Multi-objective particle swarm optimization method based on unexpected epidemic mechanism and dynamic network

Abstract

The application discloses a multi-objective particle swarm optimization method based on unexpected epidemic mechanism and dynamic network, and belongs to the technical field of intelligent optimization algorithm. Firstly, a small-world network based on distance is constructed as a knowledge propagation topology; then, the most potential leading particles are identified from the group through unexpected epidemic decision; the particle swarm is divided into an exploration subgroup and a development subgroup, the former of which maintains diversity through friendly neighbor learning, and the latter of which follows global leading examples to accelerate convergence; meanwhile, an external storage is maintained to save a non-dominated solution set, and an adaptive grid mechanism is adopted to control the uniformity of the solution distribution; and the knowledge network is dynamically updated in the iteration process to strengthen the successful learning path. The application adopts the above multi-objective particle swarm optimization method based on unexpected epidemic mechanism and dynamic network, effectively avoids premature convergence through collective wisdom decision, realizes fast convergence to the real Pareto front while maintaining the diversity of the solution set, and improves the solution quality and efficiency of the multi-objective optimization problem.

Description

Technical Field

[0001] This invention relates to the field of intelligent optimization algorithm technology, and in particular to a multi-objective particle swarm optimization method based on unexpected popularity mechanism and dynamic network. Background Technology

[0002] With the continuous development of science and technology and engineering practice, multi-objective optimization problems are prevalent in many fields such as resource allocation, production scheduling, engineering design, parameter configuration, and path planning. Unlike single-objective optimization problems, multi-objective optimization problems require the simultaneous optimization of multiple conflicting objective functions. Typically, there is no single globally optimal solution, but rather a set of Pareto optimal solutions with trade-offs. How to efficiently search for a uniformly distributed Pareto front with good convergence has always been a core challenge in the field of multi-objective optimization.

[0003] Particle Swarm Optimization (PSO) has been widely used since its inception due to its simplicity, few parameters, and fast convergence. Multi-Objective PSO (MOPSO) extends PSO to the multi-objective optimization domain by introducing strategies such as external repositories and grid mechanisms to handle trade-offs between multiple objectives. However, existing MOPSO algorithms still face problems such as premature convergence, insufficient global guidance mechanisms, imbalance between exploration and exploitation, topological solidification in knowledge propagation, and uneven distribution of Pareto fronts. Existing improvements, such as comprehensive learning strategies, heterogeneous subpopulation design, and dynamic topology mechanisms, while improving search performance to some extent, still struggle to effectively identify potential search directions in multi-objective optimization scenarios, are susceptible to the "tyranny of the majority," and fail to fully utilize the potential intelligence within the swarm.

[0004] Surprisingly popular algorithms, as an effective collective decision-making method, have demonstrated their ability to tap into the wisdom of informed minorities in sociology, but they have not yet been systematically introduced into the field of multi-objective optimization. How to combine this collective wisdom decision-making mechanism with multi-objective particle swarm optimization, construct an adaptive knowledge propagation network and a heterogeneous subgroup collaborative mechanism, and achieve a dynamic balance between exploration and exploitation, thereby improving the solution quality and efficiency of complex multi-objective optimization problems, has become a key issue that urgently needs to be addressed. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-objective particle swarm optimization method based on the unexpected popularity mechanism and dynamic networks, addressing the problems of premature convergence, insufficient global guidance, and imbalance between exploration and exploitation in existing multi-objective particle swarm optimization algorithms. By innovatively introducing the unexpected popularity decision-making mechanism from sociology into multi-objective optimization, constructing a dynamic adaptive knowledge propagation network, and designing a heterogeneous subgroup cooperative strategy, efficient search for Pareto optimal solutions is achieved.

