A mobile edge computing offloading method based on multi-population dynamic co-evolution

Abstract

A mobile edge computing offloading method based on multi-population dynamic co-evolution. The method is aimed at the strict requirements of mobile augmented reality in terms of delay and energy consumption, and studies the problems of network traffic, service preference and edge server load changes caused by user mobility. By introducing the CO-SC mechanism of computing offloading and service caching, the user location and direction information are combined to formalize the cooperative caching strategy into a multi-objective optimization problem. A multi-population dynamic co-evolution optimization algorithm DCMOA is proposed, which uses regional mobility feature perception, multi-subpopulation co-evolution and dynamic feedback mechanism to efficiently solve the optimal CO-SC decision in the dynamic MEC environment. Simulation experiments show that the method is superior to existing algorithms in terms of delay and energy consumption, effectively improving system performance and resource utilization.

Description

Technical Field

[0001] This invention belongs to the field of Internet of Things (IoT), specifically relating to a mobile edge computing offloading method based on dynamic collaborative evolution of multiple populations. Background Technology

[0002] With the rapid development of 5G mobile communication technology and the computing power of smart terminals, mobile augmented reality (MAR) technology is gradually moving from concept to large-scale commercial application. MAR creates an immersive human-computer interaction experience by overlaying computer-generated virtual information (such as 3D models, videos, and audio) onto the user's perception of the real world in real time. Its applications have widely penetrated into several key areas, including real-time road condition analysis for autonomous driving, obstacle recognition, mixed reality navigation, remote industrial operation and maintenance guidance, as well as virtual try-on and interactive games.

[0003] However, the limited computing and storage resources of mobile terminals make it difficult to meet the low latency and high computing power requirements of MAR applications. To address this contradiction, mobile edge computing has been proposed. Edge computing significantly reduces data transmission latency and bandwidth consumption and improves system response speed by migrating computing and data storage tasks from the central cloud to the network edge closer to the data source. In an MEC environment, edge servers can provide near-field computing and caching support to terminal devices, thereby alleviating network pressure while ensuring service quality. Although compute offloading has become a core direction of MEC research, traditional static offloading strategies often fail to achieve ideal results in complex network environments due to the heterogeneity of tasks and services and the uncertainty of resource allocation. Furthermore, device mobility changes network traffic and direction, negatively impacting the access frequency and preferences of MAR services. In addition, changes in access frequency also affect the workload of MAR caching services, leading to an imbalance in the workload of edge servers. In recent years, researchers in this field have proposed a collaborative optimization strategy combining caching and offloading to balance task latency and energy consumption, addressing the contradiction between the high-performance requirements of mobile augmented reality applications and the limited edge resources. Summary of the Invention

[0004] This invention proposes a multi-objective optimization algorithm based on dynamic co-evolution of multiple populations, called DCMOA. First, DCMOA designs a multi-subpopulation co-evolution method to quickly find high-quality CO-SC solutions before environmental changes occur. Second, DCMOA develops a dynamic feedback mechanism that integrates diversity-based, memory-based, and prediction-based dynamic feedback methods to effectively respond to environmental changes, aiming to simultaneously minimize latency, energy consumption, and load balancing in dynamic environments. Simulation results demonstrate that the proposed algorithm outperforms several other algorithms.

[0005] The mobile edge computing offloading method based on dynamic co-evolution of multiple populations provided by this invention includes the following steps:

[0006] First, initialize multiple subgroups, each subgroup corresponding to a specific set of objectives, to process dynamic multi-objective optimization problems in parallel;

[0007] Second, utilize regional mobility characteristic perception algorithms to perceive user mobility characteristics and business preferences;

[0008] 2.1 Trajectory Completion: Complete the user trajectory and handle missing stops in the middle;

[0009] 2.2 Service Preference Estimation: Calculate service preferences based on the completed trajectory set;

[0010] 2.3 Network latency awareness: computing system latency;

[0011] 3. Design a multi-population co-evolution method to utilize knowledge transfer between subpopulations to co-evolve each subpopulation;

[0012] 3.1 Local evolution strategy: Divide individuals into a winner set and a loser set through a competition mechanism based on angle matching;

[0013] 3.2 Global Co-evolution Strategy: Integrate the winner sets of different subgroups into an external knowledge pool, and extract the global optimal solution set based on the Pareto non-dominance criterion;

[0014] Fourth, by responding to environmental changes through a dynamic feedback mechanism, high-quality solutions for subspecies populations can be obtained quickly.

[0015] Furthermore, step 1 employs Dynamic Multi-Objective Optimization (DMOP). Depending on the different dynamic constraints in the real world, DMOP can be expressed in various ways. Generally, the mathematical expression of DMOP can be represented as:

[0016] (1)

[0017] in, yes Bounded by decision space The decision vector of dimension, It is a time parameter. yes Objective function. For the service caching / edge computing problem of this invention, it is defined as:

[0018] (2)

[0019] in, This represents the average system latency, which needs to be minimized. Represents the total energy consumption of the system. Represents load balancing in the system. A negative value representing the system cache hit rate.

[0020] The key to solving DMOP is to find the dynamic Pareto optimal set or dynamic Pareto optimal front based on dynamic Pareto dominance, which is defined as follows:

[0021] Definition 1: Dynamic Pareto Advantage

[0022] At time, a decision vector This is known as another decision vector dominated by Pareto. , If and only if

[0023] (3)

[0024] Definition 2 Dynamic Pareto Optimal Set (DPSO)

[0025] time The dynamic Pareto optimal set at time t is denoted as DPSO(t), including time t. All solutions that are not dominated by any other solution are defined as follows:

[0026] (4)

[0027] Definition 3 Dynamic Pareto Optimal Front (DPOF)

[0028] Dynamic Pareto optimal frontier in time The above is represented as , is in the target space The mapping of solutions is represented as follows:

[0029] (5)

[0030] To reduce the complexity of direct search for high-dimensional targets, a target decomposition strategy is adopted to decompose the original problem (the aim is to minimize latency, energy consumption, and system load balancing while maximizing the system's service cache hit rate). Decomposed into a set of low-dimensional subproblems, the subproblems are divided as follows: Subproblem 1: Minimize Subproblem 2: Minimize Subproblem 3: Minimize Subproblem 4: Minimize The original optimization problem The reconstruction involves solving the aforementioned sub-problems in parallel, thereby quickly discovering good local structures in a lower-dimensional search space and merging them into an approximate dynamic Pareto front through global collaboration. To ensure consistency across different target scales, dynamic normalization of each target is required during the search process to avoid search bias caused by scale differences.

