Multi-target discrete particle swarm optimization navigator selection method based on set operation

Abstract

The invention relates to the technical field of multi-agent system control, and discloses a set operation-based multi-target discrete particle swarm optimization navigator selection method, which comprises the following steps of: acquiring communication topological data of a multi-agent system and constructing a system error and convergence rate-based fitness function; adopting a triple guidance mechanism based on set operation, and performing iterative updating on the candidate navigator set through guidance of an individual historical optimal set, a global optimal set and a neighbor set in sequence; traversing different weight parameters of the fitness function, and outputting a corresponding global optimal navigator set; and finally, screening based on a fitness value difference threshold value and Pareto undifferentiated characteristics to obtain a final navigator set. According to the method, discrete nodes are directly processed through set operation, information loss caused by binary mapping is avoided, local optimum is effectively avoided through a neighbor guiding mechanism, and efficient cooperative control over a multi-agent system is achieved.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent system control technology, specifically relating to a leader selection method for multi-objective discrete particle swarm optimization based on set operations. Background Technology

[0002] Multi-Agent Systems (MASs), relying on a distributed communication framework, enable information exchange, state updates, and collaborative control among agents. They have been widely applied in key areas such as intelligent transportation systems, wireless sensor networks, mobile robot platooning, industrial automation, and the Internet of Things (IoT). Among various control paradigms in MASs, the leader-follower framework is an important control method. In this framework, the leader acts as the system's control core, inputting external control signals and guiding the system's dynamic behavior. Followers adjust their own behavior by receiving states from the leader and other followers. Therefore, the appropriate selection of the leader directly determines the system's collaborative efficiency and control accuracy.

[0003] Existing multi-agent systems rely heavily on greedy algorithms for navigator selection, but these algorithms have significant limitations: on the one hand, their decisions depend on local search strategies, making them susceptible to local features and prone to getting stuck in local optima, making it difficult to traverse the entire solution space to select the globally optimal set of navigators; on the other hand, greedy algorithms are computationally inefficient when faced with optimization objectives with high time complexity, especially in dynamic scenarios where they take even longer and are difficult to adapt to real-time control requirements.

[0004] In multi-agent system node selection problems, which share similarities with leader selection, particle swarm optimization (PSO) has also found widespread and significant applications due to its distributed search characteristics and relatively low control parameter complexity. It is often used to explore better node selection schemes to suit system performance requirements. However, the core update formulas of existing PSO algorithms are mostly based on continuous space design or rely on binary mapping mechanisms, which are poorly suited to the essential requirement of optimizing discrete node sets in the leader selection problem, making it difficult to directly and efficiently explore the optimal leader combination. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a leader selection method for multi-objective discrete particle swarm optimization based on set operations, so as to avoid the problems of information loss, local optima and poor dynamic topology adaptability of traditional algorithms. Through a triple guidance mechanism driven by set operations and Pareto solution optimization, more efficient and robust collaborative control of MASs can be achieved.

[0006] To address the aforementioned technical problems, this invention provides a leader selection method based on set operations for multi-objective discrete particle swarm optimization, comprising the following steps:

[0007] S1. Obtain the topology data of the multi-agent system and construct a fitness function based on the optimization objective. The multi-agent system includes a leader agent and follower agents.

[0008] S2. Initialization parameters, including the triple guidance mechanism trigger threshold, candidate navigator set, individual historical best set, global best navigator set, and fitness function weight parameter set. ;

[0009] S3. In each iteration, the candidate leader set is updated sequentially through the individual historical best set, the global best set, and the neighbor set. Then, the individual historical best leader set and the global best leader set of the particle swarm are updated based on the fitness value.

[0010] S4. Repeat step S3 until the maximum number of iterations, then output the globally optimal navigator set under the current weight parameters;

[0011] S5. Repeat steps S3 and S4 to output the set of weight parameters. The globally optimal navigator set for each weight parameter. ;

[0012] S6. Calculate the globally optimal set of navigators. The fitness values ​​of any two sets are compared with a fitness difference threshold. Sets with fitness values ​​less than the fitness difference threshold are retained. Then, Pareto indifference screening is performed on the retained sets, and the indifference solutions obtained by the screening are used as the final navigator output set.