[0006] To achieve the above objectives, this invention provides a multi-objective particle swarm optimization method based on the unexpected popularity mechanism and dynamic networks, comprising the following steps: S1. Initialize the particle swarm in the solution space and calculate the multi-objective fitness, and construct and initialize the knowledge propagation network and external repository. S2, Particle State Co-update: The particle swarm is divided into functionally heterogeneous exploratory and development subgroups: exploratory subgroup particles update their position and velocity only based on the selected learning object; development subgroup particles update their position and velocity by combining the learning object and the global guiding paradigm generated by unexpected popular decision-making mechanisms. The learning targets are determined based on the current knowledge dissemination network; S3. Calculate the multi-target fitness value of the new position of all particles, and update the individual historical best position of each particle accordingly. S4. Update the external repository and apply an adaptive grid mechanism to manage the distribution and size of the repository; based on the updated population and network state, execute the unexpected popularity decision mechanism to select a global guiding paradigm for the next iteration step S2. S5. Dynamically adjust the topology of the knowledge dissemination network based on the search performance and distribution of particles; S6. Monitor the changing trends of the external repository size, solution set quality, and function evaluation count to evaluate the algorithm's convergence status; S7. Determine if any of the following termination conditions are met: the number of function evaluations reaches the preset upper limit, the number of iterations reaches the preset upper limit, or the change in the size of the external repository over multiple consecutive generations is less than a set threshold. If any condition is not met, return to step S2 to continue iterating; otherwise, terminate the iteration and output the solution set in the external repository.

[0007] Preferably, step S1 specifically includes: S11, Set population size Exploring the size of subgroups Development Subgroup Size The initial connection parameters of the knowledge dissemination network, the capacity of the external repository, and the grid partitioning parameters; S12. Within the predetermined solution space, randomly generate the initial position and initial velocity of each particle; S13. Fitness Assessment and Network Construction: Calculate the multi-objective fitness of the initial particles and construct an initial small-world network as a knowledge propagation network based on the spatial distance between particles; S14. Extract non-dominated solutions from the initial population, store them in an external repository, and apply an adaptive grid mechanism for initial management.

[0008] Preferably, step S13 further includes calculating the Pareto level of each particle based on the fast non-dominated sorting algorithm. This serves as the basis for scalar fitness in network construction and subsequent decision-making.

[0009] Preferably, step S2, which involves selecting a learning object for each particle, specifically includes: Based on the adjacency relationships of the current knowledge dissemination network, determine the neighbors of each particle; For particles exploring a subgroup, there is a 60% probability of selecting the Pareto-optimal particle among its neighbors, and a 40% probability of randomly selecting a neighbor; for particles developing a subgroup, there is a direct selection of the Pareto-optimal particle among its neighbors as the learning target.

[0010] Preferably, in step S2, the velocity update formula for the exploration subgroup is: ; in, , for Uniformly distributed random numbers in an interval This represents the current iteration number. For the first Subgroup particle exploration The velocity vector, Inertial weight; To explore the learning factor, it was decreased from 3 to 1.5. For the first Sub-particles The optimal position of the selected learning object. For the first Subgroup particle exploration The position vector of the particle in the exploration subgroup is used to update the velocity of the particle only by considering the influence of its own historical best position and the selected learning object. The formula for the speed update of developing subgroups is: ; in, , As a global guiding example, For the first Sub-particles The optimal position of the selected learning object; For neighboring learning factors, As a global guiding factor, For the first Subgroup particles The velocity vector, For the first Subgroup particles The position vector, Decrease from 2.5 to 0.5 (the influence of friendly neighbors weakens); Increasing from 0.5 to 2.5 (global guidance enhancement), the velocity update of the subswarm particles considers their own historical best position, the selected learning object, and the global guidance paradigm selected by the unexpected popularization decision mechanism. The impact; After updating the particle position and velocity, perform boundary processing steps: when the particle's position in any dimension exceeds the solution space boundary, reverse the velocity in that dimension and adjust the position in that dimension back within the boundary, specifically: For exploring subgroup particles The Wei, when or At that time, execute: 、 ; in, and These are the upper and lower bounds of the solution space, respectively. For the first Sub-particles In the Positional components of a dimension, For the first Sub-particles In the The velocity components of the dimension; the boundary treatment steps for developing subgroup particles are consistent with those for exploring subgroup particles.

