A multi-cloud heterogeneous computing power scheduling method and system

Abstract

The present invention belongs to the field of cloud technology, and specifically relates to a multi-cloud heterogeneous computing power scheduling method and system, the method comprising: step 1: using the partial differential equation of node resources to describe the distribution of each node resource evolving over time; step 2: comparing the macroscopic available resource vector with the measured time-varying task requirements to form a feasibility constraint; step 3: constructing a comprehensive optimization objective function; the objectives of the comprehensive optimization objective function include resource mismatch, delay, and energy consumption; step 4: constructing a KKT system using the primal-dual interior point method, combining it with a large-scale nonlinear optimization problem, solving the overall problem of the partial differential equation containing node resources, and obtaining a solution result. The present invention can accurately describe the dynamic evolution and spatial distribution of resources, reasonably deal with the time-varying and uncertainty of task requirements, effectively control the risks in the resource scheduling process, and achieve global optimization in terms of resource mismatch, delay, and energy consumption.

Description

Technical Field

[0001] The present invention belongs to the field of cloud technology, and specifically relates to a multi-cloud heterogeneous computing power scheduling method and system. Background Art

[0002] With the rapid development of cloud computing technology, the demand for computing resources has exploded. Cloud computing not only provides businesses and individuals with efficient and flexible computing capabilities, but also drives the development of emerging technologies such as big data, artificial intelligence, and the Internet of Things. In practice, cloud computing platforms typically consist of multiple data centers, each containing a large number of heterogeneous nodes. The types and capabilities of resources vary significantly between nodes. These resources include, but are not limited to, hardware such as CPUs, GPUs, and memory bandwidth. To meet complex application requirements, users need to assign tasks to these nodes for execution. Efficient resource scheduling and task allocation have become key technical challenges that need to be addressed in the current cloud computing field.

[0003] Currently, a wealth of research and technology has been published on cloud computing resource scheduling. Most of these methods are based on static resource descriptions, heuristic scheduling algorithms, and linear programming models. However, in real-world multi-cloud heterogeneous environments, these traditional approaches have limitations, primarily manifested in the following aspects: First, existing resource modeling approaches are overly simplified and fail to truly reflect the dynamic distribution and topological characteristics of resources within nodes. In traditional resource scheduling systems, hardware resources such as CPUs, GPUs, and memory are typically abstracted as discrete, fixed units. For example, CPU resources are described as a certain number of cores, GPU resources are represented as several computing units, and memory resources are viewed as a linear space of fixed capacity. While this discrete resource modeling approach is easy to implement, it seriously overlooks the dynamic evolution of node resources. Node resources exhibit significant temporal dynamics and spatial heterogeneity during actual operation, such as CPU core load shifting between different tasks, uneven GPU memory usage due to the distribution of computing tasks, and localized memory bandwidth congestion due to varying task access patterns. If traditional discretization methods are used, these subtle resource variations cannot be accurately captured, resulting in resource waste or decreased task execution performance during resource allocation in the scheduling system. Secondly, existing technologies simplistically model task requirements and fail to fully account for the time-varying and uncertain nature of tasks. Most existing scheduling methods assume that task resource requirements are deterministic or static, such as the fixed CPU, GPU, and memory resources required throughout the task's execution cycle. However, in real-world applications, task resource requirements often change over time. For example, some data analysis tasks require significant CPU resources for data preprocessing in the initial stages, but may rely more heavily on GPUs for parallel computing in subsequent stages. Furthermore, task requirements are subject to significant uncertainty. For example, fluctuations in the scale of data input, changes in load, and the influence of the external system environment can all lead to real-time changes in task resource requirements. Existing technologies are unable to effectively model this time-varying and uncertain nature, resulting in the scheduling system's inability to make timely and appropriate adjustments to resource supply and demand fluctuations, which in turn impacts task execution stability and overall system performance. Summary of the Invention

[0004] In view of this, the main purpose of the present invention is to provide a multi-cloud heterogeneous computing power scheduling method and system, which can accurately describe the dynamic evolution and spatial distribution of resources, reasonably respond to the time-varying and uncertainty of task requirements, effectively control the risks in the resource scheduling process, and achieve global optimization in terms of resource mismatch, delay and energy consumption.

[0005] The technical solution adopted in the present invention is as follows:

[0006] A multi-cloud heterogeneous computing power scheduling method, the method comprising:

[0007] Step 1: Use the partial differential equation of node resources to describe the distribution of each node's resources over time; solve the partial differential equation of node resources and obtain the macroscopic available resource vector through spatial integration;

[0008] Step 2: Compare the macro-available resource vector with the measured time-varying task requirements to form feasibility constraints; introduce uncertainty scenarios, sample scenarios for the time-varying task requirements, and use conditional value at risk to control risks;

[0009] Step 3: Construct a comprehensive optimization objective function; the objectives of the comprehensive optimization objective function include resource mismatch, delay, and energy consumption; integrate all constraints into a large nonlinear optimization problem; the constraints include: equality constraints after discretization of partial differential equations of node resources, feasibility constraints, and allocation constraints;

[0010] Step 4: Use the primal-dual interior point method to construct the KKT system. Combined with the large-scale nonlinear optimization problem, the overall problem of the partial differential equation involving node resources is solved to obtain the solution. When the solution converges, the final solution value is discretized to obtain the final scheduling solution.

[0011] Furthermore, let the task set be ;No. tasks There is execution time ; The value range is 1 to ; is the total number of tasks; Representative tasks; let the multi-cloud collection be ; is the number of clouds in the multi-cloud set; For the cloud; Cloud There is a node collection ; The value range is 1 to ; For the Cloud The total number of nodes; Indicates the Cloud No. nodes; set Cloud The node resources in the feature space The continuous distribution, Indicates the Cloud No. nodes The hardware resource feature domain is obtained by mapping the CPU core topology, GPU array and memory channel into a continuous domain. Assume that the node resources include: CPU, GPU and MEM. CPU represents the processor occupancy, which ranges from 0 to 1; GPU represents the video memory occupancy, which ranges from 0 to 1; MEM represents the memory occupancy, which ranges from 0 to 1.

[0012] Furthermore, in step 1, the partial differential equation of node resources is used to describe the distribution of each node resource over time through the following formula:

[0013] ;

[0014] ;

[0015] ;

[0016] in, is a resource vector field describing the nodes At feature space points Place and time Available node resources; is the coordinate point in the feature space; is a time variable; It is a positive symmetric diffusion tensor obtained by measuring and modeling the node hardware topology and resource scheduling mechanism; represents the spatial gradient operator, represents the divergence operator; is the dissipation rate function, which is a scalar function or a diagonal matrix function; It is an exogenous regulatory item; is the initial condition function, giving Available node resources at the time of use, which are obtained through benchmark testing and system initial status detection; is the maximum execution time; Representation node At feature space points Place and time Available processor usage at time ; Representation node At feature space points Place and time Available video memory usage at the time Representation node At feature space points Place and time Available memory usage at time ; It is the transpose operation of the vector.

[0017] Furthermore, in step 1, the partial differential equation of node resources is solved using the following formula and then spatially integrated to obtain the macroscopic available resource vector:

[0018] ;

[0019] in, is the macro available resource vector; is the feature space The coordinate point integration variable in .

[0020] Furthermore, in step 1, the following formula is used, and in step 2, the macro-available resource vector is compared with the measured time-varying demand of the task to form a feasibility constraint using the following formula:

[0021] ;

[0022] in, Representation node In time The total amount of processor occupancy available for assignment to tasks; Representation node In time The total amount of video memory available for allocation; Representation node In time The total amount of memory available for allocation; is the resource requirement vector, representing the task In time Requirements for processor utilization, video memory utilization, and memory utilization; For the task In time Required processor resource utilization; For tasks in time Required video memory usage; For tasks in time Required memory usage.

