An edge computing dependent task offloading method based on multi-directed acyclic graph joint scheduling

Abstract

This paper presents an edge computing-dependent task offloading method based on multi-directed acyclic graph (DAG) joint scheduling, belonging to the field of mobile edge computing technology. First, a joint algorithm HRRO combining highest response rate scheduling and optimal processor selection is proposed. Then, considering the complexity of ultra-dense MEC systems, HRRO is extended to a joint offloading algorithm HRRO-BWO based on the Beluga Whale Evolutionary Learning (BWO) algorithm, achieving globally optimal joint scheduling and offloading in multi-DAG scenarios. This method constructs a three-objective optimization model comprehensively considering average completion time, energy consumption, and information timeliness, and utilizes the collaborative mechanism of HRRO and BWO to achieve a balance among multiple objectives. Extensive simulation results show that HRRO-BWO outperforms the Distributed Earliest Completion Time (DEFO) offloading algorithm and the Potential Game Theory-based (PGOA) offloading algorithm in terms of average completion time, energy consumption, and real-time performance. Therefore, HRRO-BWO is more suitable for multi-user, multi-server ultra-dense MEC systems.

Description

Technical Field

[0001] This invention relates to the field of mobile edge computing technology, specifically to an edge computing dependent task offloading method based on multi-directed acyclic graph joint scheduling. Background Technology

[0002] With the rapid development of 5G / 6G mobile communication networks and Mobile Edge Computing (MEC) technology, cloud computing power is being pushed down to the network edge, forming a cloud-edge-device collaborative computing architecture. In this architecture, mobile devices can offload computationally intensive tasks to edge servers deployed on the base station or access point side, thereby significantly reducing service latency, saving terminal energy consumption, and alleviating backbone network bandwidth pressure.

[0003] However, most existing edge computing offloading research treats computing tasks as independent units that can be executed in any order, ignoring the pervasive dependencies between tasks. First, task dependencies introduce waiting and synchronization overhead, and different scheduling orders directly affect application completion time. Second, task offloading decisions must simultaneously weigh the latency and energy consumption differences between local and edge execution; a single optimization metric is insufficient to meet the diverse service quality requirements of complex applications. Third, in ultra-dense edge networks with multiple users and servers, competition for limited computing and communication resources among tasks further exacerbates the complexity of offloading decisions. Therefore, how to jointly optimize scheduling order and offloading decisions while satisfying task dependency constraints, and achieve a balance between multiple objectives such as latency, energy consumption, and information freshness, remains a critical problem that urgently needs to be solved.

[0004] While some studies have begun to consider task dependencies, most are limited to serial dependencies or simple parallel scenarios, and do not fully consider resource competition and global optimization in multi-user, multi-server environments. To address this, this invention proposes an edge computing dependent task offloading method based on multi-directed acyclic graph joint scheduling. Through highest response ratio (HRRO) scheduling and an adaptive penalty function, it quickly determines the optimal offloading scheme in a single-user, single-server scenario. Furthermore, it introduces the White Whale Evolutionary Learning Algorithm (BWO) to achieve globally optimal joint scheduling and offloading in ultra-dense multi-user, multi-server networks, significantly reducing average completion time, system energy consumption, and information freshness. This method is suitable for computationally intensive and real-time-sensitive applications such as 5G / 6G mobile edge computing, cloud-edge collaboration, vehicle-to-everything (V2X) networks, and industrial IoT. Summary of the Invention

[0005] The purpose of this invention is to solve the challenge of joint scheduling and offloading of tasks when multiple devices concurrently request dependent tasks in mobile edge computing environments. It provides an edge computing task offloading method based on multi-directed acyclic graph joint scheduling. This invention addresses the problem that existing edge computing offloading research neglects inter-task dependencies and struggles to adapt to resource competition among multiple users and servers. Therefore, it introduces Highest Response Ratio (HRRO) scheduling and an adaptive penalty function to quickly determine the optimal offloading scheme for single-user, single-server scenarios. Furthermore, it introduces the White Whale Evolutionary Learning (BWO) algorithm for global joint scheduling and offloading in ultra-dense multi-user, multi-server networks. The extended HRRO-BWO collaborative mechanism helps capture the evolutionary characteristics of task dependencies and resource competition, and pre-determines reliable scheduling orders and offloading decisions. Through experimental simulation comparisons, this method is more suitable for computationally intensive and real-time-sensitive applications such as 5G / 6G mobile edge computing, cloud-edge collaboration, and vehicle-to-everything (V2X) networks.

