Leader selection method of multi-objective discrete particle swarm optimization based on set operation

Abstract

The present application relates to the technical field of multi-agent system control, and discloses a kind of leader selection method of multi-object discrete particle swarm optimization based on set operation, comprising: obtaining the communication topology data of multi-agent system and constructing fitness function based on system error and convergence rate;Adopt triple guiding mechanism based on set operation, in turn through individual historical optimal set, global optimal set and neighbor set guide to carry out iterative update to candidate leader set;Different weight parameters of fitness function are traversed, and the corresponding global optimal leader set is output;Finally, based on the difference threshold of fitness value and the screening of Pareto non-difference characteristics, the final leader set is obtained.The present application directly processes discrete nodes using set operation, avoiding information loss caused by binary mapping, and effectively avoiding local optimum through neighbor guiding mechanism, achieving efficient collaborative control of multi-agent system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of multi-agent system control, and particularly relates to a leader selection method based on multi-objective discrete particle swarm optimization of set operation. BACKGROUND

[0002] Multi-agent systems (MASs) rely on a distributed communication framework to realize information interaction, state updating and collaborative control among agents, and have been widely applied to key fields such as intelligent transportation systems, wireless sensor networks, mobile robot formation, industrial automation and the Internet of Things. Among various control paradigms of MASs, the leader-follower framework is an important control method, in which the leader inputs external control signals as the core of system control and dominates the dynamic behavior of the system, and the follower adjusts its behavior by accepting the state of the leader and other followers. Therefore, the reasonable selection of the leader directly determines the collaborative efficiency and control accuracy of the system.

[0003] Existing leader selection of multi-agent systems relies on greedy algorithms, but the algorithm has significant limitations: on the one hand, its decision-making relies on local search strategies, which is easily trapped in local optimization by local features and is difficult to traverse the entire solution space to filter out the global optimal leader set; on the other hand, the greedy algorithm has low computational efficiency in the face of high time complexity optimization objectives, especially in dynamic scenarios, which takes longer and is difficult to adapt to real-time control requirements.

[0004] In the multi-agent system node selection problem similar to the leader selection idea, the particle swarm algorithm has also been widely and importantly applied due to its distributed search characteristics and lower control parameter complexity, and is often used to explore better node selection schemes to adapt to system performance requirements. However, the core update formula of the existing particle swarm algorithm is mostly designed based on continuous space or relies on a binary mapping mechanism, which has low adaptability to the essential needs of discrete node set optimization in the leader selection problem, and it is difficult to directly and efficiently explore the optimal leader combination. SUMMARY

[0005] The technical problem to be solved by the present application is to provide a leader selection method based on multi-objective discrete particle swarm optimization of set operation, which avoids the problems of information loss, local optimum and poor dynamic topology adaptability of traditional algorithms, and realizes more efficient and more robust collaborative control of MASs through a three-way guidance mechanism driven by set operation and Pareto solution optimization.

[0006] To solve the above technical problems, the present application provides a leader selection method based on multi-objective discrete particle swarm optimization of set operation, which comprises 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 , then for the particle Trigger operation: randomly select an agent from the difference set and remove it from the candidate leader set , and randomly select an agent from the difference set to join the candidate leader set , represents the individual historical optimal leader set of the particle.

[0020] As a further improvement of the leader selection method of the set operation-based multi-objective discrete particle swarm optimization of the present application:

[0021] The global optimal set guide is:

[0022] When the generated random number is less than the second trigger threshold , then for the particle Trigger operation: randomly select an agent from the difference set and remove it from the candidate leader set , and randomly select an agent from the difference set to join the candidate leader set , represents the global optimal leader set of the particle swarm.

[0023] As a further improvement of the leader selection method of the set operation-based multi-objective discrete particle swarm optimization of the present application:

[0024] The neighbor set guide is:

[0025] When the generated random number is less than the third trigger threshold , then for the particle Trigger operation: randomly select an agent from the candidate leader set , and then determine the neighbor set of the agent ; subsequently, randomly select 1 agent from the neighbor set to replace the agent in the candidate leader set . As a further improvement of the leader selection method of the set operation-based multi-objective discrete particle swarm optimization of the present application:

[0026] The method for updating the individual historical optimal leader set of each particle and the global optimal leader set of the particle swarm based on the fitness value is:

[0027] ​

[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 leaders 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: the present application adopts a strategy of combining multi-weight iteration and Pareto non-inferiority screening, which can find the best balance point (non-inferiority solution) between system error (anti-interference ability) and asymptotic convergence rate. This method can output a set of optimal solutions that are not dominated by each other, providing flexible and high-quality leader configuration schemes for different practical application scenarios. BRIEF DESCRIPTION OF DRAWINGS

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

[0038] Figure 1 The flowchart of the leader selection method of the present application based on the set operation of multi-objective discrete particle swarm optimization.

