An enhanced data encoding-decoding algorithm

Abstract

The application belongs to the technical field of granular computing, and particularly relates to an enhanced data coding-decoding algorithm, which comprises the following steps: step 1: mining the granulation-degranulation process of data on a fuzzy set, constructing a granulation model according to a performance index J, and constructing a degranulation model according to a reconstruction error V; step 2: taking the minimization of the reconstruction error V as an objective, improving a particle swarm optimization algorithm, and adopting a grouping-crossing optimization mode when searching for a data center v by using the particle swarm optimization algorithm, so as to improve the data reconstruction accuracy. The application can effectively reduce the reconstruction error and improve the reconstruction accuracy.

Description

Technical Field

[0001] This invention belongs to the field of granular computing technology, specifically relating to an enhanced data encoding-decoding algorithm. Background Technology

[0002] The development of granular computing theory stems from the need for modeling and analyzing complex systems. In fields such as artificial intelligence, biology, and social sciences, the behavior of complex systems is often influenced by multiple factors. Traditional mathematical models and analysis methods are often insufficient to fully describe the evolution and behavior of systems. Granular computing theory, by introducing the concept of particles, provides a new approach and tool that can better characterize and understand these complex systems.

[0003] In granular computing, particles are information carriers that can express and process information, thereby describing the behavior and evolution of a system. Granulation and degranulation mechanisms are important concepts in granular computing theory, and they are of great significance for understanding and simulating the evolution and behavior of complex systems.

[0004] Granulation is the process of rationally dividing and organizing information or data in a system into particle units with specific meanings and functions. Through granulation, the information of complex systems can be abstracted into simpler and more easily processed particle forms, thus facilitating system modeling and analysis. Degranulation, on the other hand, recombines or restores granulated information to its original data form; this mechanism allows granulated information to return to its original state, thereby enabling a better understanding and interpretation of the specific details of system behavior.

[0005] By granulating system information, we can better abstract and describe system characteristics, thereby establishing more effective models and analysis methods. Conversely, degranulation mechanisms allow us to reconstruct the system's details and interactions at the particle level, helping us understand the mechanisms and patterns behind system behavior. Therefore, research on granulation-degranulation mechanisms is of great significance for promoting the development of complex systems theory, advancing interdisciplinary research, and improving the ability to model and analyze complex systems.

[0006] In the existing technology, YANG et al. proposed a trend-oriented time series granulation method, which transforms a long numerical time series into a relatively short time series composed of a set of linear fuzzy information particles (LFIG) of different sizes. The transformed fine-grained time series not only captures the main features of the original time series such as trends and fluctuations, but also saves the computational cost of time series clustering.

[0007] XU et al. proposed a novel degranulation scheme that optimizes the membership matrix through a series of matrix operations. They constructed a bidirectional generalized rotation model between the numerical data subspace and the granular prototype subspace, and based on this model, modified the prototype matrix, thereby optimizing the membership matrix and enhancing the data granulation mechanism. During the degranulation process, they utilized mathematical methods such as matrix optimization and inverse solving to modify the membership matrix, reducing reconstruction errors.

[0008] However, the above-mentioned technical solutions all focus on how to optimize the part of the granulation process in granular computing theory, while ignoring the data reconstruction error in the degranulation process. In the granulation-degranulation model, the granulation process and the degranulation process are holistic. Existing research usually ignores the data reconstruction problem in the degranulation process and only optimizes the fuzzy clustering process in the granulation process, resulting in a large data reconstruction error in the degranulation process, which affects the reconstruction accuracy. Summary of the Invention

[0009] The purpose of this invention is to provide an enhanced data encoding-decoding algorithm that can effectively reduce reconstruction errors and improve reconstruction accuracy.

[0010] The specific technical solution adopted by this invention is as follows:

[0011] An enhanced data encoding-decoding algorithm includes the following steps:

[0012] Step 1: Mining data through the granulation-degranulation process on fuzzy sets, constructing a granulation model based on performance index J, and constructing a degranulation model based on reconstruction error V;

[0013] Step 2: With the goal of minimizing the reconstruction error V, improve the particle swarm optimization algorithm by adopting a grouping-crossover optimization mode when searching for the data center v using the particle swarm optimization algorithm to improve the data reconstruction accuracy.