[0023] Furthermore, in step 1, the following formula is used. In step 2, the following formula is used to introduce uncertainty scenarios, sample scenarios for time-varying task requirements, and use conditional value at risk to control risks:

[0024] ;

[0025] in, Describe the worst case scenario under uncertainty -Percentile expected loss; under uncertainty, different scenarios Represents possible ways to achieve task requirements; It is the cost incurred if resources are insufficient or mismatched in a given scenario; ); Therefore, when resources are insufficient to meet the scenario When the demand is will become larger; is the L2 norm; It is an auxiliary optimization variable introduced in the definition of conditional value at risk, used to linearize the definition of conditional value at risk, and is defined as a quantile or critical loss level; when Exceed hour, Taking into account excess losses, the definition of conditional value at risk is ensured to be an optimizable convex problem; is the confidence level used to determine the proportion of worst-case scenarios to be considered; is the total number of scenes.

[0026] Furthermore, in step 3, a comprehensive optimization objective function is constructed using the following formula:

[0027] ;

[0028] in, is a binary decision variable. Assign to node hour, ; otherwise 0; It's in the scene Next, the task At the initial moment of the task The resource demand vector of represents the L1 norm; is a node The delay factor; is a node Average available bandwidth to the data source; For nodes Specific node resources Energy consumption coefficient; Including: CPU, GPU and MEM; is a node In time Node resources The macro available resource vector.

[0029] Furthermore, in step 3, all constraints are integrated into a large nonlinear optimization problem through the following process: The equality constraints after discretization of the partial differential equation of the node resources are expressed by the following formula:

[0030] ;

[0031] in, for The discretization result is the step size in space. or meshing, using time steps in time Divide, represents the time step index; is a node Approximate solutions of resource vector fields at discrete grid points and discrete time levels; is the right-hand side term of the discretized partial differential equation of node resources; The coefficient matrix obtained by discretizing the partial differential equation of node resources; the allocation constraint is expressed as:

[0032] ;

[0033] The feasibility constraint is expressed as:

[0034] ;

[0035] in, Yes Yes Node In time Node resources The macro-available resource vector; Because it is in the scene Next, the task On task at time The resource demand vector.

[0036] Furthermore, in step 4, the KKT system is constructed using the primal-dual interior point method through the following process to solve the overall problem of the partial differential equation containing node resources and obtain the solution result: Construct the Lagrangian function The comprehensive optimization objective function, the partial differential equation of node resources, and the large nonlinear optimization problem that integrates all constraints are integrated to obtain the following formula:

[0037] ;

[0038] in, is the dual pairing operator; is the barrier function, which is used to ensure Do not leave the feasible region during the solution process of the primal-dual interior point method; ; Due to the final need It is a 0-1 integer decision, but it is too difficult to solve the 0-1 problem directly. , in the initial stage of the solution, it is allowed In the (0,1) interval, as the barrier parameter decreases, It will force the solution to approach 0 or 1, so that the original dual interior point method approaches the binary solution on the basis of continuous relaxation; is the dual variable of the allocation constraint, which requires that each task must be assigned to exactly one node. It measures the sensitivity of relaxing the allocation constraints to the Lagrangian function near the optimal solution; It is the dual variable of the equality constraint after the discretization of the partial differential equation of the node resources, and is used to measure the impact of relaxing or tightening the equality constraint after the discretization of the partial differential equation of the node resources on the Lagrangian function; for The dual variable of If the resource constraint of a node is tight, that is, it just satisfies the equation, will become larger, indicating that the node resource has become a bottleneck; if there are surplus node resources, If it is 0, it means that the constraint is not tight. The KKT condition is solved iteratively by the primal-dual interior point method. Each iteration performs the following process: using the current Approximate Update ; Use Newton's method to solve the linearized KKT system to find the optimal 、 and When making When the value of is the largest, stop the iteration and get The final value of ;right Perform threshold judgment, and if it is greater than the set threshold, it is assigned to the node.

[0039] A multi-cloud heterogeneous computing power scheduling system, the system comprising: an available resource calculation unit, for describing the distribution of each node resource over time using a partial differential equation of node resources; obtaining a macroscopic available resource vector by spatial integration after solving the partial differential equation of node resources; a scenario and constraint construction unit, for comparing the macroscopic available resource vector with the measured time-varying task requirements to form a feasibility constraint; introducing uncertainty scenarios, sampling scenarios for the time-varying task requirements, and controlling risks using conditional value-at-risk; an optimization target construction unit, for constructing a comprehensive optimization objective function; the objectives of the comprehensive optimization objective function include resource mismatch, delay, and energy consumption; integrating all constraints into a large nonlinear optimization problem; the constraints include: equality constraints, feasibility constraints, and allocation constraints after discretization of the partial differential equation of node resources; a scheduling unit, for constructing a KKT system using the primal-dual interior point method, solving the overall problem of the partial differential equation containing node resources in combination with the large nonlinear optimization problem to obtain a solution result; and discretizing the final solution result after convergence to obtain a final scheduling solution.

[0040] The above technical solution achieves the following beneficial effects: Using partial differential equation (PDE) modeling technology, the present invention achieves a refined description of the dynamic evolution and spatial distribution of node resources. This is a level of detail unattainable by existing technologies, as traditional approaches typically simplify node resources into a fixed number of discrete units, failing to reflect the complex spatial topology and dynamic changes of resources over time. In this invention, the resource state of each node is modeled using a continuous vector field that encompasses the availability distribution of CPU, GPU, and memory resources. By introducing diffusion, dissipation, and exogenous control terms, the distribution and evolution of node resources over space and time are precisely characterized. For example, the diffusion term reflects the migration and balancing of resources within a node, the dissipation term describes the natural decay of resources, and the exogenous control term reflects the impact of the management system on resource scheduling and adjustment. This continuous domain modeling approach eliminates the need for a crude, static description of the dynamic state of node resources and instead provides a physically precise representation, providing real, quantifiable data support for subsequent resource scheduling optimization. This allows resource allocation to no longer rely solely on rough estimates but instead be based on the real-time dynamics of node internal resources, achieving precise matching of resource supply and demand. Secondly, this invention addresses the shortcomings of existing task demand modeling techniques, which are overly simplistic and lack adaptability, by introducing time-varying demand and uncertainty scenario modeling. In real cloud computing environments, task resource requirements often vary over time and are subject to uncertainty. This invention uses scenario sampling technology to convert task requirements into a series of representative scenarios, each corresponding to a specific task demand curve. This approach not only covers a wide range of possible task demand scenarios but also allows for dynamic adjustments based on actual demand fluctuations. Furthermore, to address the impact of task demand uncertainty on system performance, this invention introduces the advanced risk control metric Conditional Value at Risk (CVaR). CVaR not only focuses on the degree to which a task's resource requirements are met under normal circumstances, but also quantifies the risk of resource mismatch in the worst-case scenario, thereby effectively controlling risk during the scheduling process. This risk control mechanism effectively mitigates the shortcomings of traditional methods, which are prone to performance degradation or task failure in the face of uncertainty. This enables this invention to provide reliable scheduling solutions even in highly uncertain environments. The present invention achieves multi-objective global optimization of resource mismatch, delay and energy consumption by constructing a comprehensive optimization objective function. In a multi-cloud heterogeneous environment, task scheduling needs to consider multiple performance indicators at the same time, including the precise matching of resource supply and demand, the response time of task execution, and the minimization of system energy consumption. Traditional methods can usually only optimize a certain indicator alone, while ignoring the balance between other indicators, resulting in poor system performance. The present invention integrates resource mismatch cost, data transmission delay cost and resource energy consumption cost into the optimization framework by constructing a comprehensive objective function.For example, the resource mismatch cost is quantified by calculating the deviation between node resources and task requirements, the delay cost is modeled based on the data transmission bandwidth and task initialization time, and the energy consumption cost is quantified based on the resource occupancy rate and the node power consumption model. This multi-objective comprehensive optimization can not only achieve the optimal matching of resource supply and demand, but also minimize the response delay and energy consumption of the system, thereby significantly improving the overall performance of the scheduling scheme. The present invention adopts the primal-dual interior point method to solve large-scale nonlinear optimization problems, effectively breaking through the solution bottleneck under high-complexity nonlinear constraints. Since the task scheduling problem involves the dynamic evolution of resources, time-varying demand and risk control, there is a high degree of nonlinear coupling between the objective function and the constraints, and traditional linear programming or heuristic algorithms are difficult to solve effectively. The present invention introduces the primal-dual interior point method, constructs the Lagrangian function and solves the KKT system, thereby realizing the alternating optimization of the primal variable and the dual variable. During the solution process, the task allocation variables are optimized by step-by-step approximation, and the allocation variables are continuously relaxed by the barrier function, and the continuous solution is finally discretized into an executable scheduling scheme. This solution method can not only find a solution close to the global optimal solution under high-complexity constraints, but also maintain high computational efficiency in large-scale task and resource scenarios, ensuring the real-time and executable nature of the scheduling solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A schematic diagram of a method flow for scheduling multi-cloud heterogeneous computing power provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0042] All features disclosed in this specification, or all steps in the disclosed methods or processes, except mutually exclusive features and / or steps, can be combined in any manner.

