between nodes i and j, such as the data transfer cost between nodes, which may be related to the product of the states of the two nodes.

[0092] Capture the higher-order coupling effects between nodes i, j, and k.

[0093] log(1+...) ensures that the potential energy function value is smooth and positive, preventing numerical overflow, while introducing nonlinear saturation characteristics.

[0094] It should be noted that, , , These are the key resource state components for nodes i, j, and k. Specifically, they can be extracted from the resource state representation points of the node, such as normalized scalar values ​​of CPU utilization, available bandwidth ratio, or memory usage.

[0095] , , The methods for determining parameters that are dynamically configured based on task characteristics and real-time system status include: It can be set based on the historical communication delay or link quality between nodes i and j, and is used to amplify or suppress the impact of data transmission between specific node pairs; It can be used to describe the contention intensity among three or more nodes due to shared physical resources such as power supply to the data center and uplink; global coefficient Used to balance the dimensions and influence of logarithmic and polynomial terms.

[0096] In this application, a preferred implementation method of the potential energy function includes:

[0097] Inter-node data transmission overhead is used to quantify the communication cost incurred in exchanging data within the set of associated nodes to complete a collaborative task. This communication cost is not only proportional to the amount of data transmitted, but also non-linearly depends on the real-time status and link condition of both communicating parties.

[0098] Inter-node data transmission overhead is typically constructed as a term related to the product of the state variables of the associated nodes. For example, if node i sends data to node j, the inter-node data transmission overhead is related not only to the amount of data allocated to the task, but also to the remaining uplink bandwidth of node i, the remaining downlink bandwidth of node j, and the current latency or packet loss rate of the link between the two nodes. This application combines state components in a product form to characterize the nonlinear phenomenon where the transmission cost per unit of data increases sharply when the sender's load is high and the receiver's bandwidth is limited. The product term is used to capture the interdependence and amplification effect between state variables.

[0099] In cross-management domain scenarios of edge computing, such as collaboration scenarios between different operators and different security trust domains, when data flows between different domains, it will trigger additional security compliance checks, data format conversions, billing and settlement processes, which are cross-domain compliance processing overhead items.

[0100] The cross-domain compliance processing overhead is activated as a conditional activation item. It is included in the total cost only when the associated nodes belong to different management domains. The value of the cross-domain compliance processing overhead item has a non-linear relationship with the total amount of data to be transmitted between domains and the security level of the data involved. For example, transmitting sensitive data may trigger more complex encryption or auditing processes, and the cost may increase superlinearly with the increase in data volume.

[0101] When multiple subtasks are scheduled to be executed on the same physical node or different nodes sharing the same resource pool, they will compete for limited resources. This causes the execution time of each subtask to increase due to resource contention, thereby increasing the overall task latency. This is the additional latency caused by resource contention.

[0102] The additional latency caused by resource contention is reflected through the cross term of the resource utilization of related nodes. For example, the potential energy may include a term representing the product of the CPU utilization of different nodes. If both node A and node B are heavily loaded, the queuing latency caused by resource saturation will be significantly amplified when nodes A and B coordinate to process tasks. The cross term is used to quantify the nonlinear amplification effect of this queuing latency: a slightly high load on a single node may not have a significant impact, but multiple related nodes simultaneously being heavily loaded will cause a sharp decline in system performance. This prompts us to avoid concentrating multiple tightly coupled subtasks on a set of already heavily loaded nodes when optimizing task allocation, thus achieving load distribution and balance.

[0103] A potential energy function is defined for each cooperative hyperedge. Through a structured function, the elusive nonlinear and multi-factor coupled costs in edge cooperation are decomposed into several modelable and quantifiable sub-items, which are then synthesized into a unified optimization objective. The potential energy function enables the distributed potential game to minimize... To clarify the objective, the associated node set is driven to adjust its resource status representation point.