[0014] Further, step 1 includes the following steps:

[0015] Step 101: Construct a traditional data granulation-degranulation model;

[0016] Step 102: Optimize the data degranulation model using the particle swarm optimization algorithm.

[0017] Furthermore, the granulation-degranulation process of the data on the fuzzy set includes the following steps:

[0018] When granulating data for fuzzy sets, after the information granulation process is complete, each data x can be described by a set of membership degrees, as follows:

[0019] G:R n →[0,1]c

[0020] Where G represents the data granulation process, n represents the dimension of the feature space, and c is the number of data centers;

[0021] Degranulation can be viewed as an inverse operation on already granulated data; that is, the goal is to reconstruct x based on the membership vector. Specifically, the degranulation process can be represented by the function G. -1 The following is an expression:

[0022] G -1 [0,1] c →R n

[0023] Among them, G -1 This represents the data degranulation process, where n represents the dimension of the feature space and c represents the number of data points.

[0024] Furthermore, the formula for calculating the performance index J is as follows:

[0025]

[0026] Where c is the number of data centers, N is the total number of data points, and u ik Representing data x k For the i-th data center v i The membership degree, m (m>1) represents the fuzziness coefficient, usually with a default value of 2.0. The distance function ||·|| used in the above formula is a weighted Euclidean function, expressed as follows:

[0027]

[0028] Where n is the number of data dimensions, σ j Let represent the standard deviation of the j-th variable.

[0029] Furthermore, the formula for calculating the reconstruction error V is as follows:

[0030]

[0031] Where N is the total number of data points. The formula for the reconstructed data is:

[0032]

[0033] Where c is the number of data centers, and matrix u is the membership matrix of data x to c data centers v, and its formula is:

[0034]

[0035] Where c is the number of data centers and m is the fuzziness coefficient.

[0036] Furthermore, step 2 includes the following steps:

[0037] Step 201: Randomly generate a particle swarm containing N particles, and divide the entire particle swarm into k groups;

[0038] Step 202: Assign different values ​​w, c1, c2 to each group, and record the optimal individual b1, b2, b3, ..., b in each group after each iteration. k And the worst individual in each group, e1, e2, e3, ..., e k ;

[0039] Step 203: Keeping the best individual in each group unchanged, replace the worst individual in each group with the best individual from the previous group, i.e., replace e2 with b1, replace e3 with b2, and so on. To maintain closed-loop stability, replace e1 with b... k ;

[0040] Step 204: Continue iterating until the maximum number of iterations is reached, then stop and output the best individual and the best fitness value in the entire particle swarm.

[0041] Furthermore, the particle swarm optimization algorithm (GCPSO) includes the following steps:

[0042] Step 1: Initialize the particle swarm P;

[0043] Step 1-1: Divide the entire particle swarm P into t groups, and denote each particle group as Pt. i Let i = 1, 2, ..., t, and set a learning factor c within each group. i1 = rand(0.8, 1.2), c i2 = rand(0.8, 1.2);

[0044] Step 1-2: Initialize particle grouping P i ={z ip}, i = 1, 2, ..., t, p = 1, 2, ..., k, where k is the number of particles in the group; each particle is represented by z. ip ={x ip v ip}, i = 1, 2, ..., t, p = 1, 2, ..., k, where x ip Let i = 1, 2, ..., t, p = 1, 2, ..., k be the position of particle p in the i-th group within the solution space. The size of the solution space is determined by the data dimension n and the number of data centers c. ip p = 1, 2, ..., k is the velocity of particle p in the i-th group within the solution space, and the initial value is randomly generated within the solution space;

[0045] Step 2: Initialize the iteration count g = 1;

[0046] Step 3: Set z igbest z is the particle with the best fitness in the current i-th group. igworst Let be the particle with the worst fitness in the current i-th group, where the fitness function is .