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

[0040] Figure 3 The system error effect comparison chart of the present application, the multi-weight greedy algorithm and the traditional DPSO algorithm.

[0041] Figure 4 The system asymptotic convergence time effect comparison chart of the present application, the multi-weight greedy algorithm and the traditional DPSO algorithm.

[0042] Figure 5 The program running time effect comparison chart of the present application, the multi-weight greedy algorithm and the traditional DPSO algorithm. DETAILED DESCRIPTION

[0043] The present application will be further described below in conjunction with specific embodiments, but the scope of protection of the present application is not limited to this:

[0044] Example 1, the leader selection method based on the set operation of multi-objective discrete particle swarm optimization, as shown in Figure 1 shown, used in the multi-agent system adopting the leader-follower control mode, for the unmanned vehicle formation system containing link noise, through this method, select the appropriate unmanned vehicle as the leader to control the unmanned vehicle formation, in order to improve the anti-noise ability of the unmanned vehicle formation and improve the consistency rate.

[0045] Step 1, unmanned vehicle system

[0046] The unmanned vehicle used in the embodiment adopts a three-layer platform structure, and a WiFi module and a laser radar navigation and obstacle avoidance device are arranged on the upper layer of the mobile chassis; an STM32 single-chip microcomputer driving board and a Jetson Nano upper computer are arranged on the middle layer of the mobile chassis; and a power supply expansion board and a Mecanum wheel are arranged on the lower layer of the mobile chassis. The WiFi module and the laser radar navigation and obstacle avoidance device are in signal connection with the upper computer, the Jetson Nano upper computer is responsible for processing data communicated between the laser radar and the unmanned vehicle, and completes control calculation, path planning and the like on the formation; the lower computer is in signal connection with the upper computer and the driving motor, and is mainly responsible for driving the motor and executing instructions issued by the upper computer.

[0047] The unmanned vehicle system in the embodiment mainly includes a controller and a multi-agent system (MASs), and the MASs include a leader unmanned vehicle and a follower unmanned vehicle, as shown in Figure 2 The controller and the leader unmanned vehicle communicate data through a WiFi module, and the control of the unmanned vehicle is realized by a lower computer. The controller only establishes a data communication link with the leader agent, and the follower agent only establishes a data communication link with the leader agent or other follower agents, so that at least one bidirectional communication link exists between each agent in the system; the controller can select any agent in the system as the leader agent. The follower unmanned vehicle only has data communication with the leader unmanned vehicle or other follower unmanned vehicles, and does not have direct data communication with the controller. The leader is selected by the method of the application.

[0048] Step 2, multi-objective optimization index calculation and fitness function construction

[0049] Based on the agent state updating model of the multi-agent system, at least one target optimization index reflecting the performance of the system is determined; then, the target optimization indexes are normalized respectively based on the characteristic extreme values corresponding to the target optimization indexes; and then a weight parameter is introduced to construct a fitness function that integrates the normalized target optimization indexes, so as to balance the optimization priorities of different target optimization indexes.

[0050] The topology data of the MASs include a communication topology graph , wherein, is the set of all unmanned vehicles, is the total number of unmanned vehicles, represents a communication link between the th unmanned vehicle and the th unmanned vehicle (i.e. a communication link between a follower unmanned vehicle and a leader unmanned vehicle, or between follower unmanned vehicles), is the set of communication links.

[0051] The state updating model of the unmanned vehicle in the multi-agent system is:

[0052] (1)

[0053] where, is the current time, is the position of the th unmanned vehicle, is the speed of the th unmanned vehicle, is the neighbor set of the th unmanned vehicle (a set consisting of unmanned vehicles that have communication with the unmanned vehicle is the th unmanned vehicle in the neighbor set of the unmanned vehicle is the desired state deviation, is white noise with mean 0 and variance , in this embodiment, the value of the white noise variance between the unmanned vehicle and the unmanned vehicle is 1, is the weight coefficient between the unmanned vehicle and the unmanned vehicle , in this embodiment, the value is , where , indicates the degree value of the unmanned vehicle . The Laplacian matrix of the MASs is defined , the element

[0054] of which is:

[0055] (2)

[0056] The optimization target system error is defined as:

[0057] (3)

[0058] where, is the Laplacian sub-matrix obtained by removing the corresponding row and column of the leader from the Laplacian matrix . The optimization target system error represents the anti-noise interference ability of the multi-agent system in the real physical world, and the lower the value, the stronger the anti-noise ability of the multi-agent system, represents the leader set. is the calculation of the matrix trace.