[0104] By optimizing the automatic search, the total collaboration overhead, which consists of data transfer, cross-domain compliance, and resource contention, is minimized while meeting the task's computational requirements.

[0105] The method for constructing the discrete-state manifold and cooperative hypergraph model is as follows:

[0106] S121 gathers the discrete state manifolds of all heterogeneous edge nodes to form the node state space of the system;

[0107] Specifically, the discrete state manifolds pre-constructed independently for each heterogeneous edge node are aggregated, and each manifold contains all feasible discrete state points of the corresponding node and their adjacency relationships.

[0108] A preferred polymerization method includes:

[0109] Furthermore, the node state space is a composite structure that preserves the product space of the internal topology of each node manifold. In the node state space, the complete system state is composed of a combination of a specific discrete state point in which each node is located, thereby establishing a mapping from the state of a single node to the global system state.

[0110] S122. Generate the corresponding set of cooperative hyperedges and their respective potential functions through the set of all tasks to be processed, forming a set of task coupling relationships;

[0111] Step S122 is used to integrate all task requirements and costs into a system coupling relationship network.

[0112] Specifically, for all computational tasks currently pending, a collaborative hyperedge is created for each task based on the candidate node set obtained from its descriptor resolution, and each hyperedge is explicitly bound to its associated node set.

[0113] For each generated cooperative hyperedge e, assign it a unique potential energy function. The independent variable x of the potential energy function is a vector composed of the resource state representation points of all nodes associated with the hyperedge.

[0114] All cooperative hyperedges and their associated potential functions together constitute a task coupling relationship set, which is used to describe the static participation relationship between tasks and nodes. The potential function defines the nonlinear coupling cost caused by executing each task under different system states, providing a quantitative target for task-level optimization.

[0115] S123. The node state space is taken as the node set of the hypergraph, and the task coupling relationship set is taken as the hyperedge set of the hypergraph. The discrete state manifold and cooperative hypergraph model are composed of the node set and the hyperedge set of the hypergraph.

[0116] Specifically, each physical node entity in the system node state space formed in step S121 is defined as a vertex of the hypergraph, forming the node set of the hypergraph.

[0117] It is important to note that each hypergraph node corresponds to a physical device, and each physical device is associated with its own discrete state manifold.

[0118] Furthermore, each cooperative hyperedge in the task coupling relationship set formed in step S122, containing the potential energy function of each cooperative hyperedge, is defined as a hyperedge of the hypergraph, forming the hyperedge set of the hypergraph.

[0119] The discrete-state manifold and cooperative hypergraph model constructed in this way is a joint model with two layers of association, which includes a node-manifold association layer and a hyperedge-potential energy association layer.

[0120] In the node-manifold association layer, each vertex of the hypergraph is a physical node, which is associated with an independent discrete state manifold. The independent discrete state manifold defines the local state space and adjacency relationship of this node.

[0121] In the hyperedge and potential energy association layer, each hyperedge of the hypergraph connects a group of vertices, namely task participating nodes, and binds a potential energy function. The potential energy function takes the current state vector of the connected nodes as input and outputs the coupling cost scalar value of the current task collaboration in the current state.

[0122] The joint model with two-layer association is the discrete state manifold and cooperative hypergraph model, which incorporates node resource allocation and task cooperation costs into the same hypergraph. Any feasible scheduling scheme in the system corresponds to a set of state representation points selected for each hypergraph node on its associated manifold. The quality of the scheme is evaluated by the overall performance of the potential function values ​​on all hyperedges, which fully encapsulates the resource constraints, task coupling and cost quantification relationships of the system.

[0123] Discrete gradient optimization is the starting point of the hierarchical collaborative optimization process. It guides each heterogeneous edge node to independently explore possible state improvement directions within a discrete, structured feasible state space based on its own local goals and constraints, without involving cross-node coordination, and outputs the results as the input strategy for distributed potential game.