[0047] Step 3-1: i = 1;

[0048] Step 3-2: Calculate the velocity for the next iteration within the i-th group using the velocity update formula. The speed update formula is:

[0049]

[0050] in, Let p be the velocity of the p-th particle in the i-th group during the g-th iteration. Let x be the position of the p-th particle in the i-th group during the g-th iteration. ipbest x represents the optimal position of the p-th particle in the i-th group during its motion. igbest Let w be the optimal position for all particles in the i-th group during their motion, and c be the inertial weight. i1 c i2 Let r1 and r2 be the learning factors for the i-th group, and r1 and r2 be random numbers.

[0051] Step 3-3: Calculate the position for the next iteration within the i-th group using the position update formula. The position update formula is:

[0052]

[0053] in, Let p be the position of the p-th particle in the i-th group during the (g+1)-th iteration. Let p be the position of the p-th particle in the i-th group during the g-th iteration. Let be the velocity of the p-th particle in the i-th group during the (g+1)-th iteration;

[0054] Steps 3-4: Update z igbest , z igworst These are the best and worst particles in the current i-th group;

[0055] Step 3-5: i = i + 1;

[0056] Step 3-6: If i ≤ t, then return to Step 3-2;

[0057] Step 4: Group each particle into its worst-performing particle z in the swarm.igworst The best particle z in the adjacent particle group i-1gbest exchange;

[0058] Step 4-1: i = 1;

[0059] Step 4-2: z igworst =z tgbest ;

[0060] Step 4-3: i = i + 1;

[0061] Step 4-4: z igworst =z i-1gbest ;

[0062] Step 4-5: If i < t, then return to Step-4-3;

[0063] Step 5: g = g + 1;

[0064] Step 6: If g ≤ G, return to Step 3; otherwise, select the best particle z for each particle group. igbest The best particle in the swarm is z, which is considered the best particle in the entire swarm. gbest , where G is the upper limit of iteration.

[0065] The technical effects achieved by this invention are as follows:

[0066] (1) The enhanced data encoding-decoding algorithm of the present invention comprehensively considers the granulation process and the degranulation process in the data granulation-degranulation process. The performance index is optimized in the granulation process, and the reconstruction error is optimized by using a new degranulation model in the degranulation process, which improves the accuracy of the whole process.

[0067] (2) The enhanced data encoding-decoding algorithm of the present invention takes into account the resource constraints in actual use, uses fewer computing resources, and ensures that the reconstruction error meets the requirements. This reduces resource waste and lowers costs.

[0068] (3) An enhanced data encoding-decoding algorithm of the present invention can search for the best data center in the solution space through the grouping-crossing particle swarm algorithm. This takes into account the problem of getting trapped in local optima in the particle swarm algorithm, effectively reducing reconstruction error and improving reconstruction accuracy. Attached Figure Description

[0069] Figure 1 This is a flowchart of the particle swarm optimization algorithm of the present invention;

[0070] Figure 2 This is an algorithm description diagram of the GCPSO algorithm of this invention;

[0071] Figure 3 This is a diagram illustrating the granulation-degranulation model of the present invention. Detailed Implementation

[0072] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0073] like Figure 1-3 As shown, an enhanced data encoding-decoding algorithm includes the following steps:

[0074] Step 1: Mining data through the granulation-degranulation process on fuzzy sets, constructing a granulation model based on performance index J, and constructing a degranulation model based on reconstruction error V;

[0075] Here, step 1 includes the following steps:

[0076] Step 101: Construct a traditional data granulation-degranulation model;

[0077] The construction of data information particles in this study is mainly based on fuzzy sets. When constructing information particles oriented towards fuzzy sets, after the information refinement process is completed, each data x can be described by a set of membership degrees, as shown below:

[0078]

[0079] Here, G represents the data granulation process, n represents the dimension of the feature space, and c is the number of information particles. The degranulation process can be viewed as performing an inverse operation on the already granulated data; that is, our goal is to reconstruct x based on the membership vector. Specifically, the degranulation process can be represented by the function G. -1 It can be represented in the following forms:

[0080] G -1 [0,1] c →R n (2)

[0081] Ideally, we expect to degranulate the data. It equals the original data x, that is in However, ideal granulation-degranulation does not exist, so non-zero reconstruction errors are introduced into the granulation-degranulation process. The ability of the resulting information particles to represent and represent the original data can be quantified by the accumulated reconstruction error, thus measuring the degree of difference between the reconstructed data and the original data. The principle of data granulation-degranulation plays an important role in granular computing. Conceptually, data granulation refers to the process of constructing a set of information particles that captures the essence of the original dataset. Each data point can then be represented by the resulting information particles. The reconstruction of the original data is achieved through the degranulation process, and the quality of the reconstruction is quantified based on the associated reconstruction error. Suppose there is a set of digital data {x1, x2, ..., x...} N}, where x i ∈R n i = 1, 2, ..., N. Various fuzzy clustering algorithms are used to generate fuzzy sets of granular data, especially the Fuzzy C-means (FCM), which has been applied as the most common method and algorithmic framework for achieving information granulation. The essence of the fuzzy data granulation-degranulation mechanism is shown in the figure below. After clustering is completed, we obtain a set of data centers and a corresponding partitioning matrix. Each digital data can be represented by the fuzzy set returned by the clustering algorithm through granulation. Then, the degranulation process realizes the reconstruction of the original data. In the granulation-degranulation process, we can imagine some optimization mechanisms involved to minimize the reconstruction error.

[0082] In granular computing theory, the granulation-degranulation model consists of two parts: the granulation process and the degranulation process. The granulation process is the process of generating data centers and membership matrices based on the original data, while the degranulation process is the process of generating reconstructed data based on the data centers and membership matrices.

[0083] Optimization of fuzzy clustering, such as the FCM algorithm used in our study, first sets the objective function J and then uses the data centers {v1, v2, ..., v...}. c} and membership matrix U = [u ik ] c×N The iteration guides the objective function J towards minimization. The performance metric J is defined as follows:

[0084]

[0085] Among them, u ik Representing data x k The membership degree of the i-th cluster, m (m>1), represents the fuzziness coefficient, typically with a default value of 2.0. The distance function ||·|| used in the above formula is a weighted Euclidean function, expressed as follows:

[0086]

[0087] Where, σ j Let represent the standard deviation of the j-th variable. By terminating the clustering process, the original data is divided into c fuzzy clusters by a matrix U = [u ik ] c×N The data is represented in the form of i = 1, 2, ..., c; k = 1, 2, ..., N. Numerical data x k The granulation result can be obtained using the membership matrix vector u(x) k )=[u 1k ,u 2k ,...u ck ] indicates that u ik The calculation method is as follows:

[0088]

[0089] During the degranulation process, x was implemented based on the data center and membership vector. k The reconstruction. Assume the function for reconstructing the data is Q, which represents minimizing the reconstructed data. With data center v i The mathematical model for the distance between them is shown below:

[0090]

[0091] A gradient-based method was used to optimize the performance metric to its minimum. Therefore, data x k The reconstruction result is shown below:

[0092]

[0093] Under ideal conditions, we expect the reconstructed data after degranulation to be identical to the original data, which means... Non-zero degranulation errors are common in practice. We need to optimize the corresponding granulation-degranulation mechanism to minimize the associated reconstruction error, thus obtaining the reconstruction error V. The performance of the granulation-degranulation mechanism can be quantified using the following performance metrics:

[0094]

[0095] Step 102: Optimize the data degranulation model using the particle swarm optimization algorithm;

[0096] Analysis reveals that optimizing the number of clusters, data centers, and fuzziness coefficients is essential for reducing error values ​​in granulation-degranulation models. Therefore, this study proposes an optimization method for granulation-degranulation models, the core step of which is to construct a degranulation model of the data using a particle swarm optimization algorithm. The specific design steps of this algorithm are as follows: First, a series of data centers v1', v'2, ..., v' are obtained through particle swarm optimization. c Then, according to formula (5), the degree to which each data belongs to the data center u is calculated. i ' k .