[0006] The edge computing dependency task offloading method based on multi-directed acyclic graph joint scheduling of the present invention mainly includes the following key steps:

[0007] 1. System Model and Problem Construction:

[0008] 1.1 Establish a task dependency model and use a directed acyclic graph (DAG) to describe the dependencies between computation tasks;

[0009] 1.2 Establish communication and computing models, including communication models, local computing models, and edge server computing models;

[0010] 1.3 Establish a dynamic scheduling model and introduce a highest response ratio priority strategy;

[0011] 1.4 Establish an information freshness (AoI) perception model;

[0012] 1.5 Construct a multi-objective optimization problem model for joint scheduling and unloading;

[0013] 2. Design of a joint scheduling strategy based on Highest Response Ratio (HRRO):

[0014] 2.1 Calculate the task response ratio and determine the task scheduling order based on task dependencies;

[0015] 2.2 Determining the optimal processor selection and offloading decision in simple scenarios;

[0016] 3. Design of a global joint unloading algorithm based on White Whale Optimization (BWO):

[0017] 3.1. The multi-objective constrained problem is transformed into an unconstrained optimization problem by using the adaptive penalty function method;

[0018] Section 3.2: The coding scheme encodes the unloading location, central processing unit frequency, and transmit power into a continuous vector;

[0019] 3.3. Global optimization is performed using the beluga whale evolutionary learning algorithm, through a three-stage iterative search involving migration, cooperative predation, and whale falls;

[0020] Step 3.4: Determine if the stopping condition is met, iterate until convergence, and output the optimal unloading solution for multi-user, multi-server scenarios.

[0021] Furthermore, the method for establishing the task dependency model in step 1.1 is as follows: Let the j-th computation task of the i-th MD request be denoted as... ,in This indicates the amount of data and instructions required to complete the task. Indicates the deadline for the computation task. This represents the unloading decision, with a value range of [value missing]. ;

[0022] The unloading decision uses a binary unloading model, task It either runs entirely locally or is unloaded to a specific local machine. One of the edge servers, represented as:

[0023]

[0024] Considering dependencies, All requested computational tasks can be represented by a DAG, i.e. = ( , ), where vertex set The edge set represents a collection of M computational tasks. Indicates the relationships between vertices;

[0025] The method for the communication and computation model in step 1.2 is as follows:

[0026] When establishing the communication model, co-channel interference caused by multiple mobile devices sharing a wireless channel to offload tasks to the same edge server is considered. The transmission rate is calculated based on channel bandwidth, transmit power, channel gain, background noise, and interference power from other devices. At the same time, an exponential approximation model is used to determine the link success probability to reflect the impact of channel quality on data transmission reliability. When the task is executed locally, this probability is set to 1.

[0027] When establishing the local computing model, the local execution latency is calculated based on the CPU clock frequency, task data volume, and computing density of the mobile device; and the local execution energy consumption is calculated based on the switching capacitor coefficient.

[0028] When establishing the edge server computing model, the task unloading process is divided into an upload stage, a processing stage, and a download stage. Among them, the upload latency is determined by the task data volume, transmission rate, and link success probability, the processing latency is determined by the task data volume, computing density, and edge server CPU frequency, and the latency of returning the computing results is negligible. The edge execution energy consumption only considers the transmission energy consumption of the mobile device, which is determined by the transmission power and transmission duration.

[0029] The method for establishing the dynamic scheduling model in step 1.3 is as follows: Establish a dynamic scheduling model, introduce the highest response ratio first strategy, calculate the average execution time of each ready task, which is the arithmetic mean of the local execution latency and the edge execution latency; calculate its waiting time, which is the maximum value of the actual completion time of all predecessor tasks.

[0030] Computational tasks The response ratio is:

[0031]

[0032] in, Indicates the average execution time. Indicates the waiting time. Indicates the response ratio;

[0033] The actual completion time of a task is determined by the sum of the waiting time and the actual time consumed by the selected execution mode. That is, the local execution latency or edge execution latency is selected based on the unloading decision and summed into the waiting time. The task energy consumption is determined based on the local energy consumption or edge energy consumption corresponding to the selected execution mode.

[0034] The method for establishing the information freshness perception model in step 1.4 is as follows: Consider the i-th mobile device in the system, whose task set forms a directed acyclic graph, and the exit task generates the final result of the application. Let the generation time of this application be denoted as . The completion time for the export task is If the task triggering cycle is The overall success probability of communication and processing for export missions is: Then define the first The application Aol is defined as follows:

[0035]

[0036] in, This represents the total latency for the application to complete; This reflects the impact of task generation interval on average information freshness. Describe the combined effect of task latency and communication reliability on system real-time performance. When the task is executed locally, the probability of successful communication is taken as... ;

[0037] The average information freshness of the system is expressed as:

[0038]

[0039] in For the number of users in the system, This indicates that the system status is updated more promptly and the information is more up-to-date.

[0040] The method for establishing the multi-objective optimization problem model for joint scheduling and offloading in step 1.5 is as follows: Weight parameters are introduced, with the offloading decisions of all mobile devices, the local execution CPU frequency, and the task transmission power as the set of optimization variables Ω. The weighting coefficients satisfy Construct the following optimization problem

[0041] OPT-1:

[0042]

[0043] in, This represents the average application completion time of the system, which is the arithmetic mean of the actual completion times of applications across all mobile devices. This represents the system's average energy consumption, which is the arithmetic average of the total energy consumption of all mobile devices. This represents the average information freshness of the system, where N is the total number of mobile devices;

[0044] The optimization process must meet the following constraints: the total energy consumption of each mobile device executing the task does not exceed its initial energy; the offloading decision is a binary variable of local execution or selection of a specific edge server; the local CPU frequency and task transmission power are within physical limits; and the actual completion time of each task does not exceed its deadline.