[0013] As an improvement to the leader selection method for multi-objective discrete particle swarm optimization based on set operations in this invention:

[0014] The fitness value is calculated as follows:

[0015]

[0016] in, Indicates the optimization objective systematic error The maximum value that can be achieved, This represents the asymptotic convergence rate of the optimization objective. The maximum value that can be achieved, It signifies the gathering of navigators. These are the weight parameters.

[0017] As a further improvement to the leader selection method for multi-objective discrete particle swarm optimization based on set operations of the present invention:

[0018] The individual historical optimal set guides the following:

[0019] When the generated random number is less than the first trigger threshold For particles Triggering operation: from the difference set Randomly select an agent from the candidate navigator set. Remove from the difference set. One agent is randomly selected from the pool to join the candidate navigator set. , This represents the set of historically best leaders for each individual.

[0020] As a further improvement to the leader selection method for multi-objective discrete particle swarm optimization based on set operations of the present invention:

[0021] The globally optimal set is guided by:

[0022] When the generated random number is less than the second trigger threshold For particles Triggering operation: from the difference set Randomly select an agent from the candidate navigator set. Remove from the difference set. One agent is randomly selected from the pool to join the candidate navigator set. , This represents the set of globally optimal navigators in a particle swarm.

[0023] As a further improvement to the leader selection method for multi-objective discrete particle swarm optimization based on set operations of the present invention:

[0024] The neighbor set guidance is as follows:

[0025] When the generated random number is less than the third trigger threshold For particles Trigger action: From the set of candidate navigators Randomly select an agent Thus, the intelligent agent is determined. Neighbor set Subsequently, from the neighborhood gathering Randomly select 1 agent Used to replace the candidate navigator set intelligent agents in .

[0026] As a further improvement to the leader selection method for multi-objective discrete particle swarm optimization based on set operations of the present invention:

[0027] The method for updating the individual historical best leader set and the global best leader set of the particle swarm based on fitness values ​​is as follows:

[0028] (1) If the fitness value Better than fitness value However, it is not better than the fitness value. Then update the set of the best historical navigators for each individual. ;

[0029] (2) If the fitness value Better than fitness value If a candidate navigator set is superior to the set of other particles in this iteration, then the individual's historical best navigator set is updated. With the global optimal navigator set of the particle swarm .

[0030] As a further improvement to the leader selection method for multi-objective discrete particle swarm optimization based on set operations of the present invention:

[0031] The method for comparing with the fitness difference threshold is as follows:

[0032] Preset fitness difference threshold Then determine: If the condition is met, it is determined to be less than the fitness difference threshold, where, Represents the set of candidate navigators fitness value, Represents the set of candidate navigators The fitness value.

[0033] The beneficial effects of this invention are mainly reflected in:

[0034] 1. Avoiding Information Loss and Improving Computational Efficiency: This invention abandons the mechanisms of binary mapping or threshold transformation relied upon in traditional discrete particle swarm optimization algorithms, and directly adopts set-based operations (such as difference set replacement) for particle updates. This method fundamentally avoids the information loss problem during the transformation from continuous space to discrete space, while reducing computational complexity, significantly shortening program execution time, and making it more adaptable to dynamic scenarios with high real-time requirements.

[0035] 2. Enhanced Global Optimization Capability: This invention innovatively proposes a triple guidance mechanism (individual historical optimality, global optimality, and neighbor set guidance). By introducing neighbor set guidance, the search range is expanded using physical topology information, effectively preventing premature convergence of the algorithm. This not only preserves the guiding role of high-quality solutions but also avoids local optima traps through neighborhood search, significantly improving the accuracy of leader selection.

