CN116611468A - Particle swarm search method based on communication-free robots - Google Patents
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Abstract
The invention provides a particle swarm search method based on no communication between robots, wherein in a two-dimensional or three-dimensional optimized search task, a plurality of robots without mutual communication capability are distributed in a search space, the swarm robots are regarded as particle swarms, each robot is regarded as particle, S & W particles in a corresponding particle swarm algorithm are replaced by S & W robots, S & W particle sets are replaced by S & W robot sets, environmental modeling is carried out, and field source signal values detected by the robots are used as adaptive value indexes of the particle swarm algorithm. According to the invention, the traditional particle swarm algorithm is improved, the unidirectional active detection capability of particles is utilized, and the particle swarm does not need to share the adaptive value and the position information in a mutual communication way, so that the particle swarm algorithm has the iterative search capability in the optimized problem space for the first time under the condition of no communication, and is applied to the group robot search task, so that the particle swarm algorithm has very excellent search performance.
Description
Technical Field
The invention relates to the field of group intelligence and group robot target search, in particular to a particle swarm algorithm variant without communication among particles and a target search method for applying the particle swarm algorithm variant to a group robot.
Background
The particle swarm algorithm is a population intelligent algorithm, also called particle swarm optimization and particle swarm algorithm, is a heuristic evolutionary algorithm proposed in 1995 by simulating shoal or shoal foraging movements of Kennedy, eberhart and the like, can effectively search and find candidate solutions in the problem containing Gao Weijie space, and is used for solving the problem of global optimization. Because of the simplicity and rapid convergence of the parameters, particle swarm optimization has been rapidly developed into a mainstream global optimization technique since the proposal, and has been successfully applied to various fields for solving practical problems. However, as the particle search in the algorithm has certain randomness, the method does not ensure that the best solution found by the method is a true best solution. Therefore, many scholars continuously propose variants of particle swarm algorithms, balancing global and local search capabilities of the swarm by various means, to effectively improve their optimization performance.
Since birth, many particle swarm algorithm variants currently require inter-particle communication to share their adaptation values and find the best position searched among particles, so as to realize effective cooperation among particles. Since current particle swarm algorithms rely on inter-particle communication, they are no longer applicable when faced with situations where communication is not smooth or there is no communication.
For a communication-free scenario, some scholars have proposed some source localization algorithms that are applied to 2-dimensional or 3-dimensional space. These source localization algorithms can solve the single-mode single-source problem in 2-dimensional or 3-dimensional space without communication. However, these communication-free source localization algorithms do not take into account high-dimensional or multi-modal multi-source issues. Thus, they cannot be directly applied to high-dimensional or multi-modal problems without extension.
Swarm robots are self-coordinating systems composed of multiple robots that combine into one organism to perform a common task. Population robotics is emerging in the field of artificial population intelligence and biological research is being conducted on the field of population behavior in insects, ants and other nature. Swarm robots are generally composed of the same type of robot that can interact with other partners and environments using simple sensors. Swarm robots aim to solve problems that cannot be solved by a single robot, or to more efficiently accomplish the goal by clustering.
When the robots are regarded as particles and the swarm robots are regarded as particle swarms, a particle swarm algorithm can be applied to the search task of the swarm robots. However, sharing adaptation values by means of inter-robot communication is challenging in some application scenarios, such as acoustic communication in an underwater environment being affected by high transmission loss, high environmental noise and high propagation delay; in the search space, the existence of strong electronic/electromagnetic interference causes unreliable communication channels; the group robot encounters some serious software or hardware faults to cause that a communication channel cannot be established; robots are in competition relationship and are not willing to share the searched adaptation value data. Therefore, it is necessary to invent a variant of the particle swarm algorithm that has excellent searching performance without communication between particles and apply it to the task of swarm robot searching.