[0011] Preferably, step S4, which involves applying an adaptive grid mechanism to manage the repository, specifically includes: Mesh partitioning and indexing: Based on the target value range of the solutions in the current repository, the target space is partitioned into... hypercube ( Typically taken as 10-20), mesh expansion parameter. Set the value to 0.1 and assign a grid index to each solution; Size control: When the number of solutions in the repository exceeds the limit, calculate the crowding of each grid and randomly delete solutions from the most crowded grid first.

[0012] Preferably, the execution of the unexpected popularity decision mechanism in step S4 specifically includes: Voting and Counting: Based on the current knowledge propagation network, each particle votes for the Pareto-optimal particle among its neighbors, and the actual vote rate received by each candidate particle is counted. ; Calculate the expected voting rate: Based on the swarm network structure, calculate the swarm's expected voting rate for each candidate particle. ; Example of selection: Calculate the unexpected popularity of each candidate particle. The particle with the highest unexpected popularity was selected as the global guiding paradigm.

[0013] Preferably, step S5 includes: S51. In each iteration, for the top Pareto rankings... The probability of a particle being selected as a learning object is set to be... The probability of other particles being selected as learning objects is set to... ,in, > Based on probability, connections are dynamically established or deleted for each particle in the adjacency matrix to form temporary learning paths. S52. Based on the search performance of particles (such as the stagnation of an individual's optimal position) and the spatial distribution of the population, dynamically add or delete connections in the knowledge propagation network to simulate the process of knowledge accumulation and forgetting.

[0014] Preferably, in step S52, the maximum number of connections allowed for each particle (knowledge limit) increases linearly with the number of iterations, and when a new connection needs to be established, an old connection is randomly deleted.

[0015] Preferably, the size of the exploration subgroup Fixed at 15, development subgroup size For population size External repository capacity limit Set it to 100 to 300.

[0016] Therefore, this invention adopts the aforementioned multi-objective particle swarm optimization method based on the unexpected flow mechanism and dynamic network. By integrating core strategies such as unexpected flow decision-making, it effectively avoids premature convergence and possesses powerful global search capabilities. It accelerates convergence to the true Pareto front, reduces the number of function evaluations, and exhibits excellent convergence performance. It ensures that the solution set is evenly distributed on the Pareto front and can handle complex front shapes. The dynamic parameter adaptive strategy makes it robust and adaptable to various multi-objective optimization problems. Furthermore, the three-layer architecture design makes the algorithm highly scalable and can be extended to higher objectives and higher-dimensional problems.

[0017] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1 This is a flowchart of a method according to an embodiment of the present invention; Figure 2This is a schematic diagram of the unexpected popular decision-making mechanism in an embodiment of the present invention; Figure 3 The following are performance evaluation results of the multi-objective optimization algorithm in this embodiment of the invention: (a) is a comparison of the algorithm results and the true Pareto front of the objective function, (b) is a convergence graph of a single best run, (c) is a graph of IGD value variation, and (d) is a graph of Spread value variation. Figure 4 The following are performance evaluation results of the multi-objective optimization algorithm in this embodiment of the invention: (a) is a graph showing the change in the number of non-dominated solutions in external storage, (b) is a graph showing the change in GD value, (c) is a graph showing the change in RNI value, and (d) is a graph showing the average convergence behavior and stability analysis. Detailed Implementation

[0019] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0020] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0021] Example 1 like Figure 1 As shown, the multi-objective particle swarm optimization method based on the unexpected popularity mechanism and dynamic networks includes the following steps: Part 1: Algorithm Initialization Phase.

[0022] Step 1: Parameter settings.

[0023] Population size (Generally taken as 40-100), explore the size of the subgroup (Typically set to 15 particles), develop subgroup size ; Network parameters: Initial number of connections Connection growth rate Number of experts (Number of experts) The range of values ​​is ,when When the number is too large, the probability of each expert being connected is too low. (The dissemination of expert information is limited when the time is too short). MOPSO parameter: Maximum repository size , number of grids Mesh expansion parameters Leaders choose pressure Remove pressure ; Termination condition: Maximum number of iterations Or the maximum number of function evaluations ; Step 2: Initialize the particle swarm and knowledge propagation network, and build an external repository.