[0036] 3. Achieving Multi-Objective Collaborative Optimization: This invention employs a strategy combining multi-weighted iteration and Pareto indifference screening, enabling it to find the optimal balance (indifference solution) between system error (anti-interference capability) and asymptotic convergence rate. This method outputs a set of mutually independent optimal solutions, providing a flexible and high-quality navigator configuration scheme for practical application scenarios with different focuses. Attached Figure Description

[0037] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0038] Figure 1 This is a flowchart of the leader selection method for multi-objective discrete particle swarm optimization based on set operations according to the present invention.

[0039] Figure 2 A schematic diagram of the communication network for a multi-agent system under the leader-follower control method.

[0040] Figure 3 This is a comparison chart of the system error performance of the present invention with that of the multi-weighted greedy algorithm and the traditional DPSO algorithm.

[0041] Figure 4 This is a comparison of the asymptotic convergence time performance of the present invention with that of the multi-weighted greedy algorithm and the traditional DPSO algorithm.

[0042] Figure 5 This is a comparison chart showing the program execution time performance of the present invention, the multi-weighted greedy algorithm, and the traditional DPSO algorithm. Detailed Implementation

[0043] The present invention will be further described below with reference to specific embodiments, but the scope of protection of the present invention is not limited thereto:

[0044] Example 1: A leader selection method for multi-objective discrete particle swarm optimization based on set operations, such as... Figure 1 As shown, this method is used in multi-agent systems employing a leader-follower control approach. Specifically, for unmanned vehicle platooning systems with link noise, this method selects a suitable unmanned vehicle as the leader to control the platoon, thereby improving the noise immunity and consistency rate of the platoon.

[0045] Step 1, Autonomous Vehicle System

[0046] The unmanned vehicle used in this embodiment adopts a three-layer platform structure. The upper layer of the mobile chassis is equipped with a WiFi module and a LiDAR navigation and obstacle avoidance device; the middle layer of the mobile chassis is equipped with a lower-level computer using an STM32 microcontroller driver board and a Jetson Nano upper-level computer; the lower layer of the mobile chassis is equipped with a power expansion board and Mecanum wheels. The WiFi module and the LiDAR navigation and obstacle avoidance device are connected to the upper-level computer via signal. The Jetson Nano upper-level computer is responsible for processing the data from the communication between the LiDAR and the unmanned vehicle, and completing the control calculations for the formation, path planning, etc.; the lower-level computer is connected to the upper-level computer and the drive motor via signal, and is mainly responsible for driving the motor and executing the instructions issued by the upper-level computer.

[0047] The autonomous vehicle system in this embodiment mainly includes controller and multi-agent systems (MASs), which include navigator autonomous vehicles and follower autonomous vehicles, such as... Figure 2 As shown. The controller and the navigator autonomous vehicle communicate via a WiFi module, and the lower-level computer controls the autonomous vehicles. The controller establishes a data communication link only with the navigator intelligent agent, and the follower intelligent agents establish data communication links only with the navigator intelligent agent or other follower intelligent agents, ensuring that each intelligent agent in the system has at least one bidirectional communication link; the controller can select any intelligent agent in the system as the navigator intelligent agent. The follower autonomous vehicles only communicate with the navigator autonomous vehicle or other follower autonomous vehicles, and do not have direct data communication with the controller. The navigator is selected by the method of this invention.

[0048] Step 2: Calculation of multi-objective optimization index and construction of fitness function

[0049] Based on the agent state update model of a multi-agent system, at least one target optimization index that can reflect the system performance is determined; then, the target optimization index is normalized based on the eigenvalues ​​corresponding to each target optimization index; finally, weight parameters are introduced. A fitness function is constructed that integrates the normalized optimization indices of each objective, thereby balancing the optimization priorities of different objective indices.

[0050] MASs topology data includes communication topology maps. ,in, For the collection of all driverless cars, The total number of driverless cars, Indicates the first The driverless car and the first Communication links between autonomous vehicles (i.e., communication links between follower autonomous vehicles and navigator autonomous vehicles, and between follower autonomous vehicles). This is a set of communication links.