[0124] S2. Using the discrete state manifold and cooperative hypergraph model, each node performs independent discrete gradient optimization on its own discrete state manifold, and performs distributed potential game on the associated nodes of each cooperative hyperedge with the goal of minimizing the potential function. The optimization instructions of all nodes are harmonized in a holistic manner to generate globally compatible system state update instructions.

[0125] The discrete gradient optimization is as follows: each node, based on the discrete state manifold model, takes the current state representation point as the starting point, calculates the discrete negative gradient direction based on the local cost function, and selects a pre-updated state point from the set of adjacent state points of its manifold that reduces the local cost estimate. This optimization process is executed in parallel and generates at least one pre-updated state point for each node.

[0126] In this application, a preferred implementation method for discrete gradient optimization includes: calculating the discrete negative gradient direction using a local cost function and selecting a pre-updated state point and executing them in parallel.

[0127] Specifically, calculating the discrete negative gradient direction of the local cost function includes determining the optimization starting point and the local objective function, determining the neighborhood state set based on the manifold topology, and performing local cost difference calculation.

[0128] Specifically, the starting point and local objective function are determined. The optimization process of each node i begins with its current state representation point, which is selected from the discrete state manifold of the node and uniquely and accurately corresponds to the actual resource occupancy combination of the node at the end of the previous optimization cycle or when the system is initialized.

[0129] Each node loads its preset local cost function, which maps any discrete state point s on the node's own manifold to a real value. The real value represents the estimated local overhead that the node will generate when it is assumed to maintain that state while processing its known and inherent computational load.

[0130] Furthermore, based on the manifold topology, the neighboring state set is determined, and node i queries the topological structure of its associated discrete state manifold.

[0131] Through the topological structure of the associated discrete state manifold, a node determines the set of all neighboring state points that are directly reachable in a single step from its current state. Each neighboring point represents the new state that can be achieved by making a minimum feasible adjustment to the node's current resource configuration, such as adding a CPU core allocation or reducing a fixed amount of memory reservation.

[0132] Furthermore, in performing local cost difference calculation, the node first calculates the value of the local cost function at the current state point, and then the node calculates the value of the local cost function at each neighboring state point of the current state point in parallel or sequentially. Finally, for each neighboring state point, the cost difference between it and the current state point is calculated.

[0133] In determining the discrete negative gradient direction, we analyze all calculated cost differences. The state transition directions represented by all neighboring state points s that satisfy the condition that the cost difference is less than 0 are collectively defined as the discrete negative gradient direction starting from the current point.

[0134] The neighboring state points s represent a set of state transition directions, which includes all feasible single-step movement options that can instantly improve the local cost estimation of the node itself.

[0135] Specifically, the selection of pre-update state points and parallel execution includes filtering pre-update points according to selection logic, generating pre-update state points, executing parallel optimization processes, and converging the set of pre-update state points.

[0136] In the selection of candidate update points based on the selection logic, each node selects at least one state point from the set of discrete negative gradient directions as a candidate update state point according to the preset selection logic.

[0137] An example of a preferred selection logic includes:

[0138] Greedy selection: Select the neighbor state that maximizes the negative value of the neighborhood cost assessment.

[0139] Random exploration selection: Randomly select a point from the set of discrete negative gradient directions with a probability distribution, or uniformly randomly select a point from the set of discrete negative gradient directions.

[0140] Comprehensive evaluation and selection: Combining the estimated benefits of state transition with the minor internal costs that the transition itself may cause, select the neighbor with the highest overall benefit.

[0141] In the generation of candidate update state points, through selection logic, a node ultimately determines one or more specific candidate update state points, denoted as set Pi. Each candidate update state point is formatted into a standard data structure, which may include: node identifier i, the unique index or coordinates of the candidate point in the manifold, and its corresponding local cost estimate.

[0142] In the parallel optimization process, the discrete gradient optimization processes of all N nodes in the system start simultaneously and run independently. The optimization calculation of node i is constrained by its own current state, local manifold and local cost function, and is not constrained by the real-time state or intermediate results of any other node.