Disclosure of Invention
Aiming at the defect that the prior particle swarm algorithm variant cannot be applied to the scene without communication among some robots, the invention provides a particle swarm search method based on the scene without communication among robots. The particle swarm algorithm of the invention is modified by utilizing the active detection capability of the particles themselves to detect the position and velocity of other particles rather than directly relying on inter-particle communication. Each particle simultaneously follows its selected leader and the detected center position of the particle swarm to search in the problem space. In the particle swarm algorithm, pbest represents an individual historical optimal position (i.e., personal best) searched by the particle itself, which corresponds to an optimal fitness value searched by the particle. The invention adopts S & W to refer to stop-and-wait, and S & W particles are particles which stay at the position of a pbest and have zero speed. When the single particle does not continuously update the pbest within the preset algebra K, the single particle is rolled back to the pbest position to become the S & W particle and added to the S & W particle group. When the total number of particles in the set of S & W particles reaches or exceeds the preset threshold M, each S & W particle randomly selects the other S & W particles as its leader. Accordingly, the particle swarm can be searched in the search space in an iterative manner without communication until the search is finished to obtain an optimal solution. By applying the particle swarm algorithm variant without communication among particles in the swarm robot search task, the invention realizes the particle swarm search method without communication among robots.
The invention is realized by the following technical scheme:
in an actual two-dimensional or three-dimensional optimized search task, a plurality of robots which do not have the capability of mutual communication are distributed in a search space, the group of robots are regarded as particle groups, each robot is regarded as particles, S & W particles (sets) in a corresponding particle swarm algorithm are replaced by S & W robots (sets), environmental modeling is carried out, and field source signal values detected by the robots are used as adaptive value indexes of the particle swarm algorithm. The method comprises the following specific steps:
step 1.1: initializing parameter settings of a particle swarm algorithm: the number of particles N, the dimension D of the optimization problem, the inertia weight omega and the constant acceleration factor c 1 And c 2 The threshold value K, S of the failure of the continuous updating of the pbest&The threshold M of the particle number of the W particle group and the maximum iteration number T.
Step 1.2: randomly initializing the initial positions and speeds of N robots, i.e. the positions of robot i And speed->Where i e {1,2,..N }.
Step 1.3: randomly initializing the leader of N robots, and marking the leader of robot i as l i 。
Step 1.4:robots do not have the ability to communicate with each other, and obtain position location and speed sensing capabilities through unidirectional active detection capabilities including, but not limited to, visual observation, radar detection, sonar search, and the like. The robots detect the positions of other robots and calculate the central position of the group robot through the positions of all the robots
Where D e {1,2,.,. D } is the D-th dimension search space of the optimization problem.
Step 1.5: traversing all robots in the group of robots, if traversed robot i has selected a leader, then executing steps 1.6 and 1.7, where i e {1, 2..N }.
Step 1.6: the speed and position of the robot are updated, and the update formulas are respectively as follows:
wherein r is 1 、r 2 Is a D-dimensional random number vector;indicating the leader position selected by robot i.
Step 1.7: evaluating its adaptation value based on the current position of the robot, updating pbest, and determining whether the robot can become an S & W robot (S & W is an abbreviation of stop-and-wait, stop and wait); if the robot can be an S & W robot, the robot returns to the pbest to wait.
Step 1.8: traversing all S & W robots in the group of robots, each S & W robot performing step 1.9.
Step 1.9: checking whether the number of robots in the S & W robot set reaches or exceeds a threshold M, and if so, randomly selecting a leader for the S & W robots.
Step 1.10: if the current iteration number is greater than the maximum iteration number T or the optimal target source is successfully searched, executing the step 1.11, otherwise returning to the step 1.4 to perform the next iteration.
Step 1.11: and returning the optimal pbest and the adaptive value thereof in all robots, and taking the optimal pbest and the adaptive value thereof as a final search result.
Further, in the step 1.3, each of the group robots {1,2,., N } is randomly selected as its leader for another robot in the group robot:
l i ＝randi({1，2，...，N}-{i})；
wherein randi (-) is a random selection function for randomly selecting one robot from a group of robots, l i Is a leader of robot i.
In the step 1.4, in the application of the actual optimized search task, the unidirectional active detection capability of the robot can be used for unidirectional active detection of the positions of other robots in the group and sensing the speeds of the other robots by configuring devices such as cameras, millimeter wave radars or sonars in the optimized search task of the air, the ground, the sea surface or the sea bottom.
In step 1.6 above, robot i follows its selected leader position at the same timeAnd group robot center position->To update its speed.
In the above step 1.7, the sub-steps are subdivided as follows:
step 1.7.1: the number of times that each robot fails to update its pbest continuously, for the minimum optimization problem, its update formula is:
for the maximum optimization problem, the update formula is as follows:
where f (-) is an adaptive value function of the optimization problem to be searched, k i Is the number of times that the pbest continuous update of robot i fails.