[0031] The initialization of the population uses a fixed-length integer encoding to represent each candidate solution. The encoding vector consists of two parts: the first part represents the service caching decision of the edge server, and the second part represents the task offloading decision for the vehicle or user. During the population initialization phase, the total population size is... The data is evenly distributed among four subgroups, meaning each subgroup is randomly generated. Initially, select individuals to ensure search diversity. Then, based on the aforementioned four sub-problems... Construct four corresponding subgroup sets:

[0032]

[0033] Each subgroup is optimized for different combinations of objectives:

[0034] (6)

[0035] Efficient exploration in low-dimensional subspaces is achieved through a multi-subgroup structure, while global collaboration maintains the diversity and convergence of the overall solution set.

[0036] Furthermore, in step 2.1, trajectory completion involves performing trajectory completion operations on all user trajectories, handling missing intermediate dwell points, and processing the trajectories accordingly.

[0037] (7)

[0038] The completed trajectory set can be obtained:

[0039] (8)

[0040] in To complete the stationing point.

[0041] During the trajectory completion phase of the RMA algorithm, firstly, RMA traverses the trajectories in the trajectory set R. And perform the completion operation, specifically, Representing the trajectory The adjacent outposts, ,in ,like or , indicating a station and If it is located in an adjacent grid, otherwise the intermediate point needs to be filled in;

[0042] RMA calculation with and Line segments and grids at endpoints Number of intersections If the number of intersection points is 2, that is... =2 indicates that the line segment passes through the grid. Its coordinates are the dwell points that need to be filled in, and the grid is then... Add trajectory completion candidate set ;

[0043] After identifying all the remaining outposts, they need to be aligned according to their grid adjacency relationships. Sort, then... Perform a depth-first search: Search The adjacent grid is used as the next dwell point until the complete trajectory is obtained. ;

[0044] For any trajectory If the number of missing dwell points is Then the trajectory completion phase of RMA is at most The process will inevitably terminate after the first selection, and all missing points will be filled in. If the candidate set... Only by of Neighborhood composition, and the filtering rules only apply to If the above selection is made, the adjacent dwelling points after completion must satisfy the adjacency constraint. If a mandatory condition is applied during candidate selection... If the completed edge satisfies the same constraint, it will not introduce any spurious migrations beyond the observation.

[0045] Step 2.2, service preference estimation, calculates service preferences based on the completed trajectory set R′ and calculates network traffic based on the number of trajectories leaving each grid. Specifically, RMA traverses all trajectories passing through each grid to determine the direction of movement (assuming the trajectory direction is consistent with the device orientation). Adjacent dwell point pairs... The coordinate difference is either 0 or 1 unit. The orientation of the equipment can be calculated by analyzing the differences between adjacent coordinates. :

[0046] (9)

[0047] Network traffic can be obtained by analyzing the orientation of devices. RMA returns the network traffic set F; then, according to formula (8), the service preference is obtained, and RMA returns the service preference set. .

[0048] In step 2.3, during network latency awareness, assuming a cache hit, RMA iterates through each service and the connectable edge server to calculate network latency, and then returns the network latency sets D and E.

[0049] Furthermore, step 3.1 employs a local evolution strategy. The main goal of local evolution is to fully explore and utilize the existing knowledge structure within the subgroup before environmental changes occur, thereby improving the quality of the current solution set and enhancing the subgroup's adaptability. Inspired by Competitive Population Optimization (CSO), individuals within the subgroup are distinguished into winners and losers through a competitive mechanism. Losers learn the behavioral characteristics of winners to achieve self-updating, thereby improving overall search capabilities and accelerating convergence to the dynamic Pareto optimal set DPSO. If the angle between the vectors of two particles in the search space is smaller, their positions in the solution space are closer and their directions are more consistent. Therefore, DCMOA calculates the angle information between particles to pair losers with the winners who are most similar in angle, thus achieving more efficient knowledge transfer.

[0050] Let the first In the iteration, the position and velocity of the loser particle are respectively and The position of the winner particle is The average position of the population is The control parameters are random coefficients The speed and position update rules for the loser are as follows:

[0051] (10)

[0052] (11)

[0053] Among them: the first item Maintain the individual's original search inertia; the second item : To learn from winner; the third item : Guide losers closer to the group center to enhance stability; for integer or discrete coding problems, the updated... Discretization and constraint repair operations are required to ensure that the solution remains in the feasible space.

[0054] (12)

[0055] To improve learning efficiency, DCMOA does not use random matching, but rather selects learning objects based on angular distance and sets... and The included angle between them is:

[0056] (13)

[0057] like The smallest value indicates that the two are closest in direction within the search space. From that study;

[0058] The evolutionary process of local evolution is as follows, with the input parameter being: the set of winning particles in the i-th subpopulation. With the Loser Particle Set First, calculate the angle values ​​of each particle in the winner's and loser's particle sets. and Let represent the number of loser and winner particles, respectively. Then, for each particle in the loser particle set, match it with the particle in the winner particle set with which it has the smallest angle. Subsequently, update the loser particle set using formulas 10 and 11. The speed and position of the particle are updated by adjusting the speed and position of the winning particle. Through learning and implementation, ultimately, the updated set of loser particles will be returned and replace the original set. The set of loser particles in the subpopulation;

[0059] Step 3.2 adopts a global co-evolution strategy, which utilizes the overlap of optimization goals of subgroups to share excellent individuals in overlapping areas of the search space to provide effective guidance, and enhances global exploration through experience sharing in non-overlapping areas. Based on this, DCMOA constructs an external experience pool to gather excellent individuals, selects elite solutions based on non-dominant relationships, and co-guides the evolution of each subgroup to achieve an efficient balance between local convergence and global exploration.