[0024] Set the population size as There are particles, and the problem dimension is... The particle swarm is divided into exploratory subgroups (scale) ) and development subgroups (scale) In the search space Internal random initialization of the particle positions of the exploration subgroup and speed The formula is: ; ; Simultaneously, the particle positions of the development subgroup are randomly initialized. and speed The formula is: ; ; in , for Uniform random numbers within an interval.

[0025] Calculate the multi-target fitness value of all particles. The Pareto dominance level of each particle is calculated using the fast non-dominated sorting algorithm. As a scalar fitness.

[0026] Set the individual optimal position and fitness for each particle: ; Extract all non-dominated solutions from the initial population and construct an external repository, Archive. Calculate the grid structure and assign a grid index to each repository member.

[0027] An initial small-world network is constructed based on the Euclidean distance between particles (the small-world network is constructed using the K-nearest neighbor rule, with an initial number of connections). The range of values ​​is (ensuring the network has both local clustering structure and appropriate long-range connections), generating an adjacency matrix. An adaptive grid mechanism is applied to the repository, dividing the target space into... A hypercube grid is used to assign a grid index to each repository member.

[0028] Based on the initial network, an unexpected flow decision is made to select... As the initial global guide for developing subgroups.

[0029] Part Two: Main Loop Iteration Process.

[0030] Step 3, Particle position update (first layer).

[0031] Optimal neighbor selection: Selecting a learning object for each dimension of each particle; According to the small-world network adjacency matrix and learning probability matrix First, calculate the learning probability of each particle ( It is the particle index (1 to Different particles have different self-learning tendencies: ; Then for each particle and each dimension Perform the following steps: Get network neighbors (from adjacency matrix) Find all particles Adjoining neighbors): ; Selecting neighbors based on subgroup type: Explore subgroups ( That is, there is a 60% probability of selecting the Pareto-optimal particle among the neighbors, and a 40% probability of randomly selecting neighbors to maintain diversity; Development Subgroup ( ): The development subgroup always directly selects the Pareto-optimal particle from its neighbors as the learning object, which accelerates convergence; ; The application of learning probability determines whether to learn from friendly neighbors; Obtain the final neighbor positions (extract the corresponding dimension values ​​from the individual optimal): ; Explore subswarm particle velocity and position updates ( ): ; ; in, For the updated number Generation of Exploration Subgroup Particles The velocity vector, For the first Generation of Exploration Subgroup Particles The velocity vector, For the updated number Generation of Exploration Subgroup Particles The position vector, For the first Generation of Exploration Subgroup Particles The position vector, For the first Sub-particles The individual optimal position vector of the selected learning object. The inertia weight (decreases with iteration); To explore the learning factor, it is decreased from 3 to 1.5; only friendly neighbors are learned, not the global optimum, to maintain diversity.

[0032] Develop subswarm particle velocity and position updates ( ): ; ; in, For the updated number Subgroup particles The velocity vector, For the first Subgroup particles The velocity vector, For the updated number Subgroup particles The position vector, For the first Subgroup particles The position vector, It is the first The position vector of the selected global guiding paradigm (global guide); Decrease from 2.5 to 0.5 (the influence of friendly neighbors weakens); The value is increased from 0.5 to 2.5 (global guidance enhancement); it simultaneously learns from friendly neighbors and the global optimum, accelerating convergence.

[0033] Boundary handling: for each dimension of all particles Conduct an inspection ( ): Judgment conditions ( and (These are the upper and lower bounds of the solution space, respectively). ; Speed ​​rebound (maintaining momentum): ; Location truncation (forced return to boundary): preserves the search direction (bounce) while ensuring feasibility (truncation). ; Step 4: Multi-objective evaluation and individual optimal update (second layer).