[0045] Furthermore, the method for calculating the task response ratio and determining the task scheduling order based on task dependencies described in step 2.1 is as follows: A breadth-first search is used to traverse the task dependency graph, identifying ready tasks without predecessors. For each ready task, its waiting time and average execution time are calculated to determine the task response ratio. The waiting time is the maximum value of the completion times of all predecessor tasks, and the average execution time is the average of the local execution latency and the edge execution latency. A priority queue is formed by sorting tasks in descending order of response ratio. The task with the highest response ratio is selected for scheduling each time. If multiple tasks have the same response ratio, one is randomly selected.

[0046] The method for determining the optimal processor selection and offloading decision in a single-user, single-server scenario, as described in step 2.2, is as follows: For each selected task, calculate its completion time when executed locally. and completion time when executed on the edge server Compare the two: if the local execution completion time is less than the edge execution completion time, select local execution and optimize the local CPU frequency; otherwise, select edge execution and optimize the transmit power; record the actual completion time and offloading decision of the task, delete the task from the task graph, repeat the above process until all tasks in the task graph are scheduled, and output the optimal offloading scheme.

[0047] Furthermore, step 3.1 uses the adaptive penalty function method to transform the multi-objective constrained problem into an unconstrained optimization problem. Let the original objective function of the multi-objective optimization problem be... The constraint set is Then the unconstrained optimization objective is defined as:

[0048]

[0049] in: To constrain The degree of violation is calculated by taking the square of the positive value for inequality constraints and by using the absolute value for equality constraints. The adaptive penalty coefficient varies with the number of iterations. Linear increments are used to balance the global exploration in the early stages of the algorithm with the feasibility convergence in the later stages;

[0050] The constraint set includes: energy constraints, processor selection constraints, deadline constraints, and physical constraints.

[0051] The method for encoding the unloading location, CPU frequency, and transmit power into a continuous vector in step 3.2 is as follows: For each task, its unloading location, CPU frequency during local execution, and transmit power during unloading execution are mapped to real numbers; wherein the unloading decision adopts discrete value mapping, and the CPU frequency and transmit power take continuous values ​​within their physical constraints; the codes of all tasks are concatenated to form a complete individual vector, which serves as the solution space carrier for the iterative search of the White Whale optimization algorithm;

[0052] The method for global optimization using the beluga whale evolutionary learning algorithm described in step 3.3 is as follows: after initializing the population, iterative optimization is performed in the following three stages:

[0053] Migration Phase: Update the positions of non-elite individuals with the exploration probability η(t) and move them toward the current optimal solution to conduct a global exploration;

[0054] Cooperative predation phase: Elite individuals use the exploitation factor α(t) and Lévy flight to randomly walk around the optimal solution and exploit local resources.

[0055] Whale fall phase: The worst individual proportion q% is reset using the whale fall probability p_wf to maintain population diversity; fitness is calculated after each generation update using the following formula.

[0056] in The value of the unconstrained objective function obtained in step 3.1 is used to iterate until the stopping condition is met;

[0057] The method for determining whether the stopping condition is met and outputting the optimal unloading scheme in step 3.4 is as follows: determine whether the current iteration number has reached the maximum value or whether the change in optimal fitness over multiple consecutive generations is less than the threshold. If not, return to the migration stage to continue iterating. If so, extract the unloading position of each task, the optimal CPU frequency, and the optimal transmit power from the optimal solution, and output the optimal unloading scheme in a multi-user, multi-server scenario.

[0058] The advantages and positive effects of this invention are:

[0059] This invention primarily designs an edge computing dependency task offloading method based on multi-directed acyclic graph joint scheduling. This method mainly studies the joint scheduling and offloading problem of multiple interdependent computing tasks in complex MEC systems. For the dependency relationship between computing tasks and deadline constraints in simple MEC systems, a joint scheduling and offloading algorithm and optimization method, HRRO, with the highest response rate, is designed and proposed. Based on heuristic algorithms, this invention further extends HRRO to HRRO-BWO, making it applicable to ultra-dense MEC systems. Through simulation of the algorithm and comparison with several existing algorithms, it is concluded that this method is more suitable for ultra-dense MEC systems under different practical conditions and has certain practical value. Attached Figure Description

[0060] Figure 1 This is a graph showing the relationship between the number of iterations of the Beluga optimization algorithm and the total average latency;

[0061] Figure 2 This is a graph showing the relationship between mobile devices and the overall average time delay.

[0062] Figure 3 This is a graph showing the relationship between the number of mobile devices and energy consumption;

[0063] Figure 4 This is a graph showing the relationship between the number of mobile devices and AOL.

[0064] Figure 5 This is a graph showing the relationship between the number of edge servers and the overall average latency.

[0065] Figure 6 This is a graph showing the relationship between the number of edge servers and system energy consumption;

[0066] Figure 7 This is a graph showing the relationship between the number of edge servers and AOL.