[0060] The process of global co-evolution is as follows: The input contains all subpopulations. A group By subscript Perform indexing;

[0061] First, to enhance the global adaptability of subgroup i, an external experience pool is first collected from the winners' set of all subgroups:

[0062] (14)

[0063] Subsequently, from The set of high-quality external individuals is obtained by screening based on the Pareto non-dominance criterion.

[0064] (15)

[0065] Then, for each winner in the i-subgroup Randomly select one External nondominated solutions And perform an integer crossover operation:

[0066] (16)

[0067] To ensure the feasibility of the solution, a repair operation is performed on the crossover results:

[0068] (17)

[0069] Final Update It will be returned to the subpopulation for the next generation of evolution.

[0070] Furthermore, step 4 addresses environmental changes through a dynamic feedback mechanism. To mitigate the issue of CO-SC (Co-Centered Cache and Task Offloading) decisions failing due to sudden environmental changes in dynamic environments, DCMOA introduces a Dynamic Feedback Mechanism (DFM). When an environmental change is detected, DFM integrates three strategies: diversity feedback (introducing random solutions to maintain population search breadth), memory feedback (reusing historical representative solutions to accelerate convergence), and prediction feedback (mining stable patterns in the historical dynamic Pareto optimal solution set (DPOS) based on a Naive Bayes model, such as edge server topology and vehicle movement patterns, to predict potential optimal solution regions in the new environment). This rapidly generates a high-quality initial subpopulation, avoiding a search from scratch. This mechanism organically integrates exploration, experience reuse, and intelligent prediction, improving the algorithm's adaptive optimization efficiency in scenarios such as dynamic vehicle networks. To achieve the aforementioned prediction function, a Naive Bayes classifier is used to analyze the historical DPOS. Let the historical DPOS set be... Each solution Corresponding multi-objective function values:

[0071] (18)

[0072] According to the Pareto dominance definition:

[0073] (19)

[0074] like No inferior to in all objectives If it is better than at least one objective, then it is called... Dominate ;

[0075] Based on this, the historical DPOS is divided into two training subsets according to the dominance relationship:

[0076] (20)

[0077] in This represents an individual that dominates at least one other solution (a sample of optimal solutions). This represents an individual (dominated solution sample) that is dominated by at least one other solution. The training dataset consists of:

[0078] (twenty one)

[0079] And it was trained using a Naive Bayes classification model:

[0080] (twenty two)

[0081] Subsequently, a large number of candidate solutions were randomly generated under the new environment. Make a prediction:

[0082] (twenty three)

[0083] Select from the predicted optimal solution categories (i.e.) The individual formation prediction solution set:

[0084] (twenty four)

[0085] Finally, a new initial subpopulation is generated by combining the three feedback mechanisms:

[0086] (25)

[0087] This hybrid initialization strategy, while ensuring diversity, can make full use of historical and predictive information to achieve efficient dynamic optimization that can quickly adapt to new environments.

[0088] The advantages and positive effects of this invention are:

[0089] The joint optimization framework proposed in this invention effectively solves the optimization problem of service caching and computation offloading in edge computing under dynamic environments by combining regional mobility awareness and dynamic co-evolutionary multi-objective optimization. Experiments show that this method not only achieves significant improvements in multi-dimensional performance indicators, but also has good scalability and practicality, providing an efficient optimization approach for future edge computing systems for MAR and other latency-sensitive applications. Attached Figure Description

[0090] Figure 1 This is a graph showing the relationship between edge server computing power and system latency;

[0091] Figure 2 This is a graph showing the relationship between edge server computing power and system energy consumption;

[0092] Figure 3 This is a diagram showing the relationship between edge server computing power and system load balancing.

[0093] Figure 4 This is a graph showing the relationship between edge server computing power and system cache hit rate;

[0094] Figure 5 This is a graph showing the relationship between edge server cache resource capacity and system latency;

[0095] Figure 6 This is a graph showing the relationship between edge server cache resource capacity and system energy consumption;

[0096] Figure 7 This is a graph showing the relationship between edge server cache resource capacity and system load balancing.

[0097] Figure 8 This relates to the relationship between edge server cache resource capacity and system cache hit rate;

[0098] Figure 9 It is the relationship between the number of system tasks and system latency;

[0099] Figure 10 This is a flowchart of the multi-objective optimization algorithm based on dynamic co-evolution of multiple populations, which is the basis of this invention. Detailed Implementation

[0100] Example 1

[0101] To verify the performance of this method on practical problems, this embodiment uses simulation experiments to verify the algorithm's effectiveness.

[0102] All experiments in this invention were conducted under the same hardware and software environment to ensure the comparability of results. The hardware environment included a computer equipped with an Intel Core i7-12700H @ 2.30GHz processor, 16 GB of RAM, and an NVIDIA GeForce RTX 4060 dedicated graphics card (6 GB of VRAM), running Windows 11 Professional 64-bit operating system. For the software environment, Python 3.10 was used as the programming language, with NumPy 1.26.4 and Matplotlib 3.8.2 being the primary scientific computing and visualization libraries. The algorithm implementation and result plotting were completed within the PyCharm 2024.1 integrated development environment.