[0051] The autonomous vehicle state update model in a multi-agent system is as follows:

[0052] (1)

[0053] in, For the current moment, For the first The location of the driverless car For the first The speed of the driverless car For the first A set of neighbors of an autonomous vehicle (with the autonomous vehicle) (A collection of driverless vehicles that are communicating) For driverless cars The first in the neighbor set A driverless car, For the desired state deviation, The mean is 0 and the variance is White noise, in this embodiment, for the unmanned vehicle With driverless cars White noise variance between The value of is 1. For driverless cars With driverless cars The weighting coefficient between them is taken as a value in this embodiment. ,in This indicates driverless cars. The degree value.

[0054] Define the Laplace matrix of MASs Its elements for:

[0055] (2)

[0056] The objective systematic error is defined as:

[0057] (3)

[0058] in, From the Laplace matrix The Laplace submatrix obtained after removing the corresponding row and column of the navigator is used to optimize the objective systematic error. In the real physical world, this represents the noise immunity of a multi-agent system; the lower the value, the stronger the noise immunity of the multi-agent system. It signifies a gathering of leaders. This is for calculating the trace of a matrix.

[0059] The asymptotic convergence rate of the optimization objective is defined as:

[0060] (4)

[0061] in, This is a matrix function used to calculate the minimum eigenvalue of an input matrix. From the Laplace matrix The corresponding degree matrix The degree matrix submatrix obtained after removing the corresponding rows and columns of the leader node. Optimize the asymptotic convergence rate of the objective. In the real physical world, it represents the asymptotic convergence rate of the positional state of a multi-agent system. The higher the value, the faster the multi-agent system converges.

[0062] Based on the optimization objective, establish the corresponding fitness function:

[0063] (5)

[0064] in, Indicates the optimization objective systematic error The maximum value that can be achieved is determined by the following logic and scenario selection criteria: the fewer the number of navigators, the weaker the anti-interference capability of the multi-agent system is usually, and the lower the corresponding target system error will be. The values ​​are often larger. Therefore, we select the minimum number of navigators scenario where "the number of navigators is limited to 1," and iterate through the cases where "all single nodes act as navigators," calculating the corresponding values ​​for each case. Finally, the maximum value among these results is taken as the result. . This represents the asymptotic convergence rate of the optimization objective. The maximum value that can be achieved is theoretically proven to be 1. and Normalization processing, These are the weight parameters.

[0065] For multi-agent systems with link noise, this method selects a suitable unmanned vehicle as the navigator to control the multi-agent system, aiming to improve the noise resistance and consistency rate of the multi-agent system.

[0066] Step 3, Parameter Settings

[0067] Particle swarm initialization specifically includes initializing the total number of nodes and defining the leader number constraint; configuring the total number of particles, the maximum number of iterations, and the trigger threshold for the triple guidance mechanism; randomly generating an initial candidate leader set, and initializing the individual optimal set, the global optimal set, and the weight parameter set of the fitness function. (m is the preset number of weight parameters).

[0068] MASs adopts an undirected connected topology. In this embodiment, the total number of unmanned vehicles (i.e., the total number of nodes) is... , number of particles Number of Navigators Maximum number of iterations The triple boot trigger threshold is set to .

[0069] In this embodiment, the weight parameters of the fitness function The values ​​were 0.25, 0.5, and 0.75, respectively, when testing different multi-objective optimization priority scenarios (focusing on asymptotic convergence rate, bi-objective equilibrium, and focusing on systematic error).

[0070] Step 4: Update the candidate navigator set using a triple-guiding mechanism based on set operations.

[0071] In each iteration, a triple guidance mechanism—guided by the individual historical best set, the global best set, and the neighbor set—combined with trigger thresholds for this triple guidance mechanism, iteratively updates the candidate leader set, expanding the solution space exploration range while preserving high-quality solutions. The trigger thresholds for the triple guidance mechanism include a first trigger threshold. Second trigger threshold and the third trigger threshold .