[0067] Figure 8 This is a graph showing the relationship between channel quality and overall average time delay;

[0068] Figure 9 This is a graph showing the relationship between channel quality and power consumption;

[0069] Figure 10 This is a graph showing the relationship between channel quality and Aol;

[0070] Figure 11 This is a graph showing the relationship between the sampling interval and the overall average time delay;

[0071] Figure 12 This is a graph showing the relationship between sampling interval and energy consumption;

[0072] Figure 13 This is a graph showing the relationship between the sampling interval and Aol;

[0073] Figure 14 This is a graph showing the relationship between the number of users and the algorithm execution.

[0074] Figure 15 This is a graph showing the relationship between the number of edge devices and algorithm execution.

[0075] Figure 16 This is a graph showing the relationship between the number of tasks and the algorithm execution.

[0076] Figure 17 This is a flowchart of the edge computing dependent task offloading method based on multi-directed acyclic graph joint scheduling of the present invention. Detailed Implementation

[0077] Example 1

[0078] This embodiment designs a method based on a Python platform to build an ultra-dense mobile edge computing simulation platform. The main objective of performance evaluation is to determine the impact of task dependencies and multi-user resource contention on joint scheduling and offloading performance. In addition, this invention aims to examine the benefits of using the proposed HRRO-BWO collaborative mechanism in ultra-dense scenarios under varying numbers of mobile devices, edge servers, and channel quality. The main implementation operations involved are: 1) constructing a 1km × 1km simulation area based on the Python platform; 2) deploying heterogeneous mobile devices and edge servers and generating interdependent DAG tasks; 3) executing the HRRO-BWO joint scheduling and offloading algorithm and recording performance metrics.

[0079] See appendix Figure 17 This embodiment is based on an edge computing dependency task offloading method using multi-directed acyclic graph joint scheduling, which mainly includes the following key steps:

[0080] 1. System Model and Problem Construction:

[0081] 1.1 Establish a task dependency model and use a directed acyclic graph (DAG) to describe the dependencies between computation tasks;

[0082] 1.2 Establish communication and computing models, including communication models, local computing models, and edge server computing models;

[0083] 1.3 Establish a dynamic scheduling model and introduce a highest response ratio priority strategy;

[0084] 1.4 Establish an information freshness (AoI) perception model;

[0085] 1.5 Construct a multi-objective optimization problem model for joint scheduling and unloading;

[0086] 2. Design of a joint scheduling strategy based on Highest Response Ratio (HRRO):

[0087] 2.1 Calculate the task response ratio and determine the task scheduling order based on task dependencies;

[0088] 2.2 Determining the optimal processor selection and offloading decision in simple scenarios;

[0089] 3. Design of a global joint unloading algorithm based on White Whale Optimization (BWO):

[0090] 3.1. The multi-objective constrained problem is transformed into an unconstrained optimization problem by using the adaptive penalty function method;

[0091] Section 3.2: The coding scheme encodes the unloading location, central processing unit frequency, and transmit power into a continuous vector;

[0092] 3.3. Global optimization is performed using the beluga whale evolutionary learning algorithm, through a three-stage iterative search involving migration, cooperative predation, and whale falls;

[0093] Step 3.4: Determine if the stopping condition is met, iterate until convergence, and output the optimal unloading solution for multi-user, multi-server scenarios.

[0094] Furthermore, the method for establishing the task dependency model communication and computation model in step 1.1 is as follows: Let the j-th computation task of the i-th MD request be denoted as... ,in This indicates the amount of data and instructions (in bits) required to complete the task. This indicates the deadline (in seconds) for the computation task. This represents the unloading decision, with a value range of [value missing]. .

[0095] The unloading decision uses a binary unloading model, task It either runs entirely locally or is unloaded to a specific local machine. One of the edge servers can be represented as:

[0096]

[0097] Considering dependencies, All requested computational tasks can be represented by a DAG, i.e. = ( , ), where vertex set The edge set represents a collection of M computational tasks. This represents the relationship between vertices.

[0098] The method for the communication and computation model in step 1.2 is as follows:

[0099] When establishing the communication model, co-channel interference caused by multiple mobile devices sharing a wireless channel to offload tasks to the same edge server is considered. The transmission rate is calculated based on channel bandwidth, transmit power, channel gain, background noise, and interference power from other devices. At the same time, an exponential approximation model is used to determine the link success probability to reflect the impact of channel quality on data transmission reliability. When the task is executed locally, this probability is set to 1.

[0100] When establishing the local computing model, the local execution latency is calculated based on the mobile device's CPU clock frequency, task data volume, and computing density (i.e., the number of CPU cycles required to process each bit of data); and the local execution energy consumption is calculated based on the switching capacitor coefficient.

[0101] When establishing the edge server computing model, the task unloading process is divided into an upload stage, a processing stage, and a download stage. The upload latency is determined by the task data volume, transmission rate, and link success probability. The processing latency is determined by the task data volume, computing density, and edge server CPU frequency. The latency of returning the computing results is negligible. The edge execution energy consumption only considers the transmission energy consumption of the mobile device, which is determined by the transmission power and transmission duration.