[0103] The experimental parameters are set as shown in Table 1:

[0104] Table 1 Parameter Settings

[0105] parameter value Number of edge servers |J| 50 Number of user devices |I| 20, 40, 60, 80, 100 Total number of cache services |S| 10*30*4 Number of grids |O| 10*30 Grid area side length 150m Grid area 2km*5km Maximum execution latency of the task [200, 400] ms Service storage resource requirements [0.5,1.8]GB Service computing resource requirements [100,300]GHz Storage capacity of edge servers [0.6,1.8]GB The computing power of edge servers [100,250]GHz Transmission speed between cloud and edge servers 70Mbps Wireless channel bandwidth W 5MHz Transmit power 5mW Noise power 1mW Number of iterations K 500 Population size N 300 Subpopulation number S 10 Single population size N / S Mutation probability 0.1 Local iteration count L 2

[0106] See appendix Figure 10 This example is based on a multi-objective optimization algorithm for dynamic co-evolution of multiple populations, and includes the following steps:

[0107] First, initialize multiple subgroups, each subgroup corresponding to a specific set of objectives, to process dynamic multi-objective optimization problems in parallel;

[0108] Second, utilize regional mobility characteristic perception algorithms to perceive user mobility characteristics and business preferences;

[0109] 2.1 Trajectory Completion: Complete the user trajectory and handle missing stops in the middle;

[0110] 2.2 Service Preference Estimation: Calculate service preferences based on the completed trajectory set;

[0111] 2.3 Network latency awareness: computing system latency;

[0112] 3. Design a multi-population co-evolution method to utilize knowledge transfer between subpopulations to co-evolve each subpopulation;

[0113] 3.1 Local evolution strategy: Divide individuals into a winner set and a loser set through a competition mechanism based on angle matching;

[0114] 3.2 Global Co-evolution Strategy: Integrate the winner sets of different subgroups into an external knowledge pool, and extract the global optimal solution set based on the Pareto non-dominance criterion;

[0115] Fourth, by responding to environmental changes through a dynamic feedback mechanism, high-quality solutions for subspecies populations can be obtained quickly.

[0116] In step 1 of this invention, Dynamic Multi-Objective Optimization (DMOP) is employed. Depending on the different dynamic constraints in the real world, DMOP can be expressed in various ways. The mathematical expression of DMOP in this invention is as follows:

[0117] (1)

[0118] in, yes Bounded by decision space The decision vector of dimension, It is a time parameter. yes Objective function. For the service caching / edge computing problem of this invention, it is defined as:

[0119] (2)

[0120] in, This represents the average system latency, which needs to be minimized. Represents the total energy consumption of the system. Represents load balancing in the system. A negative value representing the system cache hit rate.

[0121] The key to solving DMOP is to find the dynamic Pareto optimal set or dynamic Pareto optimal front based on dynamic Pareto dominance, which is defined as follows:

[0122] Definition 1: Dynamic Pareto Advantage

[0123] At time, a decision vector This is known as another decision vector dominated by Pareto. , If and only if

[0124] (3)

[0125] Definition 2 Dynamic Pareto Optimal Set (DPSO)

[0126] time The dynamic Pareto optimal set at time t is denoted as DPSO(t), including time t. All solutions that are not dominated by any other solution are defined as follows:

[0127] (4)

[0128] Definition 3 Dynamic Pareto Optimal Front (DPOF)

[0129] Dynamic Pareto optimal frontier in time The above is represented as , is in the target space The mapping of solutions is represented as follows:

[0130] (5)

[0131] To reduce the complexity of direct search for high-dimensional targets, a target decomposition strategy is adopted to decompose the original problem (the aim is to minimize latency, energy consumption, and system load balancing while maximizing the system's service cache hit rate). The problem is decomposed into a set of low-dimensional subproblems, which are divided as follows (preserving both the low-dimensional information of the single-objective combination and the global information): Subproblem 1 (P1): Minimize ,in, This represents the total latency for mobile device users to offload tasks to a specified edge server. This represents the total energy consumption of the user device during task offloading; Subproblem 2 (P2): Minimize ,in, Represents the total load of the edge servers; Subproblem 3 (P3): Minimize ,in, Represents the negative value of cache hit rate; Subproblem 4 (P4, Synthetic Subproblem): Minimize The original optimization problem The reconstruction involves solving the aforementioned sub-problems in parallel, thereby rapidly discovering favorable local structures within a lower-dimensional search space and merging them globally into an approximate dynamic Pareto front. To ensure consistency across different target scales, dynamic normalization is required for each target during the search process to avoid search bias caused by scale differences.

[0132] To initialize the population, this method uses a fixed-length integer encoding to represent each candidate solution. Specifically, the encoding vector consists of two parts: the first part represents the service caching decision of the edge server, and the second part represents the task offloading decision of the vehicle or user. During the population initialization phase, the total population size is... The data is evenly distributed among four subgroups, meaning each subgroup is randomly generated. An initial set of individuals is used to ensure search diversity. Subsequently, this invention addresses the aforementioned four sub-problems. Construct four corresponding subgroup sets:

[0133]

[0134] Each subgroup is optimized for different combinations of objectives:

[0135] (6)

[0136] The multi-subgroup structure enables efficient exploration in low-dimensional subspaces while maintaining the diversity and convergence of the overall solution set through global collaboration.

[0137] Furthermore, in step 2.1, trajectory completion is necessary because the sampling time frequency and user movement speed differ, resulting in missing records of some grid points traversed by the user, leading to discontinuous and adjacent grids. Therefore, trajectory completion is required for all user trajectories to address missing intermediate stopping points. Specifically, the trajectory is processed as follows:

[0138] (7)

[0139] The completed trajectory set can be obtained:

[0140] (8)

[0141] in To complete the stationing point.