Step 1.7.2: each robot judges the number k of times of failure of the continuous updating of the pbest i If the threshold value K is reached or exceeded, the robot is retracted to the pbest position, the leader recorded before the robot is cleared, the speed is cleared, and S is formed&W robot:
if k i ≥K
X i ＝pbest；l i ＝0；V i ＝(0 1 ，0 2 ，...，0 D )；
end
in the above step 1.9, the sub-steps are subdivided as follows:
step 1.9.1: each S & W robot actively detects other S & W robots, and all the detected S & W robots are added into the S & W robot set:
i∈P if V i ＝(0 1 ，0 2 ，...，0 D )
wherein zero velocity vector V i ＝(0 1 ，0 2 ，...，0 D ) Representing the detection of particle i as S&W robot. P represents the detected S&W robot set, P contains all S&W robot.
Step 1.9.2: when the number of robots in the set of S & W robots P reaches or exceeds the threshold M, each S & W robot randomly selects some other S & W robot as its leader:
l i ＝randi(P-{i})if|P|≥M and i∈P
where |P| denotes the number of robots in the S & W robot set, randi () is a random selection function for randomly selecting another S & W robot.
The beneficial effects are that:
the traditional particle swarm algorithm needs the mutual communication among particles to share the searched adaptation value and the position information, the unidirectional active detection capability of the particles is utilized by improving the traditional particle swarm algorithm, and the particle swarm does not need to share the adaptation value and the position information in a mutual communication way, so that the particle swarm algorithm has the iterative search capability in an optimal problem space for the first time under the condition of no communication, and is applied to a group robot search task. The swarm robot carries out a comparison experiment by applying the method and the other two particle swarm algorithm variants SPSO and CSO, and the result shows that the method has very excellent searching performance.
Drawings
FIG. 1 is a schematic diagram of a two-dimensional multi-modal search task scenario and its fitness values.
FIG. 2 is a schematic illustration of a contour line of adaptation values in a search space in a two-dimensional multi-modal search task scenario.
Fig. 3 is a schematic flow chart of the application of the method of the present invention when the swarm robot is regarded as a particle swarm.
Fig. 4 is a schematic diagram of a search process (first iteration) in a simulated dual-source environment using the method of the present invention, each of which corresponds to a state of the search process at a different number of iterations.
Fig. 5 is a schematic diagram of a search process (fourth iteration) in a simulated dual-source environment using the method of the present invention, each of which corresponds to a state of the search process at a different number of iterations.
Fig. 6 is a schematic diagram of a search process (sixth iteration) in a simulated dual-source environment using the method of the present invention, each of which corresponds to a state of the search process at a different number of iterations.
Fig. 7 is a schematic diagram of a search process (seventh iteration) in a simulated dual-source environment using the method of the present invention, each of which corresponds to a state of the search process at a different number of iterations.
Fig. 8 is a schematic diagram of a search process (tenth iteration) in a simulated dual-source environment using the method of the present invention, each of which corresponds to a state of the search process at a different number of iterations.
Fig. 9 is a schematic diagram of a search process (fifty-fifth iteration) in a simulated dual-source environment using the method of the present invention, each of which corresponds to a state of the search process at a different number of iterations.
FIG. 10 is an example function f at CEC2017 1 Next, the swarm robot applies the method of the invention and applies the convergence graph of the comparative particle swarm algorithm variant.
FIG. 11 example function f at CEC2017 9 Next, the swarm robot applies the method of the invention and applies the convergence graph of the comparative particle swarm algorithm variant.
FIG. 12 example function f at CEC2017 11 Next, the swarm robot applies the method of the invention and applies the convergence graph of the comparative particle swarm algorithm variant.
FIG. 13 example function f at CEC2017 16 Next, the swarm robot applies the method of the invention and applies the convergence graph of the comparative particle swarm algorithm variant.
FIG. 14 example function f at CEC2017 22 Next, the swarm robot applies the method of the invention and applies the convergence graph of the comparative particle swarm algorithm variant.
FIG. 15 example function f at CEC2017 26 Next, the swarm robot applies the method of the invention and applies the convergence graph of the comparative particle swarm algorithm variant.