[0102] The method for establishing the dynamic scheduling model in step 1.3 is as follows: Establish a dynamic scheduling model and introduce a highest response ratio priority strategy. For each ready task, calculate its average execution time, which is the arithmetic mean of local execution latency and edge execution latency; calculate its waiting time, which is the maximum value of the actual completion time of all predecessor tasks.

[0103] Computational tasks The response ratio is:

[0104]

[0105] in, Indicates the average execution time. Indicates the waiting time. This indicates the response ratio.

[0106] The actual completion time of a task is determined by the sum of the waiting time and the actual time consumed by the selected execution mode. That is, the local execution delay or edge execution delay is selected based on the unloading decision and summed into the waiting time; the task energy consumption is determined based on the local energy consumption or edge energy consumption corresponding to the selected execution mode.

[0107] The method for establishing the information freshness perception model in step 1.4 is as follows: Consider the i-th mobile device in the system, whose task set forms a directed acyclic graph (DAG), and the exit task generates the final result of the application. Let the generation time of this application be denoted as . The completion time for the export task is If the task triggering period (sampling interval) is The overall success probability of communication and processing for export missions is: Then define the first An application Aol can be defined as:

[0108]

[0109] in, This represents the total latency for the application to complete; This reflects the impact of task generation interval on average information freshness. Describe the combined effect of task latency and communication reliability on system real-time performance. When the task is executed locally, the probability of successful communication is taken as... .

[0110] The average information freshness of the system can be expressed as:

[0111]

[0112] in This represents the number of users in the system. (Smaller) This indicates that the system status is updated more promptly and the information is more up-to-date.

[0113] The method for establishing the multi-objective optimization problem model for joint scheduling and offloading in step 1.5 is as follows: Weight parameters are introduced, with the offloading decisions of all mobile devices, the local execution CPU frequency, and the task transmission power as the set of optimization variables Ω. The weighting coefficients satisfy The following optimization problem is constructed.

[0114] OPT-1:

[0115]

[0116] in, This represents the average application completion time of the system, which is the arithmetic mean of the actual completion times of applications across all mobile devices. This represents the system's average energy consumption, which is the arithmetic average of the total energy consumption of all mobile devices. This represents the average information freshness of the system, where N is the total number of mobile devices.

[0117] The optimization process must meet the following constraints: the total energy consumption of each mobile device executing the task does not exceed its initial energy; the offloading decision is a binary variable of local execution or selection of a specific edge server; the local CPU frequency and task transmission power are within physical limits; and the actual completion time of each task does not exceed its deadline.

[0118] Furthermore, the method for calculating the task response ratio and determining the task scheduling order based on task dependencies described in step 2.1 is as follows: a breadth-first search is used to traverse the task dependency graph to identify ready tasks without predecessors. For each ready task, its waiting time and average execution time are calculated to determine the task response ratio. The waiting time is the maximum value of the completion time of all predecessor tasks, and the average execution time is the average of the local execution latency and the edge execution latency. The tasks are arranged in descending order of response ratio to form a priority queue. The task with the highest response ratio is selected for scheduling each time. If multiple tasks have the same response ratio, one is randomly selected.

[0119] The method for determining the optimal processor selection and offloading decision in a single-user, single-server scenario, as described in step 2.2, is as follows: For each selected task, calculate its completion time when executed locally. and completion time when executed on the edge server Compare the two: if the local execution completion time is less than the edge execution completion time, select local execution and optimize the local CPU frequency; otherwise, select edge execution and optimize the transmit power; record the actual completion time and offloading decision of the task, delete the task from the task graph, repeat the above process until all tasks in the task graph are scheduled, and output the optimal offloading scheme.

[0120] Furthermore, step 3.1 uses the adaptive penalty function method to transform the multi-objective constrained problem into an unconstrained optimization problem. Let the original objective function of the multi-objective optimization problem be... The constraint set is Then the unconstrained optimization objective is defined as:

[0121]

[0122] in: To constrain The degree of violation is calculated by taking the square of the positive value for inequality constraints and by using the absolute value for equality constraints. The adaptive penalty coefficient varies with the number of iterations. The algorithm is linearly incremental to balance the global exploration in the early stages with the feasibility convergence in the later stages.

[0123] The set of constraints includes: energy constraints (total energy consumption of the task does not exceed the initial energy of the mobile device), processor selection constraints (the task can only be executed locally or on a single edge server), deadline constraints (the actual completion time of the task does not exceed the deadline), and physical constraints (CPU frequency and transmit power are within a limited range).

[0124] The method for encoding the offloading location, CPU frequency, and transmit power into a continuous vector in step 3.2 is as follows: For each task, its offloading location (local execution or each edge server), CPU frequency during local execution, and transmit power during offloading execution are mapped to real numbers; the offloading decision uses discrete value mapping (e.g., 0 represents local execution, and 1 to S are mapped to the corresponding continuous intervals of each edge server), and the CPU frequency and transmit power are continuously selected within their physical constraints; the encodings of all tasks are concatenated to form a complete individual vector, which serves as the solution space carrier for the iterative search of the White Whale optimization algorithm.