[0043] Any feature disclosed in this specification (including any appended claims and abstract), unless otherwise stated, may be replaced by other equivalent or similar features. In other words, unless otherwise stated, each feature is only an example of a series of equivalent or similar features.

[0044] Example 1: Reference Figure 1 , a multi-cloud heterogeneous computing power scheduling method, the method comprising:

[0045] Step 1: Use the partial differential equation of node resources to describe the distribution of each node's resources over time; solve the partial differential equation of node resources and obtain the macroscopic available resource vector through spatial integration;

[0046] The core principle of step 1 is to use partial differential equations (PDEs) to accurately describe the dynamic evolution of each node's resources in the time dimension and their distribution in the spatial dimension, thereby obtaining an accurate quantification of the node's resource status and providing precise data support for subsequent scheduling decisions. In a multi-cloud heterogeneous environment, different nodes have their own hardware configurations and resource characteristics, such as the distribution of CPU cores, the deployment of GPU computing units, and the transmission capacity of memory channels. These resources are not static but evolve dynamically over time and with changes in task load. Traditional resource description methods often use discrete static models, which simply summarize the node's computing resources as a fixed number of available CPUs, GPUs, and memory bandwidth parameters. This ignores the uneven distribution of resources within the node and the time evolution of resources. It is difficult to reflect the actual node resource utilization and cannot adapt to highly complex computing power scheduling requirements. The present invention introduces partial differential equations as a mathematical modeling tool, innovatively abstracting the internal resource state of the node into a dynamic field that changes with time and is continuously distributed in space. By establishing PDE to characterize the resource state and considering the diffusion, dissipation and external control factors of resources based on physical and statistical principles, the spatiotemporal change relationship of node resources can be rigorously described in the continuous domain.

[0047] Specifically, in a multi-cloud environment, each node is subject to complex resource load and management, resulting in temporal uncertainty and spatial imbalance in resource availability. For example, within a node, CPU cores may experience a diffusion of computing resources toward high-load areas due to computational load shifts. Resource allocation may also vary between GPU units due to varying interconnect bandwidths. Memory controller scheduling may also lead to localized bandwidth congestion due to the access patterns of different tasks. In such situations, the dynamic distribution of node resources can be modeled using partial differential equations (PDEs). PDEs characterize the temporal evolution and spatial migration of resources through continuous spatial gradients and time derivatives. Specifically, the diffusion term in the PDE describes the resource balancing process within the node. When resource utilization in a local area is excessively high, the system naturally diffuses to areas with lower utilization, thereby achieving dynamic resource balancing within the node. The dissipation term describes the natural loss of resources due to factors such as system maintenance threads, hardware power consumption, and frequency decay, reflecting the gradual decay of actual resource availability over time. Meanwhile, exogenous control terms represent external inputs that the hypervisor uses to proactively schedule resources at specific times. These inputs can include dynamically increasing CPU core frequency, activating GPU compute units, or adjusting memory access priorities. These inputs are controlled through system management policies, enabling proactive intervention in node resources. This PDE modeling approach allows the complete evolution of node resources through numerical solution. In practical applications, the continuous nature of the PDE allows the internal resource state of a node to be described in a high-precision feature space, thus overcoming the limitations of traditional methods that rely on coarse resource descriptions. To transform the resource distribution in this continuous space into a macrometric metric useful for scheduling, the PDE solution is integrated over the node feature space, yielding a resource availability vector for the entire node. This resource vector encompasses the node's total available CPU power, GPU power, and memory bandwidth at a given point in time, reflecting the node's overall computing power and enabling direct matching with task requirements. Through this method, the present invention achieves a refined description of node resources, not only capturing the laws of dynamic resource evolution in the time dimension, but also revealing the unevenness and diffusion characteristics of resource distribution in the spatial dimension, providing accurate data support for multi-cloud heterogeneous computing power scheduling, and can effectively improve the rationality of scheduling decisions and resource utilization.

[0048] Step 2: Compare the macro-available resource vector with the measured time-varying task requirements to form feasibility constraints; introduce uncertainty scenarios, sample scenarios for the time-varying task requirements, and use conditional value at risk to control risks;

[0049] Step 2 compares the node's macro-available resource vector with the task's time-varying requirements to establish feasibility constraints for resource allocation. Taking into account the uncertainty of task requirements, scenario sampling and conditional value-at-risk (CVaR) methods are introduced to quantify and control risk, ensuring efficient and robust task scheduling in complex multi-cloud heterogeneous environments. In multi-cloud environments, task execution requirements often change dynamically over time. For example, a task may have high CPU resource requirements during one period, while GPU or memory resource requirements surge during another. Furthermore, task requirements are often uncertain due to fluctuations in the task's workload, input data size, or external system environment. This uncertainty is extremely common in real-world scenarios. Traditional computing power scheduling methods often assume that task requirements are deterministic or simply take an average of task requirements as a basis. This approach fails to truly reflect the task's actual resource requirements and can easily lead to resource allocation mismatches, impacting overall system performance and even causing task failures during peak demand periods. The present invention introduces a scenario sampling method to convert the time-varying requirements of the task into multiple representative scenarios. Each scenario reflects the specific demand distribution of the task under certain uncertain conditions, thereby providing a more refined reference basis for task resource allocation.

[0050] In specific operations, step 2 first compares the macroscopic available resource vector obtained by solving the partial differential equation and spatially integrating it in step 1 with the task demand vector to form a feasibility constraint. The essence of this process is to check whether the node resources can meet the time-varying requirements of the task within the task execution period, ensuring the feasibility of task scheduling. If the node resources are understood as a time series vector, then the task demand is also a time series vector. The two need to be compared one by one at each time point to ensure that the resource requirements of the task are met at all times during the execution cycle. This resource-demand matching mechanism enables the scheduling method of the present invention to accurately control the relationship between resource supply and demand in the time dimension, avoiding the problem of insufficient resources during task execution. In traditional technologies, because task demands are simplified to fixed values ​​or average values, it is difficult to achieve dynamic matching of time-varying demands, resulting in a significant reduction in the accuracy of resource allocation. However, in a multi-cloud heterogeneous environment, due to the uncertainty of task demands, relying solely on a single task demand vector for scheduling is clearly insufficient. The uncertainty of task demands can arise from many factors, such as the complexity of the task itself, the randomness of input data, fluctuations in external load, and the instability of the execution environment. This uncertainty often causes actual task demands to deviate from the estimated values. If this deviation is not accounted for, the scheduling solution is prone to performance degradation or even task failure in extreme demand scenarios. Therefore, to address this uncertainty, step 2 further introduces a scenario sampling method. By scenario-based modeling of task demands, a set of demand scenarios representing different possible situations is generated. Each scenario corresponds to a specific task demand curve, which describes the resource requirements of the task under different uncertain conditions. This scenario sampling not only covers multiple possible situations of task demands, but also reflects the probability of occurrence of different scenarios through a certain probability distribution, thereby providing data support for subsequent risk control.