[0142] The following describes the trajectory completion phase of the RMA algorithm. First, RMA iterates through the trajectories in the trajectory set R. And perform the completion operation. Specifically, Representing the trajectory The adjacent dwelling point. ,in .like or , indicating a station and Located in an adjacent grid. Otherwise, intermediate points need to be filled in.

[0143] RMA calculation with and Line segments and grids at endpoints Number of intersections If the number of intersection points is 2 (i.e. =2), indicating that the line segment passes through the grid. The coordinates of these coordinates represent the points that need to be filled in. The grid... Add trajectory completion candidate set .

[0144] After identifying all the remaining outposts, they need to be aligned according to their grid adjacency relationships. Sorting. Because the user's movement direction is unique, each dwell point... exist Only one adjacent grid can be found in the middle. Then... Perform a depth-first search: Search The adjacent grid is used as the next dwell point until the complete trajectory is obtained. .

[0145] For any trajectory If the number of missing dwell points is Then the trajectory completion phase of RMA is at most The process will inevitably terminate after this selection, and all missing points will be filled in. If the candidate set... Only by of Neighborhood composition, and the filtering rules only apply to If the above selection is made, the adjacent dwelling points after completion must satisfy the adjacency constraint. If a mandatory condition is applied during candidate selection... If the completed edge satisfies the same constraint, it will not introduce any spurious migrations beyond the observation.

[0146] Step 2.2, service preference estimation, calculates service preferences based on the completed trajectory set R′ and calculates network traffic based on the number of trajectories leaving each grid. Specifically, RMA traverses all trajectories passing through each grid to determine the direction of movement (assuming the trajectory direction is consistent with the device orientation). Adjacent dwell point pairs... The coordinate difference is either 0 or 1 unit. The orientation of the equipment can be calculated by analyzing the differences between adjacent coordinates. :

[0147] (9)

[0148] Network traffic can be obtained by analyzing the orientation of devices. RMA returns the network traffic set F; then, according to formula (8), the service preference is obtained, and RMA returns the service preference set. .

[0149] In step 2.3, network latency awareness is assumed to be achieved by assuming a cache hit. RMA iterates through each service and connectable edge server to calculate network latency, and then returns the network latency sets D and E.

[0150] Furthermore, step 3.1 employs a local evolution strategy. The main goal of local evolution is to fully explore and utilize the existing knowledge structure within the subgroup before environmental changes occur, thereby improving the quality of the current solution set and enhancing the subgroup's adaptability. Inspired by Competitive Swarm Optimizer (CSO), individuals within the subgroup are distinguished into winners and losers through a competitive mechanism. Losers learn the behavioral characteristics of winners to achieve self-update, thereby improving overall search capabilities and accelerating convergence to the Dynamic Pareto Optimum (DPSO). Unlike traditional CSO, DCMOA selects learning objects based on an angle matching strategy, rather than random pairing. Specifically, the smaller the angle between the vectors of two particles in the search space, the closer their positions and the more consistent their directions are in the solution space. Therefore, DCMOA calculates the angle information between particles, pairing losers with winners who are most similar in angle, thus achieving more efficient knowledge transfer.

[0151] Let the first In the iteration, the position and velocity of the loser particle are respectively and The position of the winner particle is The average position of the population is The control parameters are random coefficients The speed and position update rules for the loser are as follows:

[0152] (10)

[0153] (11)

[0154] Among them: the first item Maintain the individual's original search inertia; the second item : To learn from winner; the third item : Guide losers closer to the group center to enhance stability. For integer or discrete coding problems, the updated Discretization and constraint repair operations are required to ensure that the solution remains in the feasible space.

[0155] (12)

[0156] To improve learning efficiency, DCMOA does not use random matching, but rather selects learning objects based on angular distance. (Settings) and The included angle between them is:

[0157] (13)

[0158] like The smallest value indicates that the two are closest in direction within the search space. From that study.

[0159] The evolutionary process of local evolution is as follows, with the input parameter being: the set of winning particles in the i-th subpopulation. With the Loser Particle Set First, calculate the angle values ​​of each particle in the winner's and loser's particle sets. Note that... and These represent the number of loser and winner particles, respectively. Then, the set of loser particles is... Each particle in the match winner particle set The particle with the smallest angle with it. Then, the loser particles are updated using formulas 10 and 11 respectively. The speed and position of the particle are updated by adjusting the speed and position of the winning particle. Learning to implement. Ultimately, the updated set of loser particles. Return and replace the original. The set of loser particles in the subpopulation.

[0160] Step 3.2 adopts a global co-evolution strategy. The core idea of ​​this mechanism is to utilize the overlap of optimization goals of subgroups, share excellent individuals in overlapping areas of the search space to provide effective guidance, and enhance global exploration through experience sharing in non-overlapping areas. Based on this, DCMOA constructs an external experience pool to gather excellent individuals, selects elite solutions based on non-dominant relationships, and co-guides the evolution of each subgroup to achieve an efficient balance between local convergence and global exploration.

[0161] The process of global co-evolution is as follows: The input contains all subpopulations. A group (by subscript) (Indexing).

[0162] First, to enhance the global adaptability of subgroup i, an external experience pool is first collected from the winners' set of all subgroups:

[0163] (14)

[0164] Subsequently, from The set of high-quality external individuals is obtained by screening based on the Pareto non-dominance criterion.

[0165] (15)

[0166] Then, for each winner in the i-subgroup Randomly select one External nondominated solutions And perform an integer crossover operation:

[0167] (16)

[0168] To ensure the feasibility of the solution, a repair operation is performed on the crossover results:

[0169] (17)

[0170] Final Update It will be returned to the subpopulation for the next generation of evolution.