[0034] Evaluate the new positions and calculate the objective function values ​​for the new positions of all particles: ; Pareto levels are obtained using Quick Nondominated Sort. (The lower the level, the better).

[0035] Individual optimal update: Update each particle according to three scenarios. : Case 1: The current solution dominates the optimal individual.

[0036] ; renew: ; ; Case 2: Individual optimally dominates the current solution.

[0037] ; Keep: ; ; Scenario 3: No mutual control, using an auxiliary indicator—Euclidean distance to the origin: Calculate the distance to the current solution: ; Calculate the optimal distance for each individual: ; Update rule: Closer to the origin = better overall performance across multiple objectives.

[0038] ; Step 5: Repository Management and Leader Selection (Third Tier).

[0039] Merge candidate solutions and include external repositories and the new positions of all particles in the current iteration Merge to form a candidate solution set : ; Extracting non-dominated solutions, and retaining only those solutions that are not dominated by any other solutions, constitutes a new generation of external repository. : ; in, express Dominate That is, it is not worse than on all objective functions and is strictly better on at least one objective function; Repository size control: Merge all current particle positions with solutions in the repository to form a candidate set; determine the dominance relationship of the candidate set, extract all non-dominated solutions to form a new repository; update the adaptive mesh structure, and reassign mesh indices to each repository member; if (Capacity limit, usually 50), execute delete: Grid congestion calculation: To control the repository size, an adaptive grid mechanism is used to calculate the congestion level of each grid. The target space is divided into... Each grid, each solution Based on its target value being assigned to a unique grid, denoted as To solve The index of the grid to which it belongs. Then the grid... The crowding degree is defined as the number of solutions contained within the grid: ; Deletion strategy (find the most crowded grid, i.e., the grid with the highest crowding): ; Randomly delete a solution from the grid; Repeat until ; Applications of adaptive mesh mechanism: The objective space extent (with expansion) is calculated. To accommodate dynamic changes in the solution set within the repository and avoid boundary effects, each objective function is first computed. The range of values ​​in the current repository Archive, and an appropriate expansion thereof: ; in, ， For the goal Value span in the repository, inflation factor (Avoid boundary effects); Mesh generation: dividing the target space into Hypercubes (typically 10×10); Assign an index to calculate the index of the grid in which each repository member resides; Unexpected popular decision updates (such as) Figure 2 ): Voting phase: Each particle According to the adjacency matrix The corresponding neighbor group vote selects the neighbor with the lowest dominance level. The particle with the smallest value is denoted as particle. The voting targets are: ; in, Represents particles Orientable particles study; The voting results of all particles constitute the voting vector. The candidate particle set is .

[0040] Actual voting rate calculation: Statistical analysis of each candidate particle Number of votes received: ; Knowledge prevalence calculation (knowledge prevalence reflects the degree of attention a particle receives in a network, measured by its in-degree, i.e., how many particles consider it a neighbor): Calculate the prevalence of each particle in the adjacency matrix. In-degree in: ; Popularity Prediction: Particles Its actual voting targets The estimated popularity is: ; This formula assumes that particles consider the cognition of their neighbors to be representative, and the more "famous" (highly popular) the neighbors are, the more likely their voting choice is to become a popular option.

[0041] For unselected options, the remaining predicted probabilities are evenly distributed: ; Expected voter turnout calculation: candidate particles The expected vote rate is the average of all particles' predicted values: ; Unexpected Popularity Score: The unexpected popularity of each candidate particle is defined as the ratio of the actual voter turnout to the expected voter turnout. ; A value greater than 1 indicates that the particle has received more actual support than the population expected, meaning it has the characteristic of "unexpected popularity".

[0042] Global Guiding Paradigm Selection: Select the particle with the highest unexpected popularity as the next generation of global guiding paradigm. ; ; Step 6: Network topology update.