Detailed Description
According to the invention, the active detection capability of the robot is fully utilized, so that the particle swarm algorithm variant without communication among particles is expanded and applied to the search task scene without communication among the robots for the first time. In the implementation of the present invention, the swarm robots are considered as particle swarms, each robot is considered as a particle, and the S & W particles (set) in the particle swarm algorithm variant are replaced by S & W particles (set). According to the particle swarm algorithm variant, a mechanism that when continuous updating of the pbest (individual history optimal position) fails when particles follow the leader and the center of the particle swarm is skillfully designed, the particle swarm algorithm falls back to the pbest position is returned, and the history optimal solution of particle searching can be fully utilized; meanwhile, the invention designs a mechanism for randomly selecting the leader from the S & W particle set by the S & W particles, and increases the leader diversity of the particle group. The two mechanisms introduced by the invention can effectively balance the global exploration and local development capabilities of the particle swarm algorithm, and compared with particle swarm algorithm variants SPSO and CSO which need to be communicated among particles in comparison, experiments show that the method has more excellent optimal searching capability.
In the particle swarm search method based on no communication between robots, in an actual two-dimensional or three-dimensional optimization search task (refer to a scene schematic diagram of an optimization search problem in fig. 1 and 2, wherein a plurality of local extremum values and a global optimum value exist, a field source signal value corresponding to a unique global optimum value and the position thereof need to be found in a search space), a plurality of robots which do not have the mutual communication capability are distributed and arranged in the search space, the swarm robots are regarded as particle swarms, each robot is regarded as particles, S & W particles (set) in a corresponding particle swarm algorithm are replaced by S & W robots (set), environment modeling is carried out, and the field source signal value detected by the robots is regarded as an adaptive value index of the particle swarm algorithm. The method can be applied to the group robot searching task and can show very excellent searching performance. In the embodiment, the particle swarm search task based on no communication between robots, that is, the technical scheme task of the invention, for example, but not limited to, can be applied to the following scenes:
harmful gas leakage source positioning: harmful gas leakage exists in a region, but leakage source information is unknown, and a plurality of entity robots with active detection capability and no mutual communication capability position the specific position of the leakage source according to gas concentration values detected at different positions and speeds of other robots detected actively;
rescue after disaster: in order to locate survivors under ruins after rescue and disaster relief, a robot with sensing equipment such as a radar life detector is used for detecting vital sign intensity values of all positions on site under the condition that communication conditions are not available, and the searching method is utilized to locate the position with the strongest vital sign.
By robot is meant in the embodiments a robot with active detection capabilities but without mutual communication capabilities, such as by way of example and not limitation, an unmanned aerial vehicle, an unmanned underwater vehicle. The active detection capability described herein includes, but is not limited to, position location capability and velocity identification capability obtained by visual observation, radar detection, sonar search, and the like.
The technical scheme of the invention is described in detail below with reference to the accompanying drawings and examples.
Examples
As shown in fig. 3, in this embodiment, a particle swarm search method that does not require communication between robots is used, and in the practical application of the optimized search task, the swarm robots need to search out the field intensity value and the position of the optimal source. And a plurality of robots which do not have the capability of mutual communication are distributed in the search space, the group robots are regarded as particle groups, each robot is regarded as particle, S & W particles (sets) in the corresponding particle swarm algorithm are replaced by S & W robots (sets), environment modeling is carried out, and the field source signal value detected by the robots is used as an adaptive value index of the particle swarm algorithm. The method specifically comprises the following steps:
step 1.1: initializing parameter settings of a particle swarm algorithm: the number of particles n=50, the dimension d=50 of the optimization problem, the inertial weight ω= 0.72984, and the constant acceleration factor c 1 = 1.496172 and c 2 Threshold k=2, s for success of pbest continuous update =1.496172&The threshold number of particles m=25 for the W particle set and the maximum number of iterations t=10000.
Step 1.2: randomly initializing the initial positions and speeds of N robots, i.e. the positions of robot i And speed->Where i e {1,2,..N }.