[0143] In the aggregation of the set of state points to be updated, after all nodes have completed their independent optimization processes, the system or central coordinator collects the output Pi from each node, and summarizes the Pi sets of all nodes to form a global set of state points to be updated, Pglobal={P1,P2,...,PN}.

[0144] The discrete gradient optimization process achieves structured, distributed local exploration by determining the starting point, neighborhood, calculating the difference, determining the direction, applying selection logic, generating candidate points, and executing and converging in parallel. Under the premise of meeting the resource constraints and local objectives of each node, it generates a systematic preliminary optimization proposal, activates and guides a distributed potential game with task coupling as the core, and thus imports the local optimization intention into the global collaborative framework.

[0145] The distributed potential game is as follows: through the cooperative hypergraph model, each cooperative hyperedge uses the pre-update state point generated by its associated nodes in discrete gradient optimization as the initial strategy to initiate a finite number of iterative games with the goal of minimizing the hyperedge potential function.

[0146] The game is played iteratively, and each iteration includes:

[0147] Potential energy calculation and broadcasting: The dominant node designated within the coordinator or hyperedge calculates the potential energy function value based on the current strategy combination x of all associated nodes and broadcasts it to all associated nodes.

[0148] Local policy exploration: Each node i independently explores all neighboring state points starting from its current policy point on its own discrete state manifold.

[0149] Strategy Proposal and Exchange: Each node calculates the estimated change in the potential function if it unilaterally changes to a neighboring node while the strategies of other nodes remain unchanged. Each node sends the new strategy point that maximizes the decrease in the estimated change to less than 0 to the game coordinator as a proposal.

[0150] Coordination and Strategy Update: The coordinator collects proposals from all nodes. If there is at least one proposal that can reduce the overall situation, multiple proposals are selected for adoption, and the corresponding nodes are notified to update their strategies.

[0151] When all nodes are unable to propose a unilateral strategy change that would reduce the potential energy during a round of iteration, a Nash equilibrium is determined to be reached, the game terminates, and a set of stable coordinated states is output for each hyperedge.

[0152] In each iteration, each node calculates its potential energy based on the current strategy combination and adjusts its own strategy based on its discrete state manifold to reduce its potential energy until a Nash equilibrium state is reached where no one can unilaterally improve the potential energy. Finally, a set of coordinated states is output for each hyperedge.

[0153] In this application, a preferred implementation method for the execution mechanism of distributed potential games includes:

[0154] Distributed potential game is a step in the hierarchical collaborative optimization framework for handling task coupling and coordination. Using the pre-constructed collaborative hypergraph model as the organizational structure, a round of collaborative decision-making process aimed at minimizing the nonlinear coupling cost of tasks is initiated and completed within the set of associated nodes defined by each collaborative hyperedge.

[0155] Specifically, each cooperative hyperedge e becomes an independent game, confined to the specific set of nodes connected by the hyperedge. The strategy of each participating node is defined as a specific state representation point on its own discrete state manifold. The initial strategy set of the game is directly provided by the output of discrete gradient optimization: each node submits at least one pre-updated state point it generates as the initial strategy for this game.

[0156] Furthermore, the game enters a finite-time iterative coordination phase with the potential function as the optimization objective. In each iteration, the potential function value attached to the hyperedge is first calculated based on the state combination x formed by the current strategies of all participating nodes. This potential function value quantifies the total coupling cost caused by performing the cooperative task under the current strategy combination. Each node then explores unilateral adjustments to its own strategy based on the topology of its discrete state manifold. On its manifold, starting from the current strategy point, each node examines all adjacent state points as alternative new strategies. Through simulation calculations, the node evaluates the expected change in the potential function if it switches to an alternative strategy while the strategies of other nodes remain unchanged. The node will adopt a strategy adjustment that unilaterally reduces the potential function value, that is, choose the state transition direction that reduces the global coupling cost.