[0043] Neighborhood relationship update: Define particles The individual optimal position stagnation counter is For stationary particles ( (This involves) re-implementing the friendly neighbor selection strategy. Particles that haven't improved over a long period may be stuck in a localized problem and require a different learning target. From the top-ranked... Expert particle generation temporary connection matrix (Temporary network of experts); Generate expert temporary network: Expert selection probability: ; Temporary adjacency matrix: Expert particles have a higher probability of being connected to other particles (learning). ; Dynamic Reconstruction of Small-World Networks: The knowledge ceiling grows dynamically: the maximum number of connections for each particle increases linearly with iteration. Let the initial number of network connections be... The connection growth rate is Then the first The maximum number of connections allowed per particle in a generation is: ; in, This is a parameter for the connection growth rate (typically taken as 1-3). When the particle... The number of neighbors reached When a new connection needs to be established, an existing neighbor is randomly deleted (the corresponding adjacency matrix element is set to 0) to simulate the knowledge forgetting process.

[0044] Network reconstruction strategy: Calculate the Euclidean distance of all particle pairs based on the current position; sort them in ascending order of distance; connect each particle to the nearest neighbor. One particle; generate a new adjacency matrix. ; Basic network temporary network of experts By merging, we obtain the adjacency matrix of the next-generation knowledge dissemination network: ; Step 7: Convergence monitoring and termination judgment.

[0045] Record convergence information: Save the current repository size to the history array: ; Early termination of judgment: Check three termination conditions: Condition 1: The number of times the function has been evaluated has reached the preset limit. ; Condition 2: The current iteration count has reached the preset limit. ; Condition 3, convergence stability, when the number of iterations... Then, the stability of the repository size is checked every 10 generations. If the standard deviation of the repository size is less than 1 for 10 consecutive generations and the number of solutions in the repository has exceeded a preset threshold (usually 20), the algorithm is considered to have converged to a stable solution set and can be terminated early. ; Progress display: Output every 50 generations or at the first iteration: current iteration number Repository size The number of times the function has been evaluated. ; Iteration termination check: If none of the above termination conditions are met, then update the iteration counter: ; Return to step 2 (particle state co-update) to continue the next iteration; otherwise, terminate the algorithm and output the final repository Archive(t) as the Pareto approximate solution set.

[0046] like Figures 3-4 This is a graph showing the performance evaluation results of the present invention, each containing four subgraphs. The algorithm's performance is verified from three aspects: solution set quality, convergence efficiency, and stability. The statistical results of the data obtained from multiple independent runs are shown in Table 1: Table 1 Statistical Results

[0047] Excellent convergence: The optimal value of the GD index reaches 0.012373, and the average value is 0.050350, indicating that the algorithm can quickly converge to the vicinity of the true Pareto front; the standard deviation of 0.034685 shows that the algorithm has good stability.

[0048] Convergence efficiency: Both the optimal running and average convergence curves show that the repository size reaches 50 (close to the upper limit) after about 5 iterations, indicating fast convergence speed; High approximation quality: The optimal value of the IGD index is 0.040398, and the median is 0.056862, indicating that while maintaining convergence, the algorithm also has a relatively comprehensive solution set distribution, covering the key regions of the Pareto front. The algorithm results highly coincide with the actual Pareto front, with GD values ​​≤ 0.02 and IGD values ​​≤ 0.05, indicating that the solution set is close to the theoretical optimum and has comprehensive coverage. Good uniformity of distribution: The average value of the Spread index is 1.249736, which is close to the ideal value, and the standard deviation is only 0.042427. This indicates that the algorithm can maintain good uniformity of solution set distribution in multiple runs and can effectively handle the convex-concave mixed region of the Pareto front.

[0049] High stability: The standard deviations of all indicators are small (GD standard deviation 0.034685, IGD standard deviation 0.018100, Spread standard deviation 0.042427), indicating that the algorithm has low dependence on the initial population and strong robustness. The RNI value is close to 0, and the proportion of high-quality non-dominated solutions is extremely high.