Step 1.3: randomly initializing the leader of N robots, and marking the leader of robot i as l i 。
Step 1.4: robots do not have the ability to communicate with each other, and obtain position location and speed sensing capabilities through unidirectional active detection capabilities, including but not limited to, visual observation, radar detection, or sonar search. The robots detect the positions of other robots through the active detection capability, and calculate the central positions of group robots through the positions of all the robots
Where D e {1,2,.,. D } is the D-th dimension search space of the optimization problem.
Step 1.5: traversing all robots in the group of robots, if traversed robot i has selected a leader, then steps 1.6 and 1.7 are performed, where i e {1, 2..N }.
Step 1.6: the speed and position of the robot are updated, and the update formulas are respectively as follows:
wherein r is 1 、r 2 Is a D-dimensional random number vector;indicating the leader position selected by robot i.
Step 1.7: evaluating its adaptation value based on the current position of the robot, updating pbest, and determining whether the robot can become an S & W robot (S & W is an abbreviation of stop-and-wait, stop and wait); if the robot can be an S & W robot, the robot returns to the pbest to wait.
Step 1.8: traversing all S & W robots in the group of robots, each S & W robot performing step 1.9.
Step 1.9: checking whether the number of robots in the S & W robot set reaches or exceeds a threshold M, and if so, randomly selecting a leader for the S & W robots.
Step 1.10: if the current iteration number is greater than the maximum iteration number T or the optimal target source is successfully searched, executing the step 1.11, otherwise returning to the step 1.4 to perform the next iteration.
Step 1.11: and returning the optimal pbest and the adaptive value thereof in all robots, and taking the optimal pbest and the adaptive value thereof as a final search result.
Further, in the step 1.3, each of the group robots {1,2,., N } is randomly selected as its leader for another robot in the group robot:
l i ＝randi({1，2，...，N}-{i})；
wherein randi (-) is a random selection function for randomly selecting one robot from a group of robots, l i Is a leader of robot i.
In the step 1.4, in the application of the actual optimized search task, the unidirectional active detection capability of the robot can be used for unidirectional active detection of the positions of other robots in the group and sensing the speeds of the other robots by configuring devices such as cameras, millimeter wave radars or sonars in the optimized search task of the air, the ground, the sea surface or the sea bottom.
In step 1.6 above, robot i follows its selected leader position at the same timeAnd group robot center position->To update its speed.
In the above step 1.7, the sub-steps are subdivided as follows:
step 1.7.1: the number of times that each robot fails to update its pbest continuously, for the minimum optimization problem, its update formula is:
for the maximum optimization problem, the update formula is as follows:
where f (-) is an adaptive value function of the optimization problem to be searched, k i Is the number of times that the pbest continuous update of robot i fails.
Step 1.7.2: each robot judges the number k of times of failure of the continuous updating of the pbest i If the threshold value K is reached or exceeded, the robot is retracted to the pbest position, the leader recorded before the robot is cleared, the speed is cleared, and S is formed&W robot:
if k i ≥K
X i ＝pbest；l i ＝0；V i ＝(0 1 ，0 2 ，...，0 D )；
end
in the above step 1.9, the sub-steps are subdivided as follows:
step 1.9.1: each S & W robot actively detects other S & W robots, and all the detected S & W robots are added into the S & W robot set:
i∈P if V i ＝(0 1 ，0 2 ，...，0 D )
wherein zero velocity vector V i ＝(0 1 ，0 2 ，...，0 D ) Representing that the detected robot i is S&W robot. P represents the detected S&W machineHuman collection, P contains all S&W robot.
Step 1.9.2: when the number of robots in the set of S & W robots P reaches or exceeds the threshold M, each S & W robot randomly selects some other S & W robot as its leader:
l i ＝randi(P-{i})if|P|≥M and i∈P
where |P| denotes the number of robots in the S & W robot set, randi () is a random selection function for randomly selecting another S & W robot.