[0157] The above iterative process continues until the system reaches a Nash equilibrium state. In this state, no node can further reduce the potential function value of the hyperedge by simply changing its own strategy (moving to another state point on its discrete state manifold). That is, under the current task context, the node set has reached a stable coordination state, and it is impossible to further improve the overall coordination efficiency through unilateral actions. At this point, the game terminates, and a set of coordinated states is output for the cooperative hyperedge. This set of states is a locally optimal resource state configuration suggestion that the node set has reached a consensus under the current task perspective.

[0158] The overall harmonization is achieved by applying Discrete Hodge decomposition to globally integrate the inconsistent post-coordination states obtained by each node from its different cooperative hyperedges.

[0159] Specifically, for each node i, the difference between the coordinated state proposals received from different hyperedges and the current state is used to obtain a set of discrete vectors on the node. The vectors of all nodes constitute a global update vector field U.

[0160] Decompose the vector field U orthogonally: U = df + δ∗v + h. Where:

[0161] df is the gradient component, which corresponds to the difference of a global situation function f, representing a consistent update trend across all task requirements.

[0162] δ∗v is the upper edge component, which is orthogonal to df.

[0163] h is the harmonic component, representing a cyclic conflict that cannot be represented by the local gradient or the upper edge term.

[0164] After decomposition, the gradient component df representing the globally consistent direction is retained and synthesized. By solving Poisson-type equations or optimization problems, a global state function f is found such that its gradient df most closely approximates the original vector field U and satisfies global compatibility. Finally, a unique target state update direction is determined for each node based on df, generating a globally compatible system state update instruction.

[0165] The Discrete Hodge decomposition decomposes the state update vector field of all nodes into globally coordinated gradient components and locally conflicting cyclic components. By synthesizing gradient components and eliminating cyclic components, a unique and globally compatible system state update instruction is generated, transforming the distributed local optimization and coupled coordination results into a joint decision that the system can execute.

[0166] Holistic harmonization is used to resolve multi-task instruction conflicts arising from distributed potential games. Based on the entire cooperative hypergraph model, it takes the potentially inconsistent coordinated state proposals received by each node from different cooperative hyperedges as input, applies Discrete Hodge decomposition to resolve conflicts and fuse instructions at the global level, and finally outputs a unique and self-consistent system state update instruction that can be executed synchronously by all nodes.

[0167] After the distributed potential game is completed, each node i may belong to multiple different cooperative hyperedges, that is, participate in multiple tasks. Therefore, it will receive multiple sets of coordinated state suggestions from the game states corresponding to these hyperedges. These multiple sets of coordinated state suggestions represent the optimal local planning of the resource state of the same node from the perspective of different tasks. There may be direct contradictions between them. The system summarizes all nodes and all the state suggestions received, and uses the difference between the current state of each node and each suggested state as a discrete vector field defined on the nodes of the cooperative hypergraph. The discrete vector field is used to represent the influence of different task requirements on the resource state of each node, with different directions and magnitudes. The inherent inconsistency is the global conflict that needs to be resolved.

[0168] Furthermore, the system performs Discrete Hodge decomposition on this hypergraph topology. Discrete Hodge decomposition is a mathematical method based on graph theory cohomology theory, used to orthogonally decompose conflict vector fields. The decomposition process analyzes the original vector field into the sum of two orthogonal components: one is the globally coordinated gradient component, which originates from the gradient of the globally defined potential function that is consistent across all nodes; the other is the locally conflicting cyclic component, which topologically manifests as a cyclic flow or harmonic field that cannot be generated by any global potential function gradient.

[0169] Furthermore, the gradient components, which contain all globally compatible valid information from local optimizations, are retained and synthesized. Cyclic components that cannot simultaneously satisfy conflicting requirements are eliminated. Through the integration and normalization of these gradient components, the Discrete Hodge decomposition algorithm generates a unique, globally compatible system state update instruction. This system state update instruction specifies a final target state representation point for each node. The target state representation point is the optimal compromise solution that mathematically best approximates all local proposals while strictly avoiding cyclic conflicts between instructions.