[0097]

[0098] Based on the searched data center v i ', i = 1, 2, ..., c, and membership value u i ' k Calculate degranulated data

[0099]

[0100] The performance of the data degranulation model obtained by the particle swarm optimization algorithm is evaluated by comparing the error value V' between the degranulated data and the original data.

[0101]

[0102] Finally, the searched data center v is continuously adjusted according to the direction that minimizes the error value. i Find the optimal data center and its corresponding membership matrix, i = 1, 2, ..., c, thereby reducing the error value of the degranulated data model.

[0103] Step 2: With the goal of minimizing the reconstruction error V, improve the particle swarm optimization algorithm (GCPSO). When using the particle swarm optimization algorithm to search for the data center v, adopt a grouping-crossover optimization mode to improve the data reconstruction accuracy.

[0104] Step 2 includes the following steps:

[0105] Step 201: Randomly generate a particle swarm containing N particles, and divide the entire particle swarm into k groups;

[0106] Step 202: Assign different values ​​w, c1, c2 to each group, and record the optimal individual b1, b2, b3, ..., b in each group after each iteration. k And the worst individual in each group, e1, e2, e3, ..., e k ;

[0107] Step 203: Keeping the best individual in each group unchanged, replace the worst individual in each group with the best individual from the previous group, i.e., replace e2 with b1, replace e3 with b2, and so on. To maintain closed-loop stability, replace e1 with b... k ;

[0108] Step 204: Continue iterating until the maximum number of iterations is reached, then stop and output the best individual and the best fitness value in the entire particle swarm.

[0109] like Figure 2-3 As shown, the above particle swarm optimization algorithm (GCPSO) includes the following steps:

[0110] Step 1: Initialize the particle swarm P;

[0111] Step 1-1: Divide the entire particle swarm P into t groups, and denote each particle group as Pt. i Let i = 1, 2, ..., t, and set a learning factor c within each group. i1 = rand(0.8, 1.2), c i2 = rand(0.8, 1.2);

[0112] Step 1-2: Initialize particle grouping P i ={z ip}, i = 1, 2, ..., t, p = 1, 2, ..., k, where k is the number of particles in the group; each particle is represented by z. ip ={x ip v ip}, i = 1, 2, ..., t, p = 1, 2, ..., k, where x ip Let i = 1, 2, ..., t, p = 1, 2, ..., k be the position of particle p in the i-th group within the solution space. The size of the solution space is determined by the data dimension n and the number of data centers c. ip p = 1, 2, ..., k is the velocity of particle p in the i-th group within the solution space, and the initial value is randomly generated within the solution space;

[0113] Step 2: Initialize the iteration count g = 1;

[0114] Step 3: Set z igbest z is the particle with the best fitness in the current i-th group. igworst Let be the particle with the worst fitness in the current i-th group, where the fitness function is .

[0115] Step 3-1: i = 1;

[0116] Step 3-2: Calculate the velocity for the next iteration within the i-th group using the velocity update formula. The speed update formula is:

[0117]

[0118] in, Let p be the velocity of the p-th particle in the i-th group during the g-th iteration. Let x be the position of the p-th particle in the i-th group during the g-th iteration. ipbest x represents the optimal position of the p-th particle in the i-th group during its motion. igbest Let w be the optimal position for all particles in the i-th group during their motion, and c be the inertial weight. i1 c i2 Let r1 and r2 be the learning factors for the i-th group, and r1 and r2 be random numbers.

[0119] Step 3-3: Calculate the position for the next iteration within the i-th group using the position update formula. The position update formula is:

[0120]

[0121] in, Let p be the position of the p-th particle in the i-th group during the (g+1)-th iteration. Let p be the position of the p-th particle in the i-th group during the g-th iteration. Let be the velocity of the p-th particle in the i-th group during the (g+1)-th iteration;

[0122] Steps 3-4: Update z igbest , z igworst These are the best and worst particles in the current i-th group;

[0123] Step 3-5: i = i + 1;

[0124] Step 3-6: If i ≤ t, then return to Step 3-2;