[0072] In this embodiment, the weighting parameter is set as follows: In one iteration, the set of candidate navigators for particle 4 was: The set of individual historical best navigators for particle 4 is The globally optimal set of navigators obtained by particle swarm optimization is: .

[0073] Step 4.1, Guiding with the Individual Historical Optimal Set

[0074] A random number and a first trigger threshold A comparison is made to determine whether the guidance of an individual's historical best set should proceed:

[0075] (6)

[0076] in, This indicates that a random number between 0 and 1 will be generated; if this is not triggered, the current set of candidate navigators will not be updated. Continue with step 4.2; if triggered, the current candidate navigator set will be updated based on the individual historical best navigator set for each particle. Specifically, this includes: for particles... candidate leaders Calculate the candidate navigator set The set of individual historical best leaders difference set (Right now There exists (Nodes that do not exist in the table) and the difference set (Right now There exists (Nodes that do not exist in the set), randomly selected from the difference set Select one agent intelligent agents from Remove from the difference set. One agent is randomly selected from the data. join in The mathematical expression for the above operation is:

[0077] (7)

[0078] In this iteration, formula (6) holds, and the individual historical optimal set guidance is triggered. Therefore, from formula (7) we get , In this iteration, agent 3 is randomly selected to replace agent 5 in the candidate leader set for particle 4. At this point, the candidate leader set for particle 4 is updated to... .

[0079] Then, guide the process with the globally optimal set.

[0080] Step 4.2, Global Optimal Set Guidance

[0081] A random number and a second trigger threshold A comparison is made to determine whether the global optimal set guidance should proceed:

[0082] (8)

[0083] If not triggered, the current set of candidate navigators will not be updated. Continue with step 4.3; if triggered, the current candidate leader set will be updated based on the global optimal set for each particle. Specifically, this includes: for particles... The pool of potential leaders Calculate the set of candidate navigators The global optimal navigator set of the particle swarm difference set and difference set Randomly from the difference set Select one agent intelligent agents from Remove from the difference set. One agent is randomly selected from the data. join in The mathematical expression for the above operation is:

[0084] (9)

[0085] In this iteration, formula (8) holds, and the guidance of the globally optimal navigator set is triggered. Therefore, from formula (9) we get , In this iteration, agent 9 is randomly selected to replace agent 7 in the candidate leader set for particle 4. At this point, the candidate leader set for particle 4 is updated to... .

[0086] Then, neighbor aggregation guidance is performed.

[0087] Step 4.3, Neighbor Gathering Guidance

[0088] A random number and a third trigger threshold A comparison is made to determine whether neighbor set guidance should be performed.

[0089] (10)

[0090] If not triggered, the current set of candidate navigators will not be updated. Continue to step 5; if triggered, the neighbor set of the candidate navigator will evaluate the current particle. To provide leadership. Specifically, this includes: targeting particles. The pool of potential leaders ,from One agent is randomly selected from the data. According to the topology of MASs Determine the agent Neighbor set Subsequently, from the neighborhood gathering Randomly select 1 agent Used to replace the candidate navigator set intelligent agents in , The agents in the text are all related to the agents. There is a connected link between them. The mathematical expression for the above operation is:

[0091] (11)

[0092] In this iteration, the condition for formula (10) was not met, and formula (11) was not triggered. Therefore, the candidate leader set for particle 4 remains unchanged. .

[0093] Step 5: Update the set of historically optimal navigators and the set of globally optimal navigators.

[0094] Update the individual's historical best leader set and the global best leader set, i.e., calculate the current particle's... The pool of potential leaders fitness value ,particle The set of individual historical best leaders fitness value The global optimal navigator set of the particle swarm fitness value Then: if the fitness value Superior However, it is not better than the fitness value. Then update the set of the individual historical best navigators for each particle. If fitness value Better than fitness value If a particle is better than the candidate leader set of other particles in this iteration, then update the particle. The set of individual historical best leaders With the global optimal navigator set of the particle swarm .