[0170] S3. Parse the globally compatible system state update instruction into specific resource allocation and task unloading strategies, and send them to the corresponding nodes for execution.

[0171] The method for parsing globally compatible system state update instructions into specific resource allocation and task unloading strategies includes: based on the preset mapping relationship between each state representation point and the set of physical resource parameters of the node in the discrete state manifold model, decoding the target state representation point of each node in the instruction into the specific allocation values ​​of the corresponding number of CPU cores, memory capacity, and bandwidth quota.

[0172] Based on the set of nodes associated with the collaborative hyperedges in the collaborative hypergraph model and their updated states, the subtask partitioning ratio, data flow direction, and computation order of each computation task among the participating nodes are determined, forming a task unloading path plan, such as... Figure 4 As shown.

[0173] Specifically, global optimization instruction parsing and execution includes resource allocation strategy generation, task unloading path planning, strategy encapsulation, and execution.

[0174] The specific implementation method for generating the resource allocation strategy includes:

[0175] In the discrete-state manifold model, each state representation point is mapped to a complete set of node physical resource configuration parameters. This mapping is based on formal modeling of node hardware capabilities and management strategies: each state point corresponds to a resource configuration scheme constrained by hardware limitations and policy constraints. Once the global optimization algorithm generates the target state representation point, it directly converts the abstract state identifier into specific resource quantification indicators by querying the pre-established mapping table.

[0176] The specific implementation method for the task unloading path planning includes:

[0177] The task unloading path planning uses the task and node association structure described by the collaborative hypergraph model as the skeleton. Combined with the updated resource status of each node, it rearranges the task execution process in the spatiotemporal dimensions. The technical logic includes decomposing the computational load into allocable sub-units based on the inherent logical dependencies of the task; dynamically mapping the sub-units to the most suitable execution position according to the real-time resource supply capacity of the nodes; and generating an execution sequence and data flow path that ensures the overall completion efficiency of the task under the constraints of data transmission cost and computation timing.

[0178] The specific implementation method of strategy encapsulation and execution includes: encapsulating the resource allocation parameters and task execution plan generated for each node into a self-contained instruction unit; ensuring that each node accurately receives its exclusive configuration during the instruction issuance process; and ensuring that each node applies the new configuration within the synchronization time window through a coordination mechanism.

[0179] After receiving the instruction, the node's agent isolates and allocates physical resources through the resource management interface. At the same time, it initiates the corresponding computing and data transmission processes according to the plan. After execution, the node reports the status information to the coordinator.

[0180] The parsed resource allocation values ​​and task unloading paths are encapsulated into control commands that can be recognized by the nodes, and sent to each target node through the system communication link. After receiving the command, each node dynamically configures its local resource manager according to its content and starts the corresponding subtask executor, and sends a status confirmation message back to the coordinator after the execution is completed.

[0181] Specifically, the heterogeneous information such as the parsed resource allocation values ​​and task unloading paths is structured and encapsulated according to a predefined node control message format to generate instruction units that each node can independently recognize and parse. The encapsulation process ensures the self-containment of the instruction content, enabling the node to execute without additional context.

[0182] The instructions are sent to each target node via the communication link.

[0183] After receiving the instruction, the node configures physical resources through its resource manager according to the instruction content, that is, adjusts the allocation and isolation strategies of resources such as CPU, memory, and bandwidth according to the specific values ​​set in the instruction. At the same time, the node starts the corresponding subtask executor, loads the computing logic according to the unloading path plan, and establishes the necessary data communication connections.

[0184] After completing resource configuration and task execution, the node sends a status confirmation message to the coordinator. The feedback message serves as both a notification of the completion of instruction execution and as key data reflecting the latest actual status of the node. The feedback message is used to update the status representation point of the corresponding node, providing accurate input basis for the next round of scheduling optimization.