[0050] Therefore, the multi-objective particle swarm optimization method based on the unexpected flow mechanism and dynamic network described above has the following beneficial effects: (1) Powerful global search capability: Unexpected popularity decision can identify the search direction with the greatest potential, effectively avoid premature convergence, and help the algorithm escape the local Pareto front; (2) Excellent convergence performance: The development of subgroup following the global guidance paradigm, combined with dynamic learning factors and inertial weights, enables the algorithm to converge quickly to the real Pareto front, reducing the number of function evaluations required to reach a high-quality solution set. (3) Good solution set diversity: The dynamic update of the small-world network, the application of the grid mechanism, the design of the exploration subgroup and the friendly neighbor learning strategy together ensure the diversity and uniformity of the solution set on the Pareto front, which can effectively handle the discontinuous and complex front shape. (4) Strong robustness and adaptability: The dynamic parameter adaptive strategy enables the algorithm to automatically adjust the ratio of exploration and development according to the search process, and is suitable for multi-objective optimization problems with different characteristics, including constrained optimization problems, etc. (5) Good scalability: The three-layer architecture makes the algorithm easy to extend to more targets and higher-dimensional problems, and it is also easy to mix with other intelligent optimization techniques (such as genetic algorithms) to build more powerful hybrid algorithms.

[0051] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A multi-objective particle swarm optimization method based on unexpected flow mechanism and dynamic network, characterized in that, Includes the following steps: S1. Initialize the particle swarm in the solution space and calculate the multi-objective fitness, and construct and initialize the knowledge propagation network and external repository. S2, Particle State Co-update: The particle swarm is divided into functionally heterogeneous exploratory and development subgroups: exploratory subgroup particles update their position and velocity only based on the selected learning object; development subgroup particles update their position and velocity by combining the learning object and the global guiding paradigm generated by unexpected popular decision-making mechanisms. The learning targets are determined based on the current knowledge dissemination network; S3. Calculate the multi-target fitness value of the new position of all particles, and update the individual historical best position of each particle accordingly. S4. Update the external repository and apply an adaptive grid mechanism to manage the distribution and size of the repository; based on the updated population and network state, execute the unexpected popularity decision mechanism to select a global guiding paradigm for the next iteration step S2. S5. Dynamically adjust the topology of the knowledge dissemination network based on the search performance and distribution of particles; S6. Monitor the changing trends of the external repository size, solution set quality, and function evaluation count to evaluate the algorithm's convergence status; S7. Determine if any of the following termination conditions are met: the number of function evaluations reaches the preset limit, the number of iterations reaches the preset limit, or the change in the size of the external repository over multiple consecutive generations is less than a set threshold; if any condition is not met, return to step S2 to continue iterating. Otherwise, terminate the iteration and output the solution set from the external repository.

2. The multi-objective particle swarm optimization method based on unexpected flow mechanism and dynamic network according to claim 1, characterized in that, Step S1 specifically includes: S11, Set population size Exploring the size of subgroups Development Subgroup Size The initial connection parameters of the knowledge dissemination network, the capacity of the external repository, and the grid partitioning parameters; S12. Within the predetermined solution space, randomly generate the initial position and initial velocity of each particle; S13. Fitness Assessment and Network Construction: Calculate the multi-objective fitness of the initial particles and construct an initial small-world network as a knowledge propagation network based on the spatial distance between particles; S14. Extract non-dominated solutions from the initial population, store them in an external repository, and apply an adaptive grid mechanism for initial management.

3. The multi-objective particle swarm optimization method based on unexpected flow mechanism and dynamic network according to claim 2, characterized in that, Step S13 also includes calculating the Pareto level of each particle based on the fast non-dominated sorting algorithm. This serves as the basis for scalar fitness in network construction and subsequent decision-making.

4. The multi-objective particle swarm optimization method based on unexpected flow mechanism and dynamic network according to claim 3, characterized in that, Step S2, which involves selecting a learning object for each particle, specifically includes: Based on the adjacency relationships of the current knowledge dissemination network, determine the neighbors of each particle; For particles exploring a subgroup, there is a 60% probability of selecting the Pareto-optimal particle among its neighbors, and a 40% probability of randomly selecting a neighbor; for particles developing a subgroup, there is a direct selection of the Pareto-optimal particle among its neighbors as the learning target.