[0095] In this iteration, the fitness function formula (5) yields the following: In this iteration... , Therefore, the individual historical best navigator set of particle 4. Updated to The set of candidate navigators for particle 4 does not affect Update.

[0096] Step 6: Termination judgment based on maximum iteration count

[0097] Determine if the current iteration count exceeds the maximum iteration count. If the number of candidates does not exceed the limit, repeat steps 4 and 5 to continue updating the candidate leader set; if the number of candidates exceeds the limit, output the globally optimal leader set under the current weight parameters and record it as . .

[0098] In this iteration, the weight parameters are: Therefore, it is recorded as .

[0099] Step 7: Determine if the weight iteration terminates.

[0100] The set of weight parameters of the fitness function are applied sequentially. Repeat steps 4 through 6 to generate each weight parameter. The corresponding globally optimal navigator set In this embodiment, the weighting parameter , and Repeat steps 4 through 6 to generate the globally optimal navigator set corresponding to each set of weight coefficients. , and .

[0101] Step 8: Pareto indifference solution screening

[0102] The initial screening uses a fitness difference threshold to identify solutions with roughly similar performance (fitness), avoiding unnecessary analysis on solutions with significant differences. However, among the solutions with similar fitness obtained from the initial screening, there may be a group of solutions that are not dominant on any objective (dominated by other solutions), and such solutions are not worth retaining. Therefore, the Pareto characteristic comparison is introduced to further screen these solutions with similar fitness to identify those that do not dominate each other and have complementary advantages on different objectives. Only solutions that satisfy this Pareto characteristic are truly indifferent solutions with complementary value in multi-objective optimization.

[0103] Step 8.1: Comparison of fitness difference thresholds

[0104] Step 7 obtains the globally optimal navigator set In this case, each weight coefficient corresponds to an independent run of the triple-guided mechanism, which ultimately outputs a unique optimal solution. The setting of different weight coefficients allows the search direction of the triple-guided mechanism to adapt to the corresponding target priority, thereby generating multiple solutions with different performance characteristics. After calculating the fitness value of each solution through the fitness function of multi-objective differentiated weight normalization (i.e., formula (5)), if the following conditions are met:

[0105] (12)

[0106] Then, if the fitness of the two sets of solutions is similar, the candidate navigator set is selected. and The solution is retained for the subsequent Pareto characteristic judgment stage; if it does not meet the requirements, the solution with poor fitness (i.e., the solution with a lower fitness value) is directly excluded and will not participate in the subsequent screening.

[0107] in, A fitness difference threshold is preset to measure the fitness difference of the global optimal solution under different weights. When the fitness difference between any two sets of solutions does not exceed this threshold, they are judged to be closely matched.

[0108] Step 8.2: Screening for indistinguishable solutions

[0109] For candidate solutions that are close in fitness and satisfy the conditions of formula (12), extract the specific target values ​​of each solution under multiple optimization objectives; compare the Pareto characteristics of the candidate solutions pairwise. If the two sets of solutions satisfy the Pareto characteristic that "there is no one set of solutions that is better than the other set in all objectives and has complementary advantages in at least one objective", then they are determined to be indifferent solutions; after eliminating candidate solutions that are dominated by other solutions (i.e., a certain set of solutions is not superior in all objectives), the remaining solutions are summarized to form a set of indifferent solutions.

[0110] In this embodiment, the globally optimal navigator set output in step 7 , and All solutions satisfy the conditions in step 8.1, therefore, it is necessary to compare the Pareto characteristics of the three solutions. The calculation results show that... , , , , , Through comparison, it can be seen that... and Superior ,and and It exhibits Pareto characteristics, therefore and This is an indistinguishable solution.

[0111] Step 9: Output Results

[0112] All indistinguishable solutions are summarized to form the optimal navigator candidate library. In this embodiment... and This is the final output result.