[0185] It is important to note that the constructions and arrangements of this application shown in several different exemplary embodiments are merely illustrative. Although only two embodiments are described in detail in this disclosure, those who consult this disclosure will readily understand that many modifications are possible without substantially departing from the novel teachings and advantages of the subject matter described in this application. These modifications may include, for example, changes in the size, dimensions, structure, shape, and proportions of various elements, as well as parameter values ​​(e.g., temperature, pressure, etc.), installation arrangements, the use of materials, colors, orientations, etc. For example, an element shown as integrally formed may be composed of multiple parts or elements, the position of elements may be inverted or otherwise altered, and the nature or number or position of discrete elements may be changed or altered. Therefore, all such modifications are intended to be included within the scope of this application. The order or sequence of any process or method steps may be changed or rearranged by alternative embodiments. Any "apparatus plus function" clause is intended to cover, and not only structurally equivalent but also equivalent structures, the structures performing the functions described herein. Other substitutions, modifications, alterations, and omissions may be made in the design, operation, and arrangement of the exemplary embodiments without departing from the scope of this application. Therefore, this application is not limited to a particular embodiment, but extends to various modifications that still fall within the scope of the appended claims.

[0186] Furthermore, in order to provide a concise description of exemplary embodiments, not all features of actual embodiments (i.e., those features that are not relevant to the best mode of performing this application as currently considered, or those features that are not relevant to implementing this application) may be omitted.

[0187] It should be understood that numerous specific implementation decisions can be made during the development of any practical implementation, such as in any engineering or design project. Such development efforts may be complex and time-consuming, but for those of ordinary skill in the art who benefit from this disclosure, the development effort will be a routine task in design, manufacturing, and production without requiring extensive experimentation.

[0188] It should be noted that the above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit it. Although this application has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of this application without departing from the spirit and scope of the technical solutions of this application, and all such modifications and substitutions should be covered within the scope of the claims of this application.

Claims

1. A method for optimizing joint resource allocation and task offloading, characterized in that, include: S1 represents the resource state of each heterogeneous edge node in the system as a representation point on a discrete state manifold, and models each computational task that requires collaboration as a collaborative hyperedge connecting all participating nodes. It defines a potential energy function for the collaborative hyperedge to quantify the cost of nonlinear coupling, and constructs a discrete state manifold and collaborative hypergraph model. S2. Using the discrete state manifold and cooperative hypergraph model, each node performs independent discrete gradient optimization on its own discrete state manifold, and performs distributed potential game on the associated nodes of each cooperative hyperedge with the goal of minimizing the potential function. The optimization instructions of all nodes are harmonized in a holistic manner to generate globally compatible system state update instructions. The method for constructing the discrete-state manifold and cooperative hypergraph model is as follows: S121. Gather the discrete state manifolds of all heterogeneous edge nodes to form the node state space of the system; S122. Generate a set of corresponding cooperative hyperedges and their respective potential functions through all the task sets to be processed, forming a set of task coupling relationships; S123. The node state space is taken as the node set of the hypergraph, and the task coupling relationship set is taken as the hyperedge set of the hypergraph. The discrete state manifold and cooperative hypergraph model is composed of the node set of the hypergraph and the hyperedge set of the hypergraph. The discrete gradient optimization is as follows: each node, based on the discrete state manifold model, takes the current state representation point as the starting point, calculates the discrete negative gradient direction based on the local cost function, and selects a pre-update state point that reduces the local cost estimate from the set of adjacent state points of its manifold. This optimization process is executed in parallel and generates at least one pre-update state point for each node. The distributed potential game is as follows: through the cooperative hypergraph model, each cooperative hyperedge uses the pre-update state point generated by its associated nodes in the discrete gradient optimization as the initial strategy to initiate a finite number of iterative games with the goal of minimizing the hyperedge potential function. In each iteration, each node calculates its potential energy based on the current strategy combination and adjusts its own strategy based on its discrete state manifold to obtain a reduction in potential energy until a Nash equilibrium state is reached where no one can unilaterally improve the potential energy. Finally, a set of coordinated states is output for each hyperedge. S3. Parse the globally compatible system state update instruction into specific resource allocation and task unloading strategies, and send them to the corresponding nodes for execution.