Fig. 4 to 9 are processes of the swarm robot performing an optimization search in a dual-source environment where two local field source signal extrema exist in a two-dimensional search space using the method of the above-described embodiment. A plurality of robots which do not have the capability of communicating with each other are distributed in the search space, the group of robots are regarded as particle groups, and each robot is regarded as particle. Wherein the parameters are set to n=20, d=2, ω=0.72984, c 1 ＝1.496172，c 2 =1.496172, k=3, m=10, the arrow direction indicates the leader that the robot follows its choice. As shown in fig. 4, at the time of the 1 st iteration initialization, all robots randomly select another robot in the group robot as a leader. As shown in fig. 5, at iteration 4, 3 robots fail to continuously update pbest and the number of failures reaches or exceeds the threshold k=3, so it becomes S&W robot. As shown in FIG. 6, at iteration 6, S&The total number of W robots exceeds the threshold m=10, so each S&W robot randomly selects another S&The W robot is a leader. As shown in FIG. 7, at iteration 7, the previous generation selects the leader S&The W robots start to search along with the leader and the group robot center at the same generation, and 3 other robots in the group robot become new S&W robot. As shown in FIG. 8, at iteration 10, a newly generated S&The total number of W robots exceeds the threshold m=10 again, these S&The W robot again randomly selects the leader. As shown in fig. 9, at iteration 55, all robots converge to a globally optimal source location as the search proceeds.
Verification of this embodiment at CEC2017 reference function test set:
to more intuitively verify the performance of the present invention in optimizing search problems, the minimization problem in complex signal environments was simulated using 29 functions (excluding unstable Function 2) in the test set of benchmark functions of CEC2017 (N.Awad, M.Ali, J.Liang, B.Qu, and p.suganthan, "Problem definitions and evaluation criteria for the CEC2017 special session and competition on single objective real-parameter numerical optimization," Nanyang Technological University, singapore and Computational Intelligence Laboratory, zhengzhou University, zhengzhou, china, technical Report, vol.10, 2017.) with only one minimum for each Function's target source and decoys for the remaining extrema.
The particle swarm algorithm variant (CfPSO) which is not required to be communicated between robots and the particle swarm algorithm variant SPSO (D.Bratton and J.Kennedy, "Defining a standard for particle swarm optimization," in IEEE Swarm Intelligence Symposium, pp.120-127,2007.) and CSO (R.Cheng and Y.jin, "" A competitive swarm optimizer for large scale optimization, "IEEE Transactions on Cybernetics, vol.45, pp.191-204,2015.) which are required to be communicated between the other two robots are respectively applied to the group robot search task, and are compared by using a CEC2017 reference function test set, each algorithm is run 51 times on each function, and the average value of the search results is taken.
TABLE 1 comparative PSO Algorithm variant parameter settings
The detailed data of the convergence accuracy comparison experiment are shown in table 2, wherein Mean marks the average search result of 51 runs, std. represents the variance of the search result, rank represents the Rank of the comparison algorithm, bold type marks the optimal search result of each function, and a.r. is the average Rank of each algorithm divided by 29 after the Rank values of 29 functions are summed.
The convergence accuracy comparison experiment shows that among all 29 functions, cfPSO is superior to SPSO over 24 functions and CSO over all functions. The overall average rank of CfPSO is 1.17, leading largely SPSO and CSO.
Table 2-CEC2017 Convergence accuracy comparison experiment
FIGS. 10-15 illustrate the application of the 6 example functions (f 1 ,f 9 ,f 11 ,f 16 ,f 22 ,f 26 ) The convergence curves on the graph are compared. Wherein CfPSO is the method of the invention, SPSO and CSO are variants of the particle swarm algorithm for comparison. From the convergence graph, the convergence speed of the method CfPSO is faster than that of SPSO. CSO has a convergence rate similar to that of CfPSO, but has far poorer convergence accuracy than CfPSO.
As can be seen from comparative experiments on CEC2017 test function sets, cfPSO has better convergence accuracy and convergence speed than SPSO and CSO. This shows that by using the method of the present invention (CfPSO), the optimal searching capability of group robots can be greatly improved without communication between robots, thereby rapidly and effectively locating the optimal target source.
While the foregoing is directed to the preferred embodiments of the present invention, it will be appreciated by those skilled in the art that changes and modifications may be made without departing from the principles of the invention, such changes and modifications are also intended to be within the scope of the invention.