[0051] On this basis, step 2 uses the risk control indicator of conditional value at risk (CVaR) to quantify and optimize the uncertainty of task requirements. CVaR is an advanced risk measurement method that not only focuses on the overall impact of task requirement uncertainty on resource allocation, but also emphasizes the impact of task requirements on system performance in the worst case scenario. Specifically, CVaR calculates the uncertainty of the task under the worst case scenario. -The average loss value in the percentile scenario, so as to accurately assess the risk of task requirements under extreme conditions. The core idea of ​​this process is that even in the most unfavorable scenario, the system can still ensure the normal execution of the task and avoid task failure or system crash due to insufficient resources. Compared with the traditional average risk measurement method, CVaR can more effectively control the risk in extreme scenarios and improve the robustness and stability of the scheduling scheme. Through the combination of scenario sampling and CVaR risk control, step 2 can not only comprehensively model the uncertainty of task requirements, but also accurately constrain the resource requirements of the task in the worst case, so that the scheduling scheme can maintain high reliability and performance in a multi-cloud heterogeneous environment. This method breaks through the limitations of the existing technology on the assumption of determinism of task requirements, and solves the problem that traditional scheduling methods are prone to performance degradation when faced with uncertain requirements. By introducing uncertain scenarios and risk control, the present invention can effectively balance the performance and risk of resource allocation, and ensure that the task scheduling scheme has high execution efficiency and resource utilization in various possible demand scenarios. In addition, this approach can flexibly adjust the confidence level parameters of CVaR according to the risk tolerance and service level agreement (SLA) requirements of different tasks, thereby achieving a more refined trade-off between performance and risk.

[0052] Step 3: Construct a comprehensive optimization objective function; the objectives of the comprehensive optimization objective function include resource mismatch, delay, and energy consumption; integrate all constraints into a large nonlinear optimization problem; the constraints include: equality constraints after discretization of partial differential equations of node resources, feasibility constraints, and allocation constraints;

[0053] In an actual multi-cloud heterogeneous environment, there are significant differences in the hardware configuration and resource capabilities of different nodes. At the same time, the demand for resources during task execution is also time-varying and uncertain, which leads to the scheduling system having to balance and optimize between resource allocation, task execution delay, and system energy consumption. There is a complex coupling relationship between these three. Resource mismatch directly affects the execution efficiency of the task, delay affects the response time of the task, and energy consumption is directly related to the operating cost and energy utilization efficiency of the system. Therefore, the key to constructing a comprehensive optimization objective function is to quantify and uniformly model these three core indicators so that they can be solved within the same optimization framework, thereby achieving global optimization of computing resource scheduling in multiple dimensions. Specifically, resource mismatch refers to the difference between the resources that a node can provide and the resources required for a task. This difference may lead to waste or insufficiency of resources during task execution, directly affecting the efficiency of task execution and the utilization of the overall system resources. In the present invention, the quantification of resource mismatch is achieved by measuring the deviation between the availability of node resources and task requirements to achieve precise control of resource supply and demand matching. By comparing resource supply and demand point by point in the time dimension, this deviation is incorporated into the objective function in a mathematically quantified form, thereby minimizing the negative impact of resource mismatch during the optimization process and ensuring that the task can fully utilize node resources while meeting demand.

[0054] Latency, on the other hand, is a key performance metric to consider during task scheduling in multi-cloud environments, particularly in terms of the time required for data transmission, task initialization, and resource allocation decisions. Inter-node network latency, bandwidth limitations, and differences in resource initialization across heterogeneous nodes all significantly impact the overall execution time of a task. In this paper, latency cost is quantified by combining the initial resource requirements of the task, the node's network bandwidth, and inter-node latency characteristics. This is then converted into an optimizable objective function term. During the solution process, a reasonable task allocation strategy is implemented to minimize latency cost, improving task response speed and overall system execution efficiency. Furthermore, energy consumption optimization is a key component of the objective function, primarily considering the relationship between actual energy consumption and resource utilization of node resources. In a multi-cloud heterogeneous environment, different types of hardware resources (such as CPUs, GPUs, and memory) have varying energy consumption characteristics under varying load conditions, and the actual resource utilization of a task is positively correlated with the energy consumption of the node. In this paper, an energy consumption coefficient is used to correlate node resource utilization with actual power consumption, minimizing the overall energy consumption of the system as one of the objectives during the optimization process. This not only helps reduce system operating costs but also improves energy efficiency to a certain extent, in line with current technological trends in green computing and sustainable development. In addition to the construction of the above-mentioned objective function, the present invention also integrates the constraints involved in steps 1 and 2 into the same large-scale nonlinear optimization problem, including the equality constraints after the discretization of the partial differential equations of node resources, the resource feasibility constraints of the tasks, and the task allocation completeness constraints. The introduction of these constraints ensures the physical feasibility and practical operability of the optimization results. For example, the PDE discretization constraints of node resources ensure that the continuity of the resource evolution process is consistent with the real physical laws, so that the optimization results can reflect the actual distribution and availability of resources. At the same time, the task allocation completeness constraint ensures that each task can be assigned to a suitable node for execution, avoiding the problem of missing or repeated task allocation, while the resource feasibility constraint ensures that the actual available resources of the node can meet the needs of the task, avoiding the phenomenon of resource overload or shortage in the resource allocation process. By integrating these objective functions and constraints into a large-scale nonlinear optimization problem, the present invention realizes the global optimization of multi-cloud heterogeneous computing power resource scheduling, and solves the problem of isolated treatment and mutual conflict of each optimization objective in traditional scheduling methods. This multi-objective unified modeling approach not only finds the optimal balance between resource supply and demand, task latency, and system energy consumption, but also ensures the overall efficiency and performance of the scheduling solution through a global optimization solution. Furthermore, by introducing nonlinear optimization methods, the present invention enables the entire system to find near-optimal scheduling solutions under highly complex constraints, further improving the accuracy and computational efficiency of resource utilization in multi-cloud heterogeneous environments.

[0055] Step 4: Use the primal-dual interior point method to construct the KKT system. Combined with the large-scale nonlinear optimization problem, the overall problem of the partial differential equation involving node resources is solved to obtain the solution. When the solution converges, the final solution value is discretized to obtain the final scheduling solution.

[0056] The complexity of the multi-cloud heterogeneous computing power scheduling problem stems from the coupling of multiple factors, including the dynamic nature of node resources, the time-varying nature of task requirements, and the nonlinear matching relationship between resources and tasks, which makes it difficult for traditional linear programming or heuristic algorithms to effectively solve such problems. The primal-dual interior point method adopted in the present invention is an efficient algorithm for solving large-scale nonlinear constrained optimization problems. By introducing dual variables and barrier functions, the constraints of the original problem are integrated into the objective function to form a Lagrangian function, thereby converting the constrained optimization problem into an unconstrained problem for solution. The entire solution process is based on the iterative idea of ​​the primal-dual interior point method. By alternating optimization between the original variables and the dual variables and gradually reducing the barrier parameters, the solution can be kept within the feasible domain in each iteration, and finally converges to the optimal solution that meets the original constraints. Specifically, the primal-dual interior point method first integrates the objective function, PDE constraints of node resources, resource feasibility constraints and task allocation constraints in the nonlinear optimization problem into a unified framework by constructing a Lagrangian function. Dual variables are introduced into the Lagrangian function to represent the "shadow price" of the constraints. These dual variables can reflect the degree of influence of the constraints on the optimal solution, thereby guiding the adjustment direction of the original variables during the optimization process. In addition, in order to deal with the binary characteristics of the task allocation decision variables, the present invention uses a barrier function to relax the task allocation variables so that they are restricted to the continuous space of (0,1) during the solution process, and by gradually reducing the barrier parameters, it ensures that the final solution can gradually approach the boundary of the binary decision. The introduction of the barrier function not only ensures the feasibility of the solution, but also effectively avoids the problem of infeasible solutions caused by overly tight constraints during the optimization process.