2. The method for optimizing joint resource allocation and task offloading as described in claim 1, characterized in that: The method for representing the resource state as representation points on a discrete state manifold is as follows: S101. The continuous resource state vector collected by each node is discretized into a finite set of states by the feasible interval defined by hardware specifications and policy constraints through uniform quantization or non-uniform quantization of the operating point; S102. The finite set of states is used as a topological structure with adjacency relationships, and the topological structure is the discrete state manifold. Each discrete state point in the finite set of states is a representation point, and each representation point uniquely corresponds to a feasible combination of resource usage for a node at a certain moment.

3. The method for optimizing joint resource allocation and task offloading as described in claim 1, characterized in that: The method for modeling each collaborative computing task as a collaborative hyperedge is as follows: S111, parse the subtask division, data dependency relationship, and latency and reliability constraints in the task descriptor issued by the system to determine the set of candidate nodes that can meet some or all of its computing needs; S112, explicitly connect all nodes in the candidate node set with a hyperedge to form a task node binding relationship. The modeling of the cooperative hyperedge is used to define the scope and coordination objects of the hierarchical collaborative optimization computation: Each collaborative hyperedge is used to define a set of associated nodes as a collaborative unit, which serves as the scope for task coupling optimization and conflict coordination. The set of all collaborative hyperedges and the intertwined node relationships constitute the coupled network structure in the overall optimization of the system.

4. The method for optimizing joint resource allocation and task offloading as described in claim 1, characterized in that: A potential energy function is constructed for each collaborative hyperedge to quantify the cost of nonlinear coupling, including: inter-node data transmission overhead, which is related to the product of the state of the associated node and the state of the link between nodes; cross-domain compliance processing overhead, which is activated when the associated nodes belong to different management domains and has a nonlinear relationship with the data volume and security level; and additional latency caused by resource contention, which is reflected through the cross term of the resource utilization of the associated nodes.

5. The method for optimizing joint resource allocation and task offloading as described in claim 1, characterized in that: The overall harmonization is as follows: for each node that obtains inconsistent harmonized states from its different cooperative hyperedges, the discrete Hodge decomposition is applied for global integration. The Discrete Hodge decomposition decomposes the state update vector field of all nodes into globally coordinated gradient components and locally conflicting cyclic components. By synthesizing gradient components and eliminating cyclic components, a unique and globally compatible system state update instruction is generated, transforming the distributed local optimization and coupled coordination results into a joint decision that the system can execute.

6. The method for optimizing joint resource allocation and task offloading as described in claim 1, characterized in that: The method for parsing globally compatible system state update instructions into specific resource allocation and task unloading strategies includes: based on the preset mapping relationship between each state representation point and the set of node physical resource parameters in the discrete state manifold model, decoding the target state representation point of each node in the instruction into specific allocation values ​​of the corresponding number of CPU cores, memory capacity, and bandwidth quota. Based on the set of nodes associated with the collaborative hyperedge in the collaborative hypergraph model and their updated states, the subtask division ratio, data flow direction and computation order of each computation task among the participating nodes are determined, thus forming a task unloading path plan.

7. The method for optimizing joint resource allocation and task offloading as described in claim 6, characterized in that: The parsed resource allocation values ​​and task unloading paths are encapsulated into control commands that can be recognized by the nodes, and sent to each target node through the system communication link. After receiving the command, each node dynamically configures its resource manager according to its content and starts the corresponding subtask executor, and sends a status confirmation message back to the coordinator after the execution is completed.

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