[0059] The optimization target asymptotic convergence rate is defined as:

[0060] (4)​​​​

[0061] wherein, is a matrix function for calculating the minimum eigenvalue of the input matrix, is the Laplacian matrix of the MAS corresponding to the degree matrix Degree matrix sub-matrix obtained after removing the corresponding row and column of the leader node. The asymptotic convergence rate of the optimization objective The asymptotic convergence rate of the position state of the multi-agent system in the real physical world, the higher the value represents the faster the multi-agent system converges to consensus.

[0062] According to the optimization objective, the corresponding fitness function is established:

[0063] (5)

[0064] wherein, represents the system error of the optimization objective The maximum value that can be taken, and the selection basis for the scene is: the fewer the number of leaders, the weaker the anti-interference ability of the multi-agent system, and the corresponding optimization objective system error is usually larger. Therefore, the "leader number limit is 1" is selected as the least leader scene, and the corresponding is calculated by iteratively traversing "all single nodes as leaders", and the maximum value in these results is finally taken, that is, . represents the asymptotic convergence rate of the optimization objective The maximum value that can be taken, and the maximum value is 1 through theoretical proof. and are normalized processing, is a weight parameter.

[0065] For multi-agent systems with link noise, this method selects appropriate unmanned vehicles as leaders to control the multi-agent system, aiming to improve the anti-noise ability of the multi-agent system and the rate of consensus.

[0066] Step 3, parameter setting

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

[0068] The MAS adopts an undirected connected topology, and the total number of unmanned vehicles (i.e. the total number of nodes) , 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 Individual historical best leader set 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 take 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 to 6 to generate a global optimal leader set corresponding to each set of weight coefficients , and .

[0101] Step 8, screening of Pareto non-difference solution

[0102] The fitness difference threshold is first used for preliminary screening to select solutions with similar performance (fitness) to avoid ineffective analysis in solutions with obvious differences. However, among the solutions with similar fitness obtained by preliminary screening, there may be solutions that are not superior in all objectives (dominated by other solutions), which are not valuable. Therefore, the Pareto property comparison is introduced to further screen solutions that are not dominated by each other and have complementary advantages in different objectives. Only solutions that meet this Pareto property are truly non-difference solutions with complementary value of multi-objective optimization.

[0103] Step 8.1, fitness difference threshold comparison

[0104] Global optimal leader set obtained in step 7 Each weight coefficient corresponds to an independent run of the triple boot mechanism, and the final output is a unique optimal solution. Different weight coefficients make the search direction of the triple boot mechanism adapt to the priority of the corresponding objective, and then generate multiple solutions with different performance characteristics. After calculating the fitness values of each solution through the multi-objective differentiated weight normalized fitness function (i.e. formula (5)), if it meets:

[0105] (12)

[0106] It is determined that the adaptability of the two solutions is similar, and the candidate leader set and are retained for subsequent Pareto property judgment; if not, the solution with poor adaptability (i.e. the solution with lower fitness value) is directly excluded and does not participate in subsequent screening.

[0107] Wherein, is the preset fitness difference threshold, which is used to measure the adaptability difference of global optimal solutions under different weights. When the fitness difference of any two solutions does not exceed this threshold, it is determined that the adaptability is similar.

[0108] Step 8.2, screening of non-difference solution

[0109] For the candidate solutions that meet the condition reserved in formula (12), the specific target values of each solution under multiple optimization targets are extracted; the Pareto characteristics of the candidate solutions are compared with each other, if two sets of solutions meet the Pareto characteristics that "there is no set of solutions that is superior to another set in all targets, and at least presents complementary advantage in one target", it is determined as non-difference solution; after eliminating the candidate solutions that are dominated by other solutions (i.e. a set of solutions is not superior in all targets), the remaining solutions are summarized to form a non-difference solution set.

[0110] In the embodiment, the global optimal leader set output by step 7 , and all meet the condition of step 8.1, so the Pareto characteristics of the three solutions need to be compared. From the calculation results, it can be seen that , , , , , . Through comparison, it can be seen that and are superior to , while and present Pareto characteristics, so and are non-difference solutions.

[0111] Step 9, output results

[0112] All non-difference solutions are summarized to form an optimal leader candidate library, in the embodiment and are the final output results.

[0113] Experiment

[0114] The experiment adopts a multi-software collaborative architecture, and the specific tools and purposes 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 operation proposed by the present application;

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

[0117] MATLAB R2021a: draws system error comparison chart, asymptotic convergence rate comparison chart and running time comparison chart to intuitively present the experimental results.