[0171] Furthermore, step 4 addresses environmental changes through a dynamic feedback mechanism. To mitigate the failure of the Co-Cache and Task Offloading (CO-SC) decision-making process due to sudden environmental changes in dynamic environments, DCMOA introduces a Dynamic Feedback Mechanism (DFM). When an environmental change is detected, DFM integrates three strategies: diversity feedback (introducing random solutions to maintain the breadth of the population search), memory feedback (reusing historical representative solutions to accelerate convergence), and prediction feedback (mining stable patterns in the historical dynamic Pareto optimal solution set (DPOS) based on a Naive Bayes model, such as edge server topology and vehicle movement patterns, to predict potential optimal solution regions in the new environment), quickly generating a high-quality initial subpopulation and avoiding searching from scratch. This mechanism organically integrates exploration, experience reuse, and intelligent prediction, significantly improving the adaptive optimization efficiency of the algorithm in scenarios such as dynamic vehicle networks. To achieve the above prediction function, this invention uses a Naive Bayes classifier to analyze the historical DPOS. Let the historical DPOS set be... Each solution Corresponding multi-objective function values:

[0172] (18)

[0173] According to the Pareto dominance definition:

[0174] (19)

[0175] like No inferior to in all objectives If it is better than at least one objective, then it is called... Dominate .

[0176] Based on this, the historical DPOS is divided into two training subsets according to the dominance relationship:

[0177] (20)

[0178] in This represents an individual that dominates at least one other solution (a sample of optimal solutions). This represents an individual (dominated solution sample) that is dominated by at least one other solution. The training dataset consists of:

[0179] (twenty one)

[0180] And it was trained using a Naive Bayes classification model:

[0181] (twenty two)

[0182] Subsequently, a large number of candidate solutions were randomly generated under the new environment. Make a prediction:

[0183] (twenty three)

[0184] Select from the predicted optimal solution categories (i.e.) The individual formation prediction solution set:

[0185] (twenty four)

[0186] Finally, a new initial subpopulation is generated by combining the three feedback mechanisms:

[0187] (25)

[0188] This hybrid initialization strategy, while ensuring diversity, can make full use of historical and predictive information to achieve efficient dynamic optimization that can quickly adapt to new environments.

[0189] In the simulation experiments, five representative algorithms were employed, including three multi-objective optimization algorithms (i.e., Dynamic Non-Dominated Sorting Genetic Algorithm II (DNSGAII), Local Multi-Objective Cuckoo Search Optimization Algorithm (LMOCSO), and Local Multi-Objective Particle Swarm Optimization Algorithm (LMPSO)) and two heuristic algorithms (i.e., Simplified Cuckoo Search Task Offloading Algorithm (SCTOA) and Randomized Algorithm (RA)). Specifically, when the environment changes, similar to DNSGAII, 80% of the solutions in LMOCSO and LMPSO are retained in the new environment, while the remainder are randomly generated. Furthermore, SCTOA is a heuristic design where service caching decisions are made using the least recently used algorithm, with each task selecting the most economical decision for offloading. RA is a randomized strategy that randomly generates and computes offloading and service caching decisions.

[0190] This experiment mainly studies the relationship between edge server computing power, edge server cache size, number of tasks, and four optimization indicators: system energy consumption, latency, load balancing, and cache hit rate. The specific experimental content is as follows:

[0191] (1) Analysis of the relationship between edge server computing power and system latency, energy consumption, load balancing, and cache hit rate:

[0192] from Figure 1 , 2 As can be seen from points 3 and 4, system latency decreases across all algorithms with increasing computing power, indicating improved computational efficiency. DCMOA and DNSGA-II perform best in terms of latency, significantly reducing it, while RA performs relatively poorly across all computing capabilities. Similar to latency, energy consumption decreases with increasing computing power. DCMOA and LMOCSO excel in reducing energy consumption, while RA's relatively high energy consumption indicates inefficiency when handling higher computing power. With increased computing power, cache hit rate improves, further reducing content retrieval time. DCMOA and LMOCSO show the best cache hit rate, utilizing the cache more effectively. Load imbalance decreases with increasing computing power, indicating more efficient task distribution across edge servers. DCMOA and LMOCSO perform well in load balancing, effectively reducing server load differences. RA, however, exhibits high load imbalance, indicating its inefficiency in this area.

[0193] (2) Analysis of the relationship between edge server caching resources and system latency, energy consumption, load balancing, and cache hit rate:

[0194] from Figure 5 , 6Figures 7 and 8 show that as computing power increases, system latency decreases across all algorithms, indicating improved computational efficiency. In terms of latency, DCMOA and DNSGA-II perform best, significantly reducing latency, while RA performs relatively poorly across all computing power levels. Similar to latency, energy consumption decreases with increasing computing power. DCMOA and LMOCSO excel in reducing energy consumption, while RA's relatively high energy consumption indicates inefficiency when handling higher computing power. With increased computing power, cache hit rate improves, further reducing content retrieval time. DCMOA and LMOCSO show the best cache hit rate, utilizing the cache more effectively. Load imbalance decreases with increasing computing power, indicating more efficient task distribution among edge servers. DCMOA and LMOCSO perform well in load balancing, effectively reducing server load differences. RA, however, exhibits high load imbalance, indicating its inefficiency in this area. These experimental results demonstrate the crucial role of edge server computing power in optimizing system performance. By balancing computational offloading and service caching, the algorithm can significantly improve the system's responsiveness, energy efficiency, and load distribution. Among them, the DCMOA algorithm performs best in all aspects and is the most effective optimization solution.