[0125] The method for global optimization using the beluga whale evolutionary learning algorithm described in step 3.3 is as follows: after initializing the population, iterative optimization is performed in the following three stages:

[0126] Migration Phase: Update the positions of non-elite individuals with the exploration probability η(t) and move them toward the current optimal solution to conduct a global exploration;

[0127] Cooperative predation phase: Elite individuals use the exploitation factor α(t) and Lévy flight to randomly walk around the optimal solution and exploit local resources.

[0128] Whale fall phase: The worst individual proportion q% is reset using the whale fall probability p_wf to maintain population diversity; fitness is calculated after each generation update using the following formula.

[0129] in The value of the unconstrained objective function obtained in step 3.1 is used to iterate until the stopping condition is met;

[0130] The method for determining whether the stopping condition is met and outputting the optimal unloading scheme in step 3.4 is as follows: determine whether the current iteration number has reached the maximum value or whether the change in optimal fitness over multiple consecutive generations is less than the threshold. If not, return to the migration stage to continue iterating. If so, extract the unloading position of each task, the optimal CPU frequency, and the optimal transmit power from the optimal solution, and output the optimal unloading scheme in a multi-user, multi-server scenario.

[0131] In this example, the present invention constructs a typical mobile edge computing simulation scenario. The system is deployed within a 1km × 1km area, which contains multiple mobile devices (MDs) and multiple heterogeneous edge servers (ESs). Each MD can establish connections with multiple edge servers within its communication range, and offload some computing tasks to appropriate servers for execution based on network conditions, computing resources, and task characteristics. The experimental parameters are shown in Table 1.

[0132] Table 1 Experimental parameters

[0133]

[0134] This simulation experiment will consider the following performance indicators: average latency, power consumption link failure, and information freshness.

[0135] The simulation results of this example are as follows:

[0136] 1. Relationship between BWO iteration count and average latency, energy consumption, and information freshness

[0137] Depend on Figure 1 It is evident that the overall average latency of the MEC system gradually converges and stabilizes with increasing BWO iteration count. This is because HRRO-BWO dynamically optimizes the population through the exploration, development, and whale fall phases of BWO, gradually eliminating individuals with lower fitness and updating the global optimum. The algorithm converges and outputs the optimal solution when the number of iterations reaches its maximum or the difference between the results of two consecutive generations is less than a threshold. Experiments show that when the number of iterations is set to 200, HRRO-BWO can obtain a convergent and effective unloading scheme.

[0138] 2. The impact of the number of mobile devices on overall average latency, energy consumption, and AOL.

[0139] like Figure 2-4As shown, this set of simulation experiments verifies the impact of mobile devices on overall average latency, energy consumption, and Aol. Clearly, compared to other algorithms, HRRO-BWO consistently exhibits the lowest overall average latency, energy consumption, and Aol. It can be seen that overall average latency, energy consumption, and Aol are directly proportional to the number of MDs (Multi-Demand Objects). This is because as the number of MDs in the MEC system increases, the number of requesting applications also increases, intensifying competition for computing and communication resources, leading to a simultaneous increase in transmission time and waiting time, which in turn is accompanied by an increase in system energy consumption and Aol. HRRO-BWO, through the global search capability of BWO, determines the optimal offloading scheme for each computing task, ensuring a reasonable scheduling order, thereby minimizing completion time and ensuring that overall average latency, energy consumption, and Aol are consistently lower than other algorithms.

[0140] 3. The impact of the number of edge servers on overall average latency, energy consumption, and AOL.

[0141] like Figure 5-7 As shown, this set of simulation experiments verifies the impact of the number of edge servers on the overall average latency, energy consumption, and AoI. Clearly, compared to other algorithms, HRRO-BWO consistently exhibits the lowest overall average latency, energy consumption, and AoI. It can be seen that the overall average latency, energy consumption, and AoI are inversely proportional to the number of edge servers. This is because with more servers, computing resources are more abundant, tasks can be offloaded to nearby servers, transmission and waiting times are shortened simultaneously, and energy consumption and AoI decrease accordingly.

[0142] 4. The impact of channel quality on overall average latency, energy consumption, and AOL.

[0143] Figure 8-10 The results show that as channel quality improves, the overall average latency decreases significantly and gradually converges, with HRRO-BWO showing the largest decrease. This is because better channel quality leads to faster transmission rates, thus significantly reducing average latency, energy consumption, and AOL. Furthermore, when the number of servers is less than 5, the average latency of HRRO-BWO is slightly higher than that of DEFO and PGA. This is because the latter two algorithms offload tasks to the same server, making it easier to utilize server resources in scenarios with fewer servers. However, as the number of servers increases, DEFO and PGA require traversing the EFT, drastically increasing computational complexity, making them unsuitable for ultra-dense MEC systems.