[0118] The experimental data is generated based on a standardized multi-agent system simulation environment, and the specific configuration is as follows:

[0119] Network model: The Watts-Strogatz (WS) undirected connected network model is adopted, 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 switching communication topology of MAS;

[0120] Topological parameters: the average node degree d = 2, the communication link has 100, the reconnection probability is 10%, and the topology has the sparse connected characteristics of the real multi-agent system;

[0121] Environmental parameters: the topology structure distribution of each formation system is independently and randomly initialized to avoid the randomness of the 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 types of mainstream existing technologies are selected as the comparison benchmarks, as follows:

[0123] 1. Multi-weight greedy algorithm: This method is based on the improvement of the traditional greedy algorithm, supporting single-objective and double-objective weight balance optimization. The core logic is: preset the number of leader unmanned vehicles k and the weight coefficient, iterate m times, calculate the corresponding system error and the minimum eigenvalue related to the asymptotic convergence rate for each remaining candidate node, score according to the preset strategy, select the optimal node to join the leader set, and finally output the target set and performance indicators;

[0124] 2. Traditional discrete particle swarm optimization algorithm (DPSO): The reference source is the method proposed by Gong et al. in “Influence maximization in social networks based on discrete particle swarm optimization”, which uses a binary mapping mechanism and a threshold function to realize discrete optimization, and strictly follows the parameter configuration of the original literature, sharing basic parameters such as the number of particles and the maximum number of iterations with the present invention.

[0125] Experiment process overview:

[0126] The experiment takes the number of leaders k as the core variable, which is gradually increased in order from 1 to 34. Each time k is adjusted, a newly generated subgraph is randomly selected from the switching topology set of the corresponding system as the current communication topology. The present invention method, the multi-weight greedy algorithm and the traditional DPSO algorithm are run synchronously, and the three algorithms are executed according to their own core logic and standard configuration to ensure the fairness of the experiment.

[0127] Under the same scenario, each algorithm is independently run 25 times to exclude random interference, and the system error, asymptotic convergence rate and running time are recorded in real time. After all the tests are completed, the data is pre-processed: the mean of each index is calculated, and the base 10 logarithmic transformation is performed on the system error, and finally the complete experimental data set is formed to support the result analysis.

[0128] Result analysis: Figure 3 and Figure 4 It is shown that the solution quality of the method of the present application is similar to that of the multi-weighted greedy algorithm and the conventional DPSO algorithm, and is significantly better than that of the multi-weighted greedy algorithm. Moreover, under the condition that the population size and the experimental setting are consistent, the calculation cost of the multi-weighted greedy algorithm and the conventional DPSO algorithm shows a sharp upward trend in Figure 5 This is because the increase in the number of leaders will cause the particle dimension k to increase accordingly, significantly increasing the calculation overhead of the neighborhood search in each iteration update, and thus prolonging the overall execution time. The method of the present application effectively avoids this problem, and when the maximum number of iterations is fixed, the increase in the number of leaders k will cause the running time to steadily decrease, because after the number of leaders increases, the dimension of the sub-matrix involved in the related calculation decreases, and the overall calculation amount decreases accordingly.

[0129] Finally, it should be noted that the above enumeration is only a few specific embodiments of the present application. Obviously, the present application is not limited to the above embodiments, and there can be many variations. All variations that can be directly derived or inferred from the disclosure of the present application by those of ordinary skill in the art should be considered as falling within the scope of the present application.

Claims

1. A leader selection method based on set operation of multi-objective discrete particle swarm optimization, 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 a follower agent. For unmanned vehicle platooning systems with link noise, the unmanned vehicle system mainly includes the controller and the multi-agent system MASs, which includes the leader unmanned vehicle and the follower unmanned vehicle. S2, initializing parameters, including triple booting mechanism trigger threshold, candidate leader set, individual historical optimal set, global optimal leader set and weight parameter set of fitness function ; The autonomous vehicle state update model in a multi-agent system is as follows: （1） 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 group of neighbors of driverless cars, 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, driverless car With driverless cars White noise variance between The value of is 1. For driverless cars With driverless cars The weighting coefficients between them ,in This indicates driverless cars The degree value; 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, then output the globally optimal navigator set under the current weight parameters; S5, repeating steps S3 and S4, outputting the weight parameter set the global optimal leader set of each weight parameter in the middle ; S6、calculating a global optimal leader set The difference between the fitness values of any two sets is calculated and compared with a fitness difference threshold; the sets with a fitness value difference less than the fitness difference threshold are retained, and then the retained sets are screened for Pareto non-inferiority, and the non-inferior solutions obtained by screening are output as the final leader 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: wherein, represents the optimization target system error the maximum value that can be taken, represents the optimization target asymptotic convergence rate the maximum value that can be taken, represents the set of pilots, is a weight parameter.

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 , then for the particle Trigger operation: randomly select an agent from the difference set and remove it from the candidate leader set , and randomly select an agent from the difference set and add it to the candidate leader set , represents the individual historical optimal leader set.

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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