[0057] During the solution process, the primal-dual interior point method simultaneously optimizes both the primal and dual variables by solving the KKT system (Karush-Kuhn-Tucker conditions). The KKT system is a mathematical framework that describes optimality conditions for optimization problems, encompassing primal feasibility conditions, dual feasibility conditions, and complementary slackness conditions. In each iteration, the algorithm linearizes the KKT system and solves its Newton directions to obtain updates to the primal and dual variables. During this process, the primal variables (including the task allocation variables and the discrete PDE solution) are adjusted based on the optimization direction of the objective function, while the dual variables are updated based on the degree of slackness of the constraints. This ensures that the solution gradually approaches the optimal objective value while satisfying the constraints. Furthermore, to ensure iterative stability and convergence, the algorithm implements step size control during each update, using line search to ensure that the new solution remains within the feasible region, avoiding violations of the constraints due to excessive step sizes. A key feature of the primal-dual interior point method is its ability to efficiently handle large-scale nonlinear constrained problems in continuous space and to find solutions close to the global optimum through successive approximations. In the present invention, the PDE constraints of node resources are discretized into a set of linear equations, which describe the dynamic distribution and evolution of node resources in time and space, while resource feasibility constraints and task allocation constraints ensure the feasibility and integrity of the scheduling scheme. In the solution process, the original dual interior point method effectively integrates these constraints to achieve simultaneous optimization of multi-dimensional constraints, so that the entire scheduling scheme achieves the best balance between resource supply and demand matching, task delay minimization and system energy consumption optimization. When the algorithm converges to the vicinity of the optimal solution, the continuous solution of the task allocation variable will gradually approach 0 or 1. At this time, the task allocation variable is discretized by setting a threshold, that is, the solution close to 1 is regarded as a sign that the task is assigned to the corresponding node, while the solution close to 0 indicates that the task is not assigned to the node. Through this discretization operation, the present invention can convert the continuous relaxation solution into an actual executable task scheduling scheme, ensure that the scheduling scheme can be implemented in the actual system, and meet the matching requirements of task demand and resource availability.

[0058] Example 2: Assume that the task set is ;No. tasks There is execution time ; The value range is 1 to ; is the total number of tasks; Representative tasks; let the multi-cloud collection be ; is the number of clouds in the multi-cloud set; For the cloud; Cloud There is a node collection ; The value range is 1 to ; For the Cloud The total number of nodes; Indicates the Cloud No. nodes; set Cloud The node resources in the feature space The continuous distribution, Indicates the Cloud No. nodes The hardware resource feature domain is obtained by mapping the CPU core topology, GPU array and memory channel into a continuous domain. Assume that the node resources include: CPU, GPU and MEM. CPU represents the processor occupancy, which ranges from 0 to 1; GPU represents the video memory occupancy, which ranges from 0 to 1; MEM represents the memory occupancy, which ranges from 0 to 1.

[0059] Specifically, in traditional computing resource scheduling methods, CPU, GPU, and memory resources are often simply viewed as discrete units. For example, CPU resources are described as several independent cores, GPUs as several computing units, and memory as fixed storage space. While computationally simple, this discrete modeling approach fails to fully reflect the spatial topology of hardware resources and their dynamic distribution within nodes. In real multi-cloud heterogeneous environments, a node's computing resources are not static; they exhibit significant spatial structure and dynamic migration characteristics, such as the topological interconnection between CPU cores, the parallel computing distribution of GPU arrays, and the data transfer bandwidth of memory channels. These physical structures and spatial characteristics have a profound impact on task scheduling performance. Ignoring these factors can lead to resource mismatch and even system performance degradation in scheduling decisions. Mapping the CPU core topology involves abstracting the core structure of a node's CPU, including the number of cores, the interconnection topology between cores, the cache hierarchy, and the frequency characteristics, into a dimension within a continuous domain. In traditional methods, CPU cores are described as single, independent entities. In this invention, through continuous mapping, the availability of CPU resources is treated as a spatially continuously distributed field quantity. For example, in a multi-core CPU, cores are connected via caches and high-speed interconnects. Load migration and computational scheduling between different cores can lead to dynamic changes in resource usage. Through continuous domain modeling, this inter-core interconnection and resource distribution can be described as a continuous function, more accurately reflecting the utilization and availability of CPU resources within the node. Similar to CPUs, mapping a GPU array abstracts the GPU's internal computing units, memory access bandwidth, and data transfer structure into another dimension within a continuous domain. In a GPU, computing units (such as CUDA cores or stream processors) exhibit parallel computing characteristics, but the load and memory usage of different computing units are uneven. Especially when executing large-scale parallel tasks, resource usage exhibits distinct spatial distribution characteristics. For example, some computing units may be highly loaded, while others are idle or lightly loaded. In this invention, through continuous domain mapping, the resource utilization of the GPU array is treated as a continuously distributed vector field quantity. This allows the system to use mathematical tools to model and optimize the distribution of GPU resources, thereby achieving more refined task scheduling. For memory channel mapping, this invention abstracts the memory controller, number of channels, and data bandwidth characteristics into a continuous domain, reflecting the dynamic distribution of memory resource occupancy and access bandwidth. In multi-cloud heterogeneous environments, memory channel access performance has a critical impact on task execution efficiency. In particular, in high-throughput tasks, memory bandwidth bottlenecks often become the limiting factor in system performance. In traditional methods, memory resources are often simply viewed as fixed capacity or bandwidth, while ignoring the dynamic distribution of data access.In the present invention, by mapping the memory channel into a continuous domain, the memory occupancy state can be described as a continuous function in time and space, thereby revealing the actual usage status of memory resources and providing a more realistic memory performance evaluation for task scheduling.

[0060] Example 3: In step 1, the partial differential equation of node resources is used to describe the distribution of each node resource evolving over time using the following formula:

[0061] ;

[0062] ;

[0063] ;

[0064] in, is a resource vector field describing the nodes At feature space points Place and time Available node resources; is the coordinate point in the feature space; is a time variable; It is a positive symmetric diffusion tensor obtained by measuring and modeling the node hardware topology and resource scheduling mechanism; represents the spatial gradient operator, represents the divergence operator; is the dissipation rate function, which is a scalar function or a diagonal matrix function; It is an exogenous regulatory item; is the initial condition function, giving Available node resources at the time of use, which are obtained through benchmark testing and system initial status detection; is the maximum execution time; Representation node At feature space points Place and time Available processor usage at time ; Representation node At feature space points Place and time Available video memory usage at time ; Representation node At feature space points Place and time Available memory usage at time ; It is the transpose operation of the vector.

[0065] Specifically, Contains the available ratio of CPU, GPU, MEM and other resources of the node at the location (feature space coordinate). For example, if (corresponding to CPU, GPU, and MEM respectively), it means that at the coordinate Place, time At this time, the CPU availability is 80%, the GPU availability is 50%, and the memory bandwidth availability is 90%. This reflects the dynamic distribution of resource availability across time and space within the node's different hardware units. is a node This feature space is an abstract mapping of the node's internal hardware structure, representing the CPU core topology, GPU unit distribution, memory channels, etc. in a continuous spatial domain. A point in this space corresponds to a virtual "resource location" or "resource fragment" within a node. Node resource availability changes dynamically over time. For example, node cooling, turbo frequency mechanisms, and changes in task load can all cause resource utilization to fluctuate over time. Describe this dynamic process that evolves over time. Describes the ability of resources to diffuse across different feature spaces within a node. Like the diffusion coefficient in heat conduction, resource availability can also be "diffused" or balanced within a node. For example, if there are high-speed interconnects between CPU cores, the total availability can be evenly distributed across adjacent regions. This tensor describes the resource balancing capability determined by the hardware interconnection structure. This tensor is obtained by measuring and modeling the node hardware topology and resource scheduling mechanism. Indicates the rate of change of resource availability in space. This represents the resource reallocation process caused by uneven spatial distribution. Resources will spread from high-availability areas to low-availability areas to achieve a certain balance. This value describes the degree to which resources degrade over time without external replenishment. Just like heat dissipation, resource availability decreases without external maintenance. For example, underlying system maintenance processes, hardware aging, and frequency reduction strategies can all cause the actual available resource percentage to decrease over time. This value can be derived by fitting data such as node power consumption and frequency fluctuations in an unloaded state. Indicates active intervention of the hypervisor on node resources. For example, At any given moment, the dispatch system can (For example, a group of CPU cores) increase the frequency (equivalent to These external controls come from the automated policy controller, which dynamically adjusts based on the current load, energy consumption strategy, and SLA optimization goals. The basic resource availability ratio. For example, the CPU frequency of a newly started node may be at the baseline level (CPU availability is high), the GPU unit is not loaded when it is just activated (GPU availability is close to 1), and the memory bandwidth is not initially underutilized. This is obtained through benchmark testing and system initial status detection. .