Claims (5)
1. A particle swarm search method based on no communication between robots is characterized in that in a two-dimensional or three-dimensional optimized search task, a plurality of robots without mutual communication capability are distributed in a search space, swarm robots are regarded as particle swarms, each robot is regarded as particle, S & W particles in a corresponding particle swarm algorithm are replaced by S & W robots, S & W particle sets are replaced by S & W robot sets, environmental modeling is carried out, and field source signal values detected by the robots are used as adaptive value indexes of the particle swarm algorithm; the method comprises the following specific steps:
step 1.1: initializing parameter settings of a particle swarm algorithm: the number of particles N, the dimension D of the optimization problem, the inertia weight omega and the constant acceleration factor c 1 And c 2 Threshold value K, S for continuous updating failure of individual history optimal position pbest&A particle number threshold M of the W particle group and a maximum iteration number T;
step 1.2: randomly initializing the initial positions and speeds of N robots, i.e. the positions of robot i And speed->Where i ε {1,2, …, N };
step 1.3: randomly initializing the leader of N robots, and marking the leader of robot i as l i ；
Step 1.4: the robots detect the positions of other robots and calculate the central position of the group robot through the positions of all the robots
Wherein D ε {1,2, …, D } is the D-th dimension search space of the optimization problem;
step 1.5: traversing all robots in the group of robots, if traversed robot i has selected a leader, executing step 1.6 and step 1.7, wherein i is {1,2, …, N };
step 1.6: the speed and position of the robot are updated, and the update formulas are respectively as follows:
wherein r is 1 、r 2 Is a D-dimensional random number vector;indicating a leader position selected by the robot i;
step 1.7: evaluating an adaptation value of the robot based on the current position of the robot, updating the pbest, and determining whether the robot can become an S & W robot; if the robot can be an S & W robot, returning to a pbest for waiting;
step 1.8: traversing all S & W robots in the group robots, wherein each S & W robot executes step 1.9;
step 1.9: checking whether the number of robots in the S & W robot set reaches or exceeds a threshold M, and if so, randomly selecting a leader for the S & W robots;
step 1.10: if the current iteration times are greater than the maximum iteration times T or the optimal target source is successfully searched, executing the step 1.11, otherwise returning to the step 1.4 to perform the next iteration;
step 1.11: and returning the optimal pbest and the adaptive value thereof in all robots, and taking the optimal pbest and the adaptive value thereof as a final search result.
2. The method for searching for particle swarm based on no-communication between robots according to claim 1, wherein in said step 1.3, each of the swarm robots {1,2, …, N } is randomly selected as a leader thereof for another robot in the swarm robots:
l i ＝randi({1，2，…，W}-{i})；
wherein randi (-) is a random selection function for randomly selecting one robot from a group of robots, l i Is a leader of robot i.
3. The method for searching for particle swarm based on no-communication between robots according to claim 1, wherein in said step 1.6, the robot i follows its selected leader position at the same timeAnd group robot center position->To update its speed.
4. The method for searching for particle swarm based on no-communication between robots according to claim 1, wherein in said step 1.7, the method is subdivided into the following sub-steps:
step 1.7.1: the number of times that each robot fails to update its pbest continuously, for the minimum optimization problem, its update formula is:
for the maximum optimization problem, the update formula is as follows:
where f (-) is an adaptive value function of the optimization problem to be searched, k i The number of times that the pbest continuous update of the robot i fails;
step 1.7.2: each robot judges the number k of times of failure of the continuous updating of the pbest i If the threshold value K is reached or exceeded, the robot is retracted to the pbest position, the leader recorded before the robot is cleared, the speed is cleared, and S is formed&W robot:
if k i ≥K
X i ＝pbest；l i ＝0；V i ＝(0 1 ,0 2 ,…,0 D )；
End。
5. the method for searching for particle swarm based on no-communication between robots according to claim 1, wherein in said step 1.9, the method is subdivided into the following sub-steps:
step 1.9.1: each S & W robot actively detects other S & W robots, and all the detected S & W robots are added into the S & W robot set:
i∈P if V i ＝(0 1 ,0 2 ,…,0 D )
wherein zero velocity vector V i ＝(0 1 ,0 2 ,…,0 D ) Representing the detection of particle i as S&A W robot; p represents the detected S&W robot set, P contains all S&A W robot;
step 1.9.2: when the number of robots in the set of S & W robots P reaches or exceeds the threshold M, each S & W robot randomly selects some other S & W robot as its leader:
l i ＝randi(P-{i}) if|P|≥M and i∈P
where |P| denotes the number of robots in the S & W robot set, randi () is a random selection function for randomly selecting another S & W robot.
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