[0195] (3) Analysis of the relationship between the number of system tasks and system latency, energy consumption, load balancing, and cache hit rate:

[0196] like Figure 9 As shown, in terms of specific performance, latency increases for all algorithms with increasing tasks, but DCMOA consistently maintains the lowest latency, significantly outperforming other methods even when the task load reaches 300. This indicates that the present invention is more robust in scheduling and cache coordination, effectively alleviating queuing and transmission bottlenecks under high pressure. Regarding energy consumption, the overall curve rises with increasing task count, but DCMOA exhibits the slowest energy consumption increase, demonstrating better energy efficiency management. In contrast, RA and SCTOA show a sharp increase in energy consumption with increasing tasks, indicating a lack of global optimization for energy efficiency in their resource allocation. As for cache hit rate, it generally decreases with increasing task count, reflecting more frequent contention and replacement of cache resources. Nevertheless, DCMOA consistently maintains the highest hit rate, remaining above 70% even under high load scenarios, significantly higher than other algorithms by 5–10 percentage points. This demonstrates that DCMOA maintains superior cache utilization efficiency even with expanding task scale. Regarding load balancing, the curves for all algorithms rise with increasing tasks, indicating a widening pressure gap between nodes. However, DCMOA experienced the slowest growth and had the lowest overall imbalance, indicating that it better controlled congestion at hot nodes and achieved balanced task scheduling.

Claims

1. A mobile edge computing offloading method based on multi-population dynamic co-evolution, characterized in that... The method includes the following steps: First, initialize multiple subgroups, each subgroup corresponding to a specific set of objectives, to process dynamic multi-objective optimization problems in parallel; Second, utilize regional mobility characteristic perception algorithms to perceive user mobility characteristics and business preferences; 2.1 Trajectory Completion: Complete the user trajectory and handle missing stops in the middle; 2.2 Service Preference Estimation: Calculate service preferences based on the completed trajectory set; 2.3 Network latency awareness: computing system latency; 3. Design a multi-population co-evolution method to utilize knowledge transfer between subpopulations to co-evolve each subpopulation; 3.1 Local evolution strategy: Divide individuals into a winner set and a loser set through a competition mechanism based on angle matching; 3.2 Global Co-evolution Strategy: Integrate the winner sets of different subgroups into an external knowledge pool, and extract the global optimal solution set based on the Pareto non-dominance criterion; Fourth, by responding to environmental changes through a dynamic feedback mechanism, high-quality solutions for subspecies populations can be obtained quickly.

2. The mobile edge computing offloading method based on multi-population dynamic co-evolution as described in claim 1, characterized in that, The mathematical expression for the dynamic multi-objective optimization (DMOP) in step 1 is as follows: (1) in, yes Bounded by decision space The decision vector of dimension, It is a time parameter. yes The objective function, for the service caching / edge computing problem, is defined as: (2) in, This represents the average system latency, which needs to be minimized. Represents the total energy consumption of the system. Represents load balancing in the system. A negative value representing the system cache hit rate; In DMOP, the dynamic Pareto optimal set or dynamic Pareto optimal frontier based on dynamic Pareto dominance is defined as follows: Definition 1: Dynamic Pareto Advantage At time, a decision vector This is known as another decision vector dominated by Pareto. , If and only if (3) Definition 2 Dynamic Pareto Optimal Set (DPSO) time The dynamic Pareto optimal set at time t is denoted as DPSO(t), including time t. All solutions that are not dominated by any other solution are defined as follows: (4) Definition 3 Dynamic Pareto Optimal Front (DPOF) Dynamic Pareto optimal frontier in time The above is represented as , is in the target space The mapping of solutions is represented as follows: (5) To reduce the complexity of direct search for high-dimensional targets, a target decomposition strategy is adopted to simplify the original problem. It is decomposed into a set of low-dimensional subproblems. The subproblems are divided as follows: Subproblem 1: Minimize Subproblem 2: Minimize Subproblem 3: Minimize Subproblem 4: Minimize The original optimization problem The reconstruction involves solving the aforementioned sub-problems in parallel, thereby quickly discovering good local structures in a lower-dimensional search space and merging them into an approximate dynamic Pareto front through global collaboration. To ensure consistency across different target scales, dynamic normalization of each target is required during the search process to avoid search bias caused by scale differences. Population initialization uses fixed-length integer encoding to represent each candidate solution. The encoding vector consists of two parts: the first part represents the service caching decision of the edge server, and the second part represents the task offloading decision for the vehicle or user. During population initialization, the total population size is... The data is evenly distributed among four subgroups, meaning each subgroup is randomly generated. Initially, select individuals to ensure search diversity. Then, based on the aforementioned four sub-problems... Construct four corresponding subgroup sets: Each subgroup is optimized for different combinations of objectives: (6) Efficient exploration in low-dimensional subspaces is achieved through a multi-subgroup structure, while global collaboration maintains the diversity and convergence of the overall solution set.

3. The mobile edge computing offloading method based on multi-population dynamic co-evolution as described in claim 1, characterized in that, Step 2.1, trajectory completion, involves performing trajectory completion operations on all user trajectories, handling missing intermediate dwell points. The trajectory processing method is as follows: (7) The completed trajectory set is obtained as follows: (8) in To supplement the existing outposts; During the trajectory completion phase of the RMA algorithm, firstly, RMA traverses the trajectories in the trajectory set R. And perform the completion operation, specifically, Representing the trajectory The adjacent outposts, ,in ,like or , indicating a station and If it is located in an adjacent grid, otherwise the intermediate point needs to be filled in; RMA calculation with and Line segments and grids at endpoints Number of intersections If the number of intersection points is 2, that is... =2 indicates that the line segment passes through the grid. The coordinates of these coordinates represent the points that need to be filled in. The grid... Add trajectory completion candidate set ; After identifying all the remaining outposts, they need to be aligned according to their grid adjacency relationships. Sort, then... Perform a depth-first search: Search The adjacent grid is used as the next dwell point until the complete trajectory is obtained. ; For any trajectory If the number of missing dwell points is Then the trajectory completion phase of RMA is at most The process will inevitably terminate after this selection, and all missing points will be filled in. If the candidate set... Only by of Neighborhood composition, and the filtering rules only apply to If the above selection is made, the adjacent dwelling points after completion must satisfy the adjacency constraint. If the candidate selection is subject to a mandatory condition... If the completed edge satisfies the same constraint, it will not introduce any spurious migrations beyond the observation. In step 2.2, service preference estimation is performed. Service preference is calculated based on the completed trajectory set R′, and network traffic is calculated based on the number of trajectories leaving each grid. RMA traverses all trajectories passing through each grid to determine the direction of movement, and adjacent dwell point pairs are used. The coordinate difference is either 0 or 1 unit. The orientation of the equipment can be calculated by analyzing the differences between adjacent coordinates. : (9) Network traffic can be obtained by analyzing the orientation of devices. RMA returns the network traffic set F; then, according to formula (8), the service preference is obtained, and RMA returns the service preference set. ; In step 2.3, during network latency awareness, assuming a cache hit, RMA iterates through each service and the connectable edge server to calculate network latency, and then returns the network latency sets D and E.