[0113] experiment

[0114] The experiment employs a multi-software collaborative architecture. Specific tools and their uses are as follows:

[0115] Visual Studio Code: Runs the core code of the multi-objective discrete particle swarm optimization leader selection method based on set operations proposed in this invention;

[0116] PyCharm Community Edition 2024.2.4: Performs mean calculation on the raw data output by the algorithm;

[0117] MATLAB R2021a: Plotting system error comparison charts, asymptotic convergence rate comparison charts, and runtime comparison charts to visually present experimental results.

[0118] The experimental data was generated based on a standardized multi-agent system simulation environment, with the following specific configuration:

[0119] Network Model: The Watts-Strogatz (WS) undirected connected network model is adopted, and 25 independent MASs are randomly generated. Each system contains 100 unmanned vehicles, and each formation system has 14 generated subgraphs to consider the scenario of MAS switching communication topology.

[0120] Topology parameters: average node degree d=2, 100 communication links, reconnection probability 10%, ensuring that the topology has the sparse connectivity characteristics of a real multi-agent system;

[0121] Environmental parameters: The topology distribution of each formation system is initialized independently and randomly to avoid the randomness of results caused by a single topology and to ensure the statistical significance of the data;

[0122] To ensure the comprehensiveness and fairness of the comparison, two mainstream existing technologies were selected as the comparison benchmarks, as follows:

[0123] 1. Multi-weighted Greedy Algorithm: This method is an improvement on the traditional greedy algorithm, supporting single-objective and dual-objective weight balance optimization. The core logic is as follows: preset the number of navigator autonomous vehicles k and weight coefficients, iterate m times, each time traversing the remaining candidate nodes, calculating the minimum eigenvalue related to the corresponding system error and asymptotic convergence rate, scoring according to the preset strategy, selecting the optimal node to add to the navigator set, and finally outputting the target set and performance indicators;

[0124] 2. Traditional Discrete Particle Swarm Optimization (DPSO): The method cited is proposed by Gong et al. in "Influencemaximization in social networks based on discrete particle swarmoptimization". It uses a binary mapping mechanism and a threshold function to achieve discrete optimization, strictly follows the parameter configuration of the original literature, and shares basic parameters such as particle number and maximum number of iterations with this invention.

[0125] Overview of the experimental procedure:

[0126] The experiment uses the number of navigators, k, as the core variable, increasing progressively from 1 to 34. Each time k is adjusted, a newly generated subgraph is randomly selected from the corresponding system's switching topology set as the current communication topology. The method of this invention, the multi-weight greedy algorithm, and the traditional DPSO algorithm are run simultaneously. All three algorithms are executed according to their core logic and standard configuration to ensure experimental fairness.

[0127] In the same scenario, each algorithm was run independently 25 times to eliminate random interference, and the system error, asymptotic convergence rate, and running time were recorded in real time. After all tests were completed, the data were preprocessed: the mean of each index was calculated, and the system error was transformed by a base-10 logarithm. Finally, the data were summarized to form a complete experimental dataset to support the results analysis.

[0128] Results analysis: Figure 3 and Figure 4 The results show that the solution quality of the method of this invention is similar to that of the multi-weighted greedy algorithm and the traditional DPSO algorithm, and significantly better than that of the multi-weighted greedy algorithm. Furthermore, with the same population size and experimental settings, the computational cost of the multi-weighted greedy algorithm and the traditional DPSO algorithm is significantly lower. Figure 5 The number of navigators exhibits a sharp upward trend. This is because an increase in the number of navigators leads to a corresponding increase in the particle dimension k, significantly amplifying the computational overhead of neighborhood search in each iteration update, thereby prolonging the overall execution time. The method of this invention effectively avoids this problem, achieving a maximum iteration count... When the number of navigators k is fixed, increasing the number of navigators k will cause the running time to decrease smoothly. This is because as the number of navigators increases, the dimension of the submatrix involved in the relevant calculations decreases, and the overall computational load decreases accordingly.