[0125] Step 4: Group each particle into its worst-performing particle z in the swarm. igworst The best particle z in the adjacent particle group i-1gbest exchange;

[0126] Step 4-1: i = 1;

[0127] Step 4-2: z igworst =z tgbest ;

[0128] Step 4-3: i = i + 1;

[0129] Step 4-4: z igworst =zi-1gbest ;

[0130] Step 4-5: If i < t, then return to Step-4-3;

[0131] Step 5: g = g + 1;

[0132] Step 6: If g ≤ G, return to Step 3; otherwise, select the best particle z for each particle group. igbest The best particle in the swarm is z, which is considered the best particle in the entire swarm. gbest , where G is the upper limit of iteration.

[0133] In the data granulation-degranulation process, this invention considers the entire process simultaneously, improving resource consumption, reducing reconstruction errors, and enhancing model performance. Specifically:

[0134] 1. Consideration of data reconstruction during degranulation: This invention comprehensively considers the granulation and degranulation processes in the data granulation-degranulation process. It optimizes performance indicators during the granulation process and uses a novel degranulation model to optimize reconstruction errors during the degranulation process, which improves the accuracy of the entire process.

[0135] 2. Reduced computational resource usage: This invention fully considers the resource constraints in actual use, employing fewer computational resources while ensuring that the reconstruction error meets requirements. This reduces resource waste and lowers costs.

[0136] 3. Comprehensive Optimization: This invention proposes a data granulation-degranulation model based on an improved particle swarm optimization algorithm. It can search for the optimal data center in the solution space through a grouping-crossover particle swarm algorithm. This takes into account the problem of getting trapped in local optima in the particle swarm algorithm, effectively reducing reconstruction error and improving reconstruction accuracy.

[0137] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained in this invention are implemented according to conventional methods in the art unless otherwise specified or limited.

Claims

1. An enhanced data encoding-decoding algorithm, characterized in that: comprising the following steps: Step 1: Mine the granulation-degranulation process of data on fuzzy sets, construct a granulation model according to the performance index J, and construct a degranulation model according to the reconstruction error V; Step 2: With the goal of minimizing the reconstruction error V, improve the particle swarm optimization algorithm, adopt a group-cross optimization mode when using the particle swarm optimization algorithm to search for the data center v, so as to improve the accuracy of data reconstruction.

2. The enhanced data encoding-decoding algorithm according to claim 1, characterized in that: Said Step 1 comprises the following steps: Step 101: Construct a traditional data granulation-degranulation model; Step 102: Use the particle swarm optimization algorithm to optimize the data degranulation model.

3. The enhanced data encoding-decoding algorithm according to claim 1, characterized in that: Said process of performing granulation-degranulation of data on fuzzy sets comprises the following steps: When performing data granulation for fuzzy sets, after the information granulation process is completed, each data x can be described by a membership set, which is expressed as follows: G:R n →[0,1] c wherein G represents the data granulation process, n represents the dimension of the feature space, and c is the number of data centers; Degranulation can be viewed as an inverse operation on already granulated data; that is, the goal is to reconstruct x based on the membership vector. Specifically, the degranulation process can be represented by the function G. -1 The following is an expression: G -1 :[0,1] c →R n Among them, G -1 This represents the data degranulation process, where n represents the dimension of the feature space and c is the number of data points.

4. The enhanced data encoding-decoding algorithm according to claim 1, characterized in that: The calculation formula of said performance index J is: Where c is the number of data centers, N is the total number of data points, and u ik Representing data x k For the i-th data center v i The membership degree, m (m>1) represents the fuzziness coefficient, usually with a default value of 2.

0. The distance function ||·|| used in the above formula is a weighted Euclidean function, expressed as follows: Where n is the number of data dimensions, σ j Let represent the standard deviation of the j-th variable.

5. An enhanced data encoding-decoding algorithm according to claim 1, characterized in that: The calculation formula of said reconstruction error V is: Where N is the total number of data points. The formula for the reconstructed data is: wherein c is the number of data centers, the matrix u is the membership matrix of the data x to c data centers v, and its formula is: wherein c is the number of data centers, and m is the fuzzification coefficient.