5. The multi-objective particle swarm optimization method based on unexpected flow mechanism and dynamic network according to claim 2, characterized in that, In step S2, the velocity update formula for the exploration subgroup is: ; in, , for Uniformly distributed random numbers in an interval This represents the current iteration number. For the first Generation of Exploration Subgroup Particles The velocity vector, Inertial weight; To explore the learning factor, the value was decreased from 3 to 1.

5. For the first Sub-particles The optimal position of the selected learning object. For the first Generation of Exploration Subgroup Particles The position vector of the particle in the exploration subgroup is used to update the velocity of the particle only by considering the influence of its own historical best position and the selected learning object. The formula for the speed update of developing subgroups is: ; in, , As a global guiding example, For the first Sub-particles The optimal position of the selected learning object; For neighboring learning factors, As a global guiding factor, For the first Subgroup particles The velocity vector, For the first Subgroup particles The position vector, Decrease from 2.5 to 0.5; Increasing from 0.5 to 2.5, the velocity update of the subswarm particles simultaneously considers their own historical best position, the selected learning object, and the global guiding paradigm selected by the unexpected popularization decision mechanism. The impact; After updating the particle position and velocity, perform boundary processing steps: when the particle's position in any dimension exceeds the solution space boundary, reverse the velocity in that dimension and adjust the position in that dimension back within the boundary, specifically: For exploring subgroup particles The Wei, when or At that time, execute: 、 ; in, and These are the upper and lower bounds of the solution space, respectively. For the first Sub-particles In the Positional components of a dimension, For the first Sub-particles In the The velocity components of the dimension; the boundary treatment steps for developing subgroup particles are consistent with those for exploring subgroup particles.

6. The multi-objective particle swarm optimization method based on unexpected flow mechanism and dynamic network according to claim 1, characterized in that, Step S4, which involves applying an adaptive grid mechanism to manage the repository, specifically includes: Mesh partitioning and indexing: Based on the target value range of the solutions in the current repository, the target space is partitioned into... Hypercube, Mesh Expansion Parameters Set the value to 0.1 and assign a grid index to each solution; Size control: When the number of solutions in the repository exceeds the limit, calculate the crowding of each grid and randomly delete solutions from the most crowded grid first.

7. The multi-objective particle swarm optimization method based on unexpected flow mechanism and dynamic network according to claim 1, characterized in that, The execution of the unexpected flow decision mechanism in step S4 specifically includes: Voting and Counting: Based on the current knowledge propagation network, each particle votes for the Pareto-optimal particle among its neighbors, and the actual vote rate received by each candidate particle is counted. ; Calculate the expected voting rate: Based on the swarm network structure, calculate the swarm's expected voting rate for each candidate particle. ; Example of selection: Calculate the unexpected popularity of each candidate particle. The particle with the highest unexpected popularity was selected as the global guiding paradigm.

8. The multi-objective particle swarm optimization method based on unexpected flow mechanism and dynamic network according to claim 1, characterized in that, Step S5 includes: S51. In each iteration, for the top Pareto rankings... The probability of a particle being selected as a learning object is set to be... The probability of other particles being selected as learning objects is set to... ,in, > Based on probability, connections are dynamically established or deleted for each particle in the adjacency matrix to form temporary learning paths. S52. Based on the particle search performance and population spatial distribution, dynamically add or delete connections in the knowledge dissemination network to simulate the knowledge accumulation and forgetting process.

9. The multi-objective particle swarm optimization method based on unexpected flow mechanism and dynamic network according to claim 8, characterized in that, In step S52, the maximum number of connections allowed for each particle increases linearly with the number of iterations. When a new connection needs to be established, an old connection is randomly deleted.

10. The multi-objective particle swarm optimization method based on unexpected flow mechanism and dynamic network according to claim 2, characterized in that, Explore the size of the subgroup Fixed at 15, development subgroup size For population size External repository capacity limit Set it to 100 to 300.

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