[0129] Finally, it should be noted that the above examples are merely some specific embodiments of the present invention. Obviously, the present invention is not limited to the above embodiments and many variations are possible. All variations that can be directly derived or conceived by those skilled in the art from the disclosure of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A leader selection method for multi-objective discrete particle swarm optimization based on set operations, characterized in that... The steps include: S1. Obtain the topology data of the multi-agent system and construct a fitness function based on the optimization objective. The multi-agent system includes a leader agent and follower agents. S2. Initialization parameters, including the triple guidance mechanism trigger threshold, candidate navigator set, individual historical best set, global best navigator set, and fitness function weight parameter set. ; S3. In each iteration, the candidate leader set is updated sequentially through the individual historical best set, the global best set, and the neighbor set. Then, the individual historical best leader set and the global best leader set of the particle swarm are updated based on the fitness value. S4. Repeat step S3 until the maximum number of iterations, and output the global best leader set under the current weight parameters. S5. Repeat steps S3 and S4 to output the set of weight parameters. The globally optimal navigator set for each weight parameter. ; S6. Calculate the globally optimal set of navigators. The fitness values ​​of any two sets are compared with a fitness difference threshold. Sets with fitness values ​​less than the fitness difference threshold are retained. Then, Pareto indifference screening is performed on the retained sets, and the indifference solutions obtained by the screening are used as the final navigator output set.

2. The leader selection method for multi-objective discrete particle swarm optimization based on set operations according to claim 1, characterized in that: The fitness value is calculated as follows: in, Indicates the optimization objective systematic error The maximum value that can be achieved, This represents the asymptotic convergence rate of the optimization objective. The maximum value that can be achieved, It signifies the gathering of navigators. These are the weight parameters.

3. The leader selection method for multi-objective discrete particle swarm optimization based on set operations according to claim 2, characterized in that: The individual historical optimal set guides the following: When the generated random number is less than the first trigger threshold For particles Triggering operation: from the difference set Randomly select an agent from the candidate navigator set. Remove from the difference set. One agent is randomly selected from the pool to join the candidate navigator set. , This represents the set of historically best leaders for each individual.

4. The leader selection method for multi-objective discrete particle swarm optimization based on set operations according to claim 3, characterized in that: The globally optimal set is guided by: When the generated random number is less than the second trigger threshold For particles Triggering operation: from the difference set Randomly select an agent from the candidate navigator set. Remove from the difference set. One agent is randomly selected from the pool to join the candidate navigator set. , This represents the set of globally optimal navigators in a particle swarm.

5. The leader selection method for multi-objective discrete particle swarm optimization based on set operations according to claim 4, characterized in that: The neighbor set guidance is as follows: When the generated random number is less than the third trigger threshold For particles Trigger action: From the set of candidate navigators Randomly select an agent Thus, the intelligent agent is determined. Neighbor set Subsequently, from the neighborhood gathering Randomly select 1 agent Used to replace the candidate navigator set intelligent agents in .

6. The leader selection method for multi-objective discrete particle swarm optimization based on set operations according to claim 5, characterized in that: The method for updating the individual historical best leader set and the global best leader set of the particle swarm based on fitness values ​​is as follows: (1) If the fitness value Better than fitness value However, it is not better than the fitness value. Then update the set of the best historical leaders for each individual. ; (2) If the fitness value Better than fitness value If a candidate navigator set is superior to the set of other particles in this iteration, then the individual's historical best navigator set is updated. With the global optimal navigator set of the particle swarm .

7. The leader selection method for multi-objective discrete particle swarm optimization based on set operations according to claim 6, characterized in that: The method for comparing with the fitness difference threshold is as follows: Preset fitness difference threshold Then determine: If the condition is met, it is determined to be less than the fitness difference threshold, where, Represents the set of candidate navigators fitness value, Represents the set of candidate navigators The fitness value.

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