[0066] Example 4: In step 1, the partial differential equation of node resources is solved using the following formula and then spatially integrated to obtain the macroscopic available resource vector:

[0067] ;

[0068] in, is the macro available resource vector; is the feature space The coordinate point integration variable in .

[0069] Specifically, Indicates that the node Internal feature space The resource utilization rate of the distribution field The overall resource availability vector is obtained after spatial integration. In other words, it aggregates the fine-grained resource distribution information within the node into a macro metric, which allows us to use a simple vector in the subsequent steps Indicates that the node is at time For example, Indicates time The total amount of CPU, GPU, and MEM resources that the node can devote to task scheduling.

[0070] Example 5: In step 1, the following formula is used. In step 2, the macro-available resource vector is compared with the measured time-varying demand of the task to form a feasibility constraint using the following formula:

[0071] ;

[0072] in, Representation node In time The total amount of processor occupancy available for assignment to tasks; Representation node In time The total amount of video memory available for allocation; Representation node In time The total amount of memory available for allocation; is the resource requirement vector, representing the task In time Requirements for processor utilization, video memory utilization, and memory utilization; For the task In time Required processor resource utilization; For tasks in time Required video memory usage; For tasks in time Required memory usage.

[0073] Specifically, For example, For the task In time Required CPU resource utilization. For example, 0.6 indicates that the task requires 60% CPU availability on the node. This requirement is typically collected and fitted from historical run logs and performance analysis tools (such as perf, GPU profiler, and memory bandwidth counters).

[0074] Example 6: In step 1, the following formula is used. In step 2, the following formula is used to introduce uncertainty scenarios, perform scenario sampling on time-varying task requirements, and use conditional value at risk to control risk:

[0075] ;

[0076] in, Describe the worst case scenario under uncertainty -Percentile expected loss; under uncertainty, different scenarios Represents possible ways to achieve task requirements; It is the cost incurred if resources are insufficient or mismatched in a given scenario; ); Therefore, when resources are insufficient to meet the scenario When the demand is will become larger; is the L2 norm; It is an auxiliary optimization variable introduced in the definition of conditional value at risk, used to linearize the definition of conditional value at risk, and is defined as a quantile or critical loss level; when Exceed hour, Taking into account excess losses, the definition of conditional value at risk is ensured to be an optimizable convex problem; is the confidence level used to determine the proportion of worst-case scenarios to be considered; is the total number of scenes.

[0077] Specifically, It is an indicator function of conditional value-at-risk. It measures the worst case - Average loss per percentile (i.e., in the most adverse scenario exceeding a certain loss level). When considering the resource misallocation loss of tasks under uncertain scenarios hour, Point out those situations where the loss is the most serious (probability mass is 1- The expected loss value under the most unfavorable scenarios. By minimizing , which ensures good performance and robustness even in the “worst” scenarios. It's in the scene The task of the general Assign to node Under uncertainty, different scenarios Represents the possible implementation methods of task requirements (such as high-load or low-load situations). The cost (e.g., increased computational latency, increased risk of execution failure) of insufficient or mismatched resources in a given scenario. This value is calculated using the previously defined method (e.g., ). Therefore, when resources are insufficient to meet the scenario When the demand is The uncertainty comes from inaccurate prediction of task requirements, temporary load fluctuations, hardware status changes, etc. By sampling or scenario analysis of uncertainty, we obtain a set of scenarios . Indicates the Possible demand scenarios, each of which gives a possible demand curve This is similar to the sample approximation of a random variable in stochastic programming. The uncertainty distribution of the task requirements is sampled and approximated in each scenario. The larger it is, the more detailed the uncertainty is characterized, but the computational complexity also increases. A variety of possible demand curves can be generated using historical data sets or Monte Carlo simulations. Usually a higher value (such as 0.95 or 0.99) is taken, indicating that the worst loss situation we are concerned about is in the worst 1- The closer it is to 1, the more we pay attention to the worst case scenario. Intuitively, when When we consider the average expected loss under the worst 5% scenario. Used to linearize the CVaR definition, it can be understood as a “percentile” or critical loss level. Exceed hour, Excess losses are taken into account to ensure that the definition of CVaR is a convex problem that can be optimized. This auxiliary variable is adaptively adjusted in the optimization to find a suitable cutoff point so that the CVaR calculation can be achieved through linear programming techniques. Less than ,but , Equal to 0, indicating that the loss of this scenario does not exceed the critical value .if Greater than , then there is a positive excess loss value. This piecewise function is conducive to calculating CVaR and focusing on the loss of scenarios exceeding the threshold. is a high confidence level (such as 0.95), then Indicates the worst 5% scenario subset of interest. CVaR focuses on this worst scenario to calculate the average loss, thereby ensuring better performance in extreme cases. In the CVaR calculation, we only consider the worst The scenarios are averaged. Since we have When we estimate CVaR, we need to perform a weighted average of the excess loss items. Ensure that the weighted average has the correct probabilistic meaning, that is, only calculate the expected value when the worst scenario subset is used.

[0078] Example 7: In step 3, a comprehensive optimization objective function is constructed using the following formula:

[0079] ;

[0080] in, is a binary decision variable. Assign to node hour, ; otherwise 0; It's in the scene Next, the task At the initial moment of the task The resource demand vector of represents the L1 norm; is a node The delay factor; is a node Average available bandwidth to the data source; For nodes Specific node resources Energy consumption coefficient; Including: CPU, GPU and MEM; is a node In time Node resources The macro available resource vector.

[0081] Specifically, is a binary decision variable. Assign to node hour, ; otherwise it is 0. This variable is used to indicate the scheduling decision result. Finally dispatched to the node If the task is executed on the node, this variable selects the node, otherwise it is not selected. This ensures that each task can only be executed by one node in the final solution. It is used to determine the critical loss level when calculating CVaR, and is used to transform the definition of CVaR into an optimizable linear (or convex) form. In this objective function, will with Appear together, Helps to robustly optimize resource mismatch losses in uncertain scenarios. The triple index can uniquely locate the Task 1 and Task 2 The first cloud provider The scheduling relationship between the nodes. is the total number of tasks, is the number of cloud service providers, It is These are problem-scale parameters that describe the overall topology and resource pool structure of the system. Metrics at worst -Expected resource mismatch losses in the quantile scenario Here, it is used as part of the optimization objective to control the risk under uncertain demand, so that the decision can still maintain good performance in the worst case scenario. ) usually requires loading initial data or initialization. In a more "average" or expected scenario The total amount of resources required at the start of the task (e.g., a certain amount of data needs to be loaded, CPU / GPU startup warm-up time, or memory initialization time). This provides the basis for the subsequent correlation between latency and bandwidth. This represents the total resource demand of the task's demand vector at the initial moment. For example, if the task initially requires 0.3 CPU, 0.2 GPU, and 0.4 MEM utilization, then the 1-norm is 0.3 + 0.2 + 0.4 = 0.9, which represents the overall resource demand at task startup. Describe from data center to node Obtain initial data and configure the required latency characteristics for the environment. For example, if the network latency is high or the node takes a long time to initialize a specific acceleration unit, This parameter is obtained by measuring indicators such as network bandwidth, RTT (round-trip time), and node initialization delay, and is used to estimate the impact of initial data loading time on final performance. Characterizes the transmission rate capability. For example, a larger bandwidth means a shorter transmission time for the same initial data volume, thus reducing startup delay. The term converts the initial demand into relative delay cost through bandwidth and delay factors. (such as CPU, GPU, MEM), The coefficient that represents the relationship between resource utilization and power consumption. Through power consumption measurement and performance counters, we can fit the increased energy consumption when resource utilization increases. This coefficient allows us to calculate the degree of resource utilization. Converted into energy consumption cost and used to reflect energy-saving requirements in optimization goals. Indicates that in the task During the execution cycle, the node provides resource types for the task The cumulative occupancy of . It reflects the usage of the resource type by the task during the entire execution time. Multiplying them together gives the energy consumption of the resource type. We need to ensure that resource requirements are met during this time and calculate the associated consumption. It can be obtained from task performance models, user requirements, or service level agreements (SLAs).