[0144] 5. The impact of sampling interval on overall average delay, energy consumption, and Aol

[0145] Figure 11-13 The results show that as channel quality improves, overall average latency, system power consumption, and information freshness all decrease significantly and tend to converge, with HRRO-BWO showing the largest decrease. This is because improved channel quality leads to faster upload speeds, significantly reducing transmission latency, power consumption, and AoI.

[0146] 6. The impact of different parameters on algorithm execution time

[0147] Considering that ultra-dense MEC systems increase the complexity of scheduling and offloading algorithms, this invention uses HRRO-BWO as an extension to better adapt to multi-user, multi-server scenarios. To evaluate its efficiency and adaptability, simulation experiments compared the execution times of HRRO-BWO and DEFO under different parameters, such as... Figure 14 As shown. Figure 15 and Figure 16 The impact of the number of edge servers and computing tasks on the algorithm's execution time was demonstrated separately. The results show that as MEC systems become more complex, the execution time increases with both the number of servers and tasks. However, overall, HRRO-BWO experiences a smaller increase, exhibiting better scalability and adaptability. Therefore, HRRO-BWO is more suitable for ultra-dense MEC scenarios with multiple users and multiple servers.

Claims

1. An edge computing dependent task offloading method based on multi-DAG joint scheduling, characterized in that, This method mainly includes the following steps:

1. System Model and Problem Construction: 1.1 Establish a task dependency model and use a directed acyclic graph (DAG) to describe the dependencies between computation tasks; 1.2 Establish communication and computing models, including communication models, local computing models, and edge server computing models; 1.3 Establish a dynamic scheduling model and introduce a highest response ratio priority strategy; 1.4 Establish an information freshness (AoI) perception model; 1.5 Construct a multi-objective optimization problem model for joint scheduling and unloading; 2. Design of a joint scheduling strategy based on Highest Response Ratio (HRRO): 2.1 Calculate the task response ratio and determine the task scheduling order based on task dependencies; 2.2 Determining the optimal processor selection and offloading decision in simple scenarios; 3. Design of a global joint unloading algorithm based on White Whale Optimization (BWO): 3.

1. The multi-objective constrained problem is transformed into an unconstrained optimization problem by using the adaptive penalty function method; Section 3.2: The coding scheme encodes the unloading location, central processing unit frequency, and transmit power into a continuous vector; 3.

3. Global optimization is performed using the beluga whale evolutionary learning algorithm, through a three-stage iterative search involving migration, cooperative predation, and whale falls; Step 3.4: Determine if the stopping condition is met, iterate until convergence, and output the optimal unloading solution for multi-user, multi-server scenarios.

2. The edge computing dependency task offloading method based on multi-directed acyclic graph joint scheduling as described in claim 1, characterized in that, The method for establishing the task dependency model in step 1.1 is as follows: Let the j-th computation task of the i-th MD request be denoted as... ,in This indicates the amount of data and instructions required to complete the task. Indicates the deadline for the computation task. This represents the unloading decision, with a value range of [value missing]. ; The unloading decision uses a binary unloading model, task It either runs entirely locally or is unloaded to a specific local machine. One of the edge servers, represented as: Considering dependencies, All requested computational tasks can be represented by a DAG, i.e. = ( , ), where vertex set The edge set represents a collection of M computational tasks. Indicates the relationships between vertices; The method for the communication and computation model in step 1.2 is as follows: When establishing the communication model, co-channel interference caused by multiple mobile devices sharing a wireless channel to offload tasks to the same edge server is considered. The transmission rate is calculated based on channel bandwidth, transmit power, channel gain, background noise, and interference power from other devices. At the same time, an exponential approximation model is used to determine the link success probability to reflect the impact of channel quality on data transmission reliability. When the task is executed locally, this probability is set to 1. When establishing the local computing model, the local execution latency is calculated based on the CPU clock frequency, task data volume, and computing density of the mobile device; and the local execution energy consumption is calculated based on the switching capacitor coefficient. When establishing the edge server computing model, the task unloading process is divided into an upload stage, a processing stage, and a download stage. Among them, the upload latency is determined by the task data volume, transmission rate, and link success probability, the processing latency is determined by the task data volume, computing density, and edge server CPU frequency, and the latency of returning the computing results is negligible. The edge execution energy consumption only considers the transmission energy consumption of the mobile device, which is determined by the transmission power and transmission duration. The method for establishing the dynamic scheduling model in step 1.3 is as follows: Establish a dynamic scheduling model, introduce the highest response ratio first strategy, calculate the average execution time of each ready task, which is the arithmetic mean of the local execution latency and the edge execution latency; calculate its waiting time, which is the maximum value of the actual completion time of all predecessor tasks. Computational tasks The response ratio is: in, Indicates the average execution time. Indicates the waiting time. Indicates the response ratio; The actual completion time of a task is determined by the sum of the waiting time and the actual time consumed by the selected execution mode. That is, the local execution latency or edge execution latency is selected based on the unloading decision and summed into the waiting time. The task energy consumption is determined based on the local energy consumption or edge energy consumption corresponding to the selected execution mode. The method for establishing the information freshness perception model in step 1.4 is as follows: Consider the i-th mobile device in the system, whose task set forms a directed acyclic graph, and the exit task generates the final result of the application. Let the generation time of this application be denoted as . The completion time for the export task is If the task triggering cycle is The overall success probability of communication and processing for export missions is: Then define the first The application Aol is defined as follows: in, This represents the total latency for the application to complete; This reflects the impact of task generation interval on average information freshness. Describe the combined effect of task latency and communication reliability on system real-time performance. When the task is executed locally, the probability of successful communication is taken as... ; The average information freshness of the system is expressed as: in For the number of users in the system, This indicates that the system status is updated more promptly and the information is more up-to-date. The method for establishing the multi-objective optimization problem model for joint scheduling and offloading in step 1.5 is as follows: Weight parameters are introduced, with the offloading decisions of all mobile devices, the local execution CPU frequency, and the task transmission power as the set of optimization variables Ω. The weighting coefficients satisfy Construct the following optimization problem OPT-1: in, This represents the average application completion time of the system, which is the arithmetic mean of the actual completion times of applications across all mobile devices. This represents the system's average energy consumption, which is the arithmetic average of the total energy consumption of all mobile devices. This represents the average information freshness of the system, where N is the total number of mobile devices; The optimization process must meet the following constraints: the total energy consumption of each mobile device executing the task does not exceed its initial energy; the offloading decision is a binary variable of local execution or selection of a specific edge server; the local CPU frequency and task transmission power are within physical limits; and the actual completion time of each task does not exceed its deadline.