4. The mobile edge computing offloading method based on multi-population dynamic co-evolution as described in claim 1, characterized in that, Step 3.1 employs a local evolution strategy. The main goal of local evolution is to fully explore and utilize the existing knowledge structure within the subgroup before environmental changes occur, thereby improving the quality of the current solution set and enhancing the subgroup's adaptability. Inspired by Competitive Group Optimization (CSO), individuals within the subgroup are distinguished into winners and losers through a competitive mechanism. Losers learn the behavioral characteristics of winners to achieve self-updating, thereby improving overall search capabilities and accelerating convergence to the Dynamic Pareto Optimum (DPSO). The smaller the angle between the vectors of two particles in the search space, the closer their positions and the more consistent their directions are in the solution space. Therefore, DCMOA calculates the angular information between particles, pairing losers with the winners most similar in angle, thus achieving more efficient knowledge transfer. Let the first In the iteration, the position and velocity of the loser particle are respectively and The position of the winner particle is The average position of the population is The control parameters are random coefficients The speed and position update rules for the loser are as follows: (10) (11) Among them: the first item Maintain the individual's original search inertia; the second item : To learn from the winner; the third item : Guide losers closer to the group center to enhance stability; for integer or discrete coding problems, the updated... Discretization and constraint repair operations are required to ensure that the solution remains in the feasible space. (12) To improve learning efficiency, DCMOA does not use random matching, but rather selects learning objects based on angular distance and sets... and The included angle between them is: (13) like The smallest value indicates that the two are closest in direction within the search space. From that study; The evolutionary process of local evolution is as follows, with the input parameter being: the set of winning particles in the i-th subpopulation. With the Loser Particle Set First, calculate the angle values ​​of each particle in the winner's and loser's particle sets. and These represent the number of loser and winner particles, respectively. Then, for each particle in the loser particle set, match it with the particle in the winner particle set with which it has the smallest angle. Subsequently, update the loser particle set using formulas 10 and 11. The speed and position of the particle are updated by adjusting the speed and position of the winning particle. Learning to achieve this, ultimately, the updated set of loser particles is returned and replaces the original set. The set of loser particles in the subpopulation; Step 3.2 adopts a global co-evolution strategy, which utilizes the overlap of optimization goals of subgroups to share excellent individuals in overlapping areas of the search space to provide effective guidance, and enhances global exploration through experience sharing in non-overlapping areas. Based on this, DCMOA constructs an external experience pool to gather excellent individuals, selects elite solutions based on non-dominant relationships, and co-guides the evolution of each subgroup to achieve an efficient balance between local convergence and global exploration. The process of global co-evolution is as follows: The input contains all subpopulations. A group By subscript Perform indexing; First, to enhance the global adaptability of subgroup i, an external experience pool is first collected from the winners' set of all subgroups: (14) Subsequently, from The set of high-quality external individuals is obtained by screening based on the Pareto non-dominance criterion. (15) Then, for each winner in the i-subgroup Randomly select one External nondominated solutions And perform an integer crossover operation: (16) To ensure the feasibility of the solution, a repair operation is performed on the crossover results: (17) Final Update It will be returned to the subpopulation for the next generation of evolution.

5. The mobile edge computing offloading method based on multi-population dynamic co-evolution as described in claim 1, characterized in that, Step 4 addresses environmental changes through a dynamic feedback mechanism. To mitigate the failure of the Co-Center for Joint Caching and Task Offloading (CO-SC) decisions due to sudden environmental changes in dynamic environments, DCMOA introduces a Dynamic Feedback Mechanism (DFM). When an environmental change is detected, DFM integrates three strategies: diversity feedback, memory feedback, and prediction feedback to quickly generate a high-quality initial subpopulation, avoiding a search from scratch. This mechanism organically integrates exploration, experience reuse, and intelligent prediction, improving the algorithm's adaptive optimization efficiency in scenarios such as dynamic vehicle networks. To achieve the aforementioned prediction function, a Naive Bayes classifier is used to analyze historical DPOS values. Let the historical DPOS set be... Each solution Corresponding multi-objective function values: (18) According to the Pareto dominance definition: (19) like No inferior to in all objectives If it is better than at least one objective, then it is called... Dominate ; Based on this, the historical DPOS is divided into two training subsets according to the dominance relationship: (20) in This represents the individual that dominates at least one other solution, i.e., the sample of optimal solutions. An individual that is dominated by at least one other solution is called a suboptimal solution sample. The training dataset consists of: (21) And it was trained using a Naive Bayes classification model: (22) Subsequently, a large number of candidate solutions were randomly generated under the new environment. Make a prediction: (23) Select from the predicted optimal solution categories (i.e.) The individual formation prediction solution set: (24) Finally, a new initial subpopulation is generated by combining the three feedback mechanisms: (25) This hybrid initialization strategy, while ensuring diversity, can make full use of historical and predictive information to achieve efficient dynamic optimization that can quickly adapt to new environments.

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