[0082] Example 8: In step 3, all constraints are integrated into a large nonlinear optimization problem through the following process: the equality constraint after discretization of the partial differential equation of the node resources is expressed by the following formula:

[0083] ;

[0084] in, for The discretization result is the step size in space. or meshing, using time steps in time Divide, represents the time step index; is a node Approximate solutions of resource vector fields at discrete grid points and discrete time levels; is the right-hand side term of the discretized partial differential equation of node resources; The coefficient matrix obtained by discretizing the partial differential equation of node resources; the allocation constraint is expressed as:

[0085] ;

[0086] The feasibility constraint is expressed as:

[0087] ;

[0088] in, Yes Yes Node In time Node resources The macro-available resource vector; Because it is in the scene Next, the task On task at time The resource demand vector of . Specifically, for Discrete version of . Using step size in space or meshing, using time steps in time , Represents the time step index. For example . is a node The approximate solution of the resource availability vector at the discrete grid point and discrete time level. It is the discrete result of the PDE solution and is used for subsequent calculations. . The continuous feature space The spatial step size used when dividing into finite elements or meshes. The smaller the time interval, the finer the spatial discretization and the higher the accuracy of the numerical solution, but the amount of calculation also increases. After discrete, Represents a moment in a time series. By discrete time, PDE is transformed from solving continuous time to solving algebraic equations at a series of time layers. The core operator that transforms continuous PDE into a set of algebraic equations, reflecting the discrete approximation of the physical laws of resource changes within the node (diffusion, dissipation, and exogenous supply). Indicates the resource field at discrete time and space grid points The influence of external inputs and fixed conditions.

[0089] Example 9: In step 4, the KKT system is constructed using the primal-dual interior point method to solve the overall problem of the partial differential equation containing node resources and obtain the solution result: Construct the Lagrangian function The comprehensive optimization objective function, the partial differential equation of node resources, and the large nonlinear optimization problem that integrates all constraints are integrated to obtain the following formula:

[0090] ;

[0091] in, is the dual pairing operator; is the barrier function, which is used to ensure Do not leave the feasible region during the solution process of the primal-dual interior point method; ; Due to the final need It is a 0-1 integer decision, but it is too difficult to solve the 0-1 problem directly. , in the initial stage of the solution, it is allowed In the (0,1) interval, as the barrier parameter decreases, It will force the solution to approach 0 or 1, so that the original dual interior point method approaches the binary solution on the basis of continuous relaxation; is the dual variable of the allocation constraint, which requires that each task must be assigned to exactly one node. It measures the sensitivity of relaxing the allocation constraints to the Lagrangian function near the optimal solution; It is the dual variable of the equality constraint after the discretization of the partial differential equation of the node resources, and is used to measure the impact of relaxing or tightening the equality constraint after the discretization of the partial differential equation of the node resources on the Lagrangian function; for The dual variable of If the resource constraint of a node is tight, that is, it just satisfies the equation, will become larger, indicating that the node resource has become a bottleneck; if there are surplus node resources, If it is 0, it means that the constraint is not tight. The KKT condition is solved iteratively by the primal-dual interior point method. Each iteration performs the following process: using the current Approximate Update ; Use Newton's method to solve the linearized KKT system to find the optimal 、 and When making When the value of is the largest, stop the iteration and get The final value of ;right Perform threshold judgment, and if it is greater than the set threshold, it is assigned to the node.

[0092] Specifically, as mentioned above, Indicates that the task Assign to node , otherwise it is 0. In the interior point method, it is temporarily allowed It can be solved by continuous relaxation and finally restored to a binary decision through a threshold. Optimization and scene loss Together, the CVaR constraint and the objective function remain convex and solvable. By optimizing the loss threshold, we can find the appropriate loss level and then obtain the CVaR value. is the intermediate variable in solving PDE. As one of the original variables, it realizes the physical consistency of node resource dynamics by satisfying the constraints of discrete PDE equations. For The constraint requires that each task must be assigned to exactly one node. It measures the sensitivity of relaxing this constraint to the objective function near the optimal solution (shadow price). It is very large, indicating that the allocation constraints of the task have a greater impact on the optimization direction of the problem. Represents the dual variable introduced for constraints such as PDE equations and resource feasibility inequalities (which may be a scalar, vector or function, corresponding to the discrete version of the continuous constraint). Dual to the PDE discrete equation system: used to measure the impact of relaxing or tightening the PDE constraints on the objective function. When the value changes, it means that the satisfaction degree of the PDE constraints is different and the intrinsic requirements for the resource field distribution change. Dual to the resource feasibility inequality: Dual variables. In the optimal solution, if a resource constraint is tight (just satisfies the equation), will be large, indicating that the resource has become a bottleneck; if there are surplus resources, Usually it is 0 or small, indicating that the constraint does not tighten the problem. It is the core object of the original dual interior point method. By solving the primal and dual problems simultaneously, we can find the optimal solution that satisfies the KKT conditions.

[0093] Embodiment 10: A multi-cloud heterogeneous computing power scheduling system, the system comprising: an available resource calculation unit, used to use the partial differential equation of node resources to describe the distribution of each node resource evolving over time; after solving the partial differential equation of node resources, a macro available resource vector is obtained by spatial integration; a scenario and constraint construction unit, used to compare the macro available resource vector with the measured time-varying task requirements to form a feasibility constraint; introduce uncertainty scenarios, sample scenarios for the time-varying task requirements, and use conditional risk value to control risks; an optimization target construction unit, used to construct a comprehensive optimization objective function; the objectives of the comprehensive optimization objective function include resource mismatch, delay, and energy consumption; all constraints are integrated into a large nonlinear optimization problem; the constraints include: equality constraints, feasibility constraints, and allocation constraints after the discretization of the partial differential equation of node resources; a scheduling unit, used to construct a KKT system using the primal-dual interior point method, and solve the overall problem of the partial differential equation containing node resources in combination with the large nonlinear optimization problem to obtain a solution result; when the solution result converges, the final solution result is discretized to obtain a final scheduling plan.

[0094] Although specific embodiments of the present invention have been described above, those skilled in the art will appreciate that these specific embodiments are merely illustrative, and that those skilled in the art may omit, substitute, and modify the details of the methods and systems described above without departing from the principles and spirit of the present invention. For example, combining the above method steps to perform substantially the same functions in substantially the same manner to achieve substantially the same results falls within the scope of the present invention. Accordingly, the scope of the present invention is limited solely by the appended claims.

Claims

1. A multi-cloud heterogeneous computing power scheduling method, characterized in that: The method comprises: Step 1: Use the partial differential equation of node resources to describe the distribution of each node's resources over time; solve the partial differential equation of node resources and obtain the macroscopic available resource vector through spatial integration; Step 2: Compare the macro-available resource vector with the measured time-varying task requirements to form feasibility constraints; introduce uncertainty scenarios, sample scenarios for the time-varying task requirements, and use conditional value at risk to control risks; Step 3: Construct a comprehensive optimization objective function; the objectives of the comprehensive optimization objective function include resource mismatch, delay, and energy consumption; integrate all constraints into a large nonlinear optimization problem; the constraints include: equality constraints after discretization of partial differential equations of node resources, feasibility constraints, and allocation constraints; Step 4: Use the primal-dual interior point method to construct the KKT system, combine it with the large nonlinear optimization problem, solve the overall problem of the partial differential equation containing node resources, and obtain the solution; when the solution converges, discretize it according to the value of the final solution to obtain the final scheduling solution; let the task set be ;No. tasks There is execution time ; The value range is 1 to ; is the total number of tasks; Representative tasks; suppose the multi-cloud collection is ; is the number of clouds in the multi-cloud set; For the cloud; Cloud There is a node collection ; The value range is 1 to ; For the Cloud The total number of nodes; Indicates the Cloud No. nodes; set Cloud The node resources in the feature space The continuous distribution, Indicates the Cloud No. nodes The hardware resource feature domain is obtained by mapping the CPU core topology, GPU array and memory channel into a continuous domain. Assume that the node resources include: CPU, GPU and MEM. CPU represents the processor occupancy, which ranges from 0 to 1; GPU represents the video memory occupancy, which ranges from 0 to 1; MEM represents the memory occupancy, which ranges from 0 to 1.