6. The enhanced data encoding-decoding algorithm according to claim 1, characterized in that: Said Step 2 comprises the following steps: Step 201: Randomly generate a particle swarm containing N particles, and divide the entire particle swarm into k groups; Step 202: Assign different values ​​w, c1, c2 to each group, and record the optimal individual b1, b2, b3, ..., b in each group after each iteration. k And the worst individual in each group, e1, e2, e3, ..., e k ; Step 203: Keep the best individual in each group unchanged, and replace the worst individual in each group with the best individual from the previous group; to maintain closed-loop stability, replace e1 with b. k ; Step 204: Continue the cyclic iteration, stop after reaching the maximum number of cycles, and output the optimal individual and the optimal fitness value in the entire particle swarm.

7. An enhanced data encoding-decoding algorithm according to claim 1, characterized in that: Said particle swarm optimization algorithm comprises the following steps: Step1: Initialize the particle swarm P; Step2: Initialize the number of iterations g=1; Step 3: Set z igbest z is the particle with the best fitness in the current i-th group. igworst Let be the particle with the worst fitness in the current i-th group, where the fitness function is . Step 4: Group each particle into its worst-performing particle z in the swarm. igworst The best particle z in the adjacent particle group i-1gbest exchange; Step5: g=g+1; Step 6: If g ≤ G, return to Step 3; otherwise, select the best particle z for each particle group. igbest The best particle in the swarm is z, which is considered the best particle in the entire swarm. gbest , where G is the upper limit of iteration.

8. An enhanced data encoding-decoding algorithm according to claim 7, characterized in that: Said Step1 comprises the following steps: Step 1-1: Divide the entire particle swarm P into t groups, and denote each particle group as Pt. i For each group i = 1, 2, ..., t, a learning factor c is set within each group. i1 = rand(0.8, 1.2), c i2 = rand(0.8, 1.2); Step 1-2: Initialize particle grouping P i ={z ip }, i = 1, 2, ..., t, p = 1, 2, ..., k, where k is the number of particles in the group; each particle is represented by z. ip ={x ip ,v ip }, i=1,2,…t,p=1,2,...,k, where x ip Let i = 1, 2, ..., t, p = 1, 2, ..., k be the position of particle p in the i-th group within the solution space. The size of the solution space is determined by the data dimension n and the number of data centers c. ip Let p = 1, 2, ..., k be the velocities of particle p in the i-th group within the solution space, with initial values ​​randomly generated within the solution space.

9. An enhanced data encoding-decoding algorithm according to claim 7, characterized in that: Said Step3 comprises the following steps: Step3-1: i=1; Step 3-2: Calculate the velocity for the next iteration within the i-th group using the velocity update formula. The speed update formula is: in, Let p be the velocity of the p-th particle in the i-th group during the g-th iteration. Let x be the position of the p-th particle in the i-th group during the g-th iteration. ipbest x represents the optimal position of the p-th particle in the i-th group during its motion. ogbest Let w be the optimal position for all particles in the i-th group during their motion, and c be the inertial weight. i1 ,c i2 Let r1 and r2 be the learning factors for the i-th group, and r1 and r2 be random numbers. Step 3-3: Calculate the position for the next iteration within the i-th group using the position update formula. The position update formula is: in, Let p be the position of the p-th particle in the i-th group during the (g+1)-th iteration. Let p be the position of the p-th particle in the i-th group during the g-th iteration. Let be the velocity of the p-th particle in the i-th group during the (g+1)-th iteration; Steps 3-4: Update z igbest , z igworst These are the best and worst particles in the current i-th group; Step3-5: i=i+1; Step3-6: If i≤t, return to Step3-2.

10. An enhanced data encoding-decoding algorithm according to claim 7, characterized in that: Said Step4 comprises the following steps: Step4-1: i=1; Step4-2:of igworst =z tgbest ; Step4-3: i=i+1; Step4-4:z igworst =z i-1gbest ; Step4-5: If i<t, return to Step-4-3.

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