3. The edge computing dependency task offloading method based on multi-directed acyclic graph joint scheduling as described in claim 1, characterized in that, The method for calculating the task response ratio and determining the task scheduling order based on task dependencies described in step 2.1 is as follows: A breadth-first search is used to traverse the task dependency graph, identifying ready tasks without predecessors. For each ready task, its waiting time and average execution time are calculated to determine the task response ratio. The waiting time is the maximum value of the completion times of all predecessor tasks, and the average execution time is the average of the local execution latency and the edge execution latency. A priority queue is formed by sorting tasks in descending order of response ratio. The task with the highest response ratio is selected for scheduling each time. If multiple tasks have the same response ratio, one is randomly selected. The method for determining the optimal processor selection and offloading decision in a single-user, single-server scenario, as described in step 2.2, is as follows: For each selected task, calculate its completion time when executed locally. and completion time when executed on the edge server Compare the two: if the local execution completion time is less than the edge execution completion time, select local execution and optimize the local CPU frequency; otherwise, select edge execution and optimize the transmit power; record the actual completion time and offloading decision of the task, delete the task from the task graph, repeat the above process until all tasks in the task graph are scheduled, and output the optimal offloading scheme.

4. The edge computing dependency task offloading method based on multi-directed acyclic graph joint scheduling as described in claim 1, characterized in that, Step 3.1: The multi-objective constrained problem is transformed into an unconstrained optimization problem using the adaptive penalty function method. Let the original objective function of the multi-objective optimization problem be... The constraint set is Then the unconstrained optimization objective is defined as: in: To constrain The degree of violation is calculated by taking the square of the positive value for inequality constraints and by using the absolute value for equality constraints. The adaptive penalty coefficient varies with the number of iterations. Linear increments are used to balance the global exploration in the early stages of the algorithm with the feasibility convergence in the later stages; The constraint set includes: energy constraints, processor selection constraints, deadline constraints, and physical constraints. The method for encoding the unloading location, CPU frequency, and transmit power into a continuous vector in step 3.2 is as follows: For each task, its unloading location, CPU frequency during local execution, and transmit power during unloading execution are mapped to real numbers; wherein the unloading decision adopts discrete value mapping, and the CPU frequency and transmit power take continuous values ​​within their physical constraints; the codes of all tasks are concatenated to form a complete individual vector, which serves as the solution space carrier for the iterative search of the White Whale optimization algorithm; The method for global optimization using the beluga whale evolutionary learning algorithm described in step 3.3 is as follows: after initializing the population, iterative optimization is performed in the following three stages: Migration Phase: Update the positions of non-elite individuals with the exploration probability η(t) and move them toward the current optimal solution to conduct a global exploration; Cooperative predation phase: Elite individuals use the exploitation factor α(t) and Lévy flight to randomly walk around the optimal solution and exploit local resources. Whale fall phase: The worst individual proportion q% is reset using the whale fall probability p_wf to maintain population diversity; fitness is calculated after each generation update using the following formula. in The value of the unconstrained objective function obtained in step 3.1 is used to iterate until the stopping condition is met; The method for determining whether the stopping condition is met and outputting the optimal unloading scheme in step 3.4 is as follows: determine whether the current iteration number has reached the maximum value or whether the change in optimal fitness over multiple consecutive generations is less than the threshold. If not, return to the migration stage to continue iterating. If so, extract the unloading position of each task, the optimal CPU frequency, and the optimal transmit power from the optimal solution, and output the optimal unloading scheme in a multi-user, multi-server scenario.

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