2. The multi-cloud heterogeneous computing power scheduling method according to claim 1, characterized in that: In step 1, the partial differential equation of node resources is used to describe the distribution of each node resource over time using the following formula: ； ； ； in, is a resource vector field describing the nodes At feature space points Place and time Available node resources; is the coordinate point in the feature space; is a time variable; It is a positive symmetric diffusion tensor obtained by measuring and modeling the node hardware topology and resource scheduling mechanism; represents the spatial gradient operator, represents the divergence operator; is the dissipation rate function, which is a scalar function or a diagonal matrix function; It is an exogenous regulatory item; is the initial condition function, giving Available node resources at the time of use, which are obtained through benchmark testing and system initial status detection; is the maximum execution time; Representation node At feature space points Place and time Available processor usage at time ; Representation node At feature space points Place and time Available video memory usage at time ; Representation node At feature space points Place and time Available memory usage at time ; It is the transpose operation of the vector.

3. The multi-cloud heterogeneous computing power scheduling method according to claim 2, characterized in that: In step 1, the partial differential equation of node resources is solved using the following formula and then spatially integrated to obtain the macroscopic available resource vector: ； in, is the macro available resource vector; is the feature space The coordinate point integration variable in .

4. The multi-cloud heterogeneous computing power scheduling method according to claim 3, characterized in that: In step 1, the following formula is used. In step 2, the macro-available resource vector is compared with the measured time-varying task requirements to form a feasibility constraint using the following formula: ； in, Representation node In time The total amount of processor occupancy available for assignment to tasks; Representation node In time The total amount of video memory available for allocation; Representation node In time The total amount of memory available for allocation; is the resource requirement vector, representing the task In time Requirements for processor utilization, video memory utilization, and memory utilization; For the task In time Required processor resource utilization; For tasks in time Required video memory usage; For tasks in time Required memory usage.

5. The multi-cloud heterogeneous computing power scheduling method according to claim 4, characterized in that: In step 1, the following formula is used. In step 2, the following formula is used to introduce uncertainty scenarios, sample scenarios for time-varying task requirements, and use conditional value at risk to control risks: ； in, Describe the worst case scenario under uncertainty -Percentile expected loss; under uncertainty, different scenarios Represents possible ways to achieve task requirements; It is the cost incurred if resources are insufficient or mismatched in a given scenario; ; Therefore, when resources are not enough to meet the scenario When the demand is will become larger; is the L2 norm; It is an auxiliary optimization variable introduced in the definition of conditional value at risk, used to linearize the definition of conditional value at risk, and is defined as a quantile or critical loss level; when Exceed hour, Taking into account excess losses, the definition of conditional value at risk is ensured to be an optimizable convex problem; is the confidence level used to determine the proportion of worst-case scenarios to be considered; is the total number of scenes.

6. The multi-cloud heterogeneous computing power scheduling method according to claim 5, characterized in that: In step 3, the comprehensive optimization objective function is constructed using the following formula: ； in, is a binary decision variable. Assign to node hour, ; otherwise 0; It's in the scene Next, the task At the initial moment of the task The resource demand vector of represents the L1 norm; is a node The delay factor; is a node Average available bandwidth to the data source; For nodes Specific node resources Energy consumption coefficient; Including: CPU, GPU and MEM; is a node In time Node resources The macro available resource vector.

7. The multi-cloud heterogeneous computing power scheduling method according to claim 6, characterized in that: In step 3, all constraints are integrated into a large nonlinear optimization problem through the following process: The equality constraints after discretization of the partial differential equations of the node resources are expressed as follows: ； in, for The discretization result is the step size in space. or meshing, using time steps in time Divide, represents the time step index; is a node Approximate solutions of resource vector fields at discrete grid points and discrete time levels; is the right-hand side term of the discretized partial differential equation of node resources; The coefficient matrix obtained by discretizing the partial differential equation of node resources; the allocation constraint is expressed as: ； The feasibility constraint is expressed as: ； in, Yes Yes Node In time Node resources The macro-available resource vector; Because it is in the scene Next, the task On task at time The resource demand vector.

8. The multi-cloud heterogeneous computing power scheduling method according to claim 7, characterized in that: In step 4, the KKT system is constructed using the primal-dual interior point method through the following process to solve the overall problem of the partial differential equation containing node resources and obtain the solution: Construct the Lagrangian function The comprehensive optimization objective function, the partial differential equation of node resources, and the large nonlinear optimization problem that integrates all constraints are integrated to obtain the following formula: ； in, is the dual pairing operator; is the barrier function, which is used to ensure Do not leave the feasible region during the solution process of the primal-dual interior point method; ; Due to the final need It is a 0-1 integer decision, but it is too difficult to solve the 0-1 problem directly. , in the initial stage of the solution, it is allowed In the (0,1) interval, as the barrier parameter decreases, It will force the solution to approach 0 or 1, so that the original dual interior point method approaches the binary solution on the basis of continuous relaxation; is the dual variable of the allocation constraint, which requires that each task must be assigned to exactly one node. It measures the sensitivity of relaxing the allocation constraints to the Lagrangian function near the optimal solution; It is the dual variable of the equality constraint after the discretization of the partial differential equation of the node resources, and is used to measure the impact of relaxing or tightening the equality constraint after the discretization of the partial differential equation of the node resources on the Lagrangian function; for The dual variable of If the resource constraint of a node is tight, that is, it just satisfies the equation, will become larger, indicating that the node resource has become a bottleneck; if there are surplus node resources, If it is 0, it means that the constraint is not tight. The KKT condition is solved iteratively by the primal-dual interior point method. Each iteration performs the following process: using the current Approximate Update ; Use Newton's method to solve the linearized KKT system to find the optimal 、 and When making When the value of is the largest, stop the iteration and get The final value of ;right Perform threshold judgment, and if it is greater than the set threshold, it is assigned to the node.

9. A multi-cloud heterogeneous computing power scheduling system, characterized in that: The system includes: an available resource calculation unit, which is used to use the partial differential equation of node resources to describe the distribution of each node resource evolving over time; after solving the partial differential equation of node resources, a macroscopic available resource vector is obtained by spatial integration; a scenario and constraint construction unit, which is used to compare the macroscopic available resource vector with the measured time-varying task demand to form a feasibility constraint; introduce uncertainty scenarios, sample scenarios for the time-varying task demand and use conditional risk value to control risks; an optimization target construction unit, which is used to construct a comprehensive optimization objective function; the objectives of the comprehensive optimization objective function include resource mismatch, delay and energy consumption; all constraints are integrated into a large nonlinear optimization problem; the constraints include: equality constraints, feasibility constraints and allocation constraints after the discretization of the partial differential equation of node resources; a scheduling unit, which is used to construct a KKT system using the primal-dual interior point method, and solve the overall problem of the partial differential equation containing node resources in combination with the large nonlinear optimization problem to obtain a solution result; when the solution result converges, it is discretized according to the value of the final solution result to obtain a final scheduling plan; let the task set be ;No. tasks There is execution time ; The value range is 1 to ; is the total number of tasks; Representative tasks; let the multi-cloud collection be ; is the number of clouds in the multi-cloud set; For the cloud; Cloud There is a node collection ; The value range is 1 to ; For the Cloud The total number of nodes; Indicates the Cloud No. nodes; set Cloud The node resources in the feature space The continuous distribution, Indicates the Cloud No. nodes The hardware resource feature domain is obtained by mapping the CPU core topology, GPU array and memory channel into a continuous domain. Assume that the node resources include: CPU, GPU and MEM. CPU represents the processor occupancy, which ranges from 0 to 1; GPU represents the video memory occupancy, which ranges from 0 to 1; MEM represents the memory occupancy, which ranges from 0 to 1.

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