A multi-agent cluster path optimization method based on a rowpa optimization algorithm

Abstract

The application relates to a multi-agent cluster path optimization method based on a ROWPA optimization algorithm, and the method is characterized in that the method comprises the following steps: step 1: presetting parameters of the ROWPA optimization algorithm; step 2: judging whether an individual wolf reaches the judgment condition of a leader wolf, if not, the wolf group performs wandering search in a solution space, that is, the wolf group enters a wandering stage, and if yes, the leader wolf is generated and a call is initiated; step 3: after the leader wolf initiates the call, other hunting wolves perform a raid according to an A* algorithm; step 4: the remaining hunting wolves turn into a siege behavior and implement a siege on a target; step 5: the wolf group is updated based on an elimination update mechanism, and the precision of the wolf group optimization is judged to see whether the preset precision is reached or the maximum iteration number is reached, if yes, the position of the leader wolf is output, that is, an optimal solution of a problem is solved, and if not, the step 2 is returned. Compared with the prior art, the application has the advantages of improving the multi-agent cluster path optimization efficiency and optimization precision and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of multi-agent cooperative control, and particularly relates to a multi-agent cluster path optimization method based on a ROWPA optimization algorithm. BACKGROUND

[0002] With the continuous development of today's engineering optimization problems, the relationship formed by a large number of processes is more and more complex, especially in the field of multi-agent cluster path optimization, using the classical optimization method to solve almost cannot get ideal results, so the wolf pack algorithm (WPA algorithm) is usually used for path optimization and cooperative hunting of multiple unmanned agents (such as unmanned aerial vehicles and unmanned ships). As a meta-heuristic swarm intelligence algorithm, although the wolf pack algorithm was born relatively late, it breaks through the limitation of the characteristics of the objective function, is not sensitive to the initial value, and can make up for the defects of the classical optimization method, so that the multi-agent cluster path optimization has the advantages of fast speed, strong convergence ability, high search precision and strong robustness, etc. The wolf pack algorithm has become a new high ground for solving optimization problems, and has shown strong vitality in the fields of information science, computer science and control science, and has broad research prospects.

[0003] However, the current research on the WPA algorithm is still shallow, the WPA algorithm is mainly applied to the solution of high-dimensional problems, and less attention is paid to low-dimensional problems such as two-dimensional and three-dimensional problems. On the other hand, in the design of the WPA algorithm, the accuracy of the wolf pack algorithm is mainly improved by adding and integrating new steps, while the defects of the algorithm itself are ignored, such as the performance decline caused by setting too many parameters. The existing WPA algorithm studies the movement state of the wolf pack in detail, and according to the different stages of the wolf pack in the foraging activity, three step lengths are proposed, namely the hunting step length, the raid step length and the hunting step length. However, in fact, these three step lengths are fixed step length formulas without feedback mechanism to respond to external changes, lack of flexibility, easy to fall into local optimal solution, and the position of the alpha wolf changes constantly, causing the algorithm to be out of order. In the existing WPA algorithm, during the first time the alpha wolf is summoned, other hunting wolves rush to the raiding process, there is a possibility that a wolf suddenly finds a better odor concentration factor and changes into a new alpha wolf, and reinitiates the summoning behavior. However, if there are multiple frequent summoning behaviors in one foraging activity, repeated position identification of the alpha wolf (i.e. the position of the target prey) and the hunting wolves in the solution space will not only pay more cost for the wolf pack hunting, but also cause the position mutation problem of the alpha wolf and each hunting wolf in the two-dimensional environment, prolong the response time, and cause the WPA algorithm to fall into a disordered state. That is, in the field of path planning of multi-agent cooperative control, the WPA algorithm may fall into a local optimal solution, and the agents may also collide with each other and share information during the hunting process. Therefore, a multi-agent cluster path optimization method is needed to overcome the above problems. SUMMARY

[0004] The present application aims to overcome the defects of the prior art and provide a multi-agent cluster path optimization method based on a ROWPA optimization algorithm.

[0005] The object of the present application can be achieved by the following technical solutions:

[0006] A multi-agent cluster path optimization method based on a ROWPA optimization algorithm, the method comprising the following steps:

[0007] Step 1: initialize the wolf pack, i.e. multiple unmanned agents, and preset the parameters of the ROWPA optimization algorithm;

[0008] Step 2: the concentration judgment factor judges whether an individual wolf reaches the judgment condition of the alpha wolf, if not, the wolf pack performs a walking search in the solution space, i.e. the wolf pack enters the walking stage, if yes, the alpha wolf is generated, i.e. the target, and a call is initiated;

[0009] Step 3: after the alpha wolf initiates the call, the other hunting wolves in the wolf pack perform path planning according to the A* algorithm and the alpha wolf replacement mechanism and gather to the position of the alpha wolf;

[0010] Step 4: the remaining hunting wolves except the alpha wolf enter the siege behavior and implement the siege of the target to obtain the position of the target;

[0011] Step 5: update the wolf pack based on the elimination and update mechanism, and judge whether the optimization precision of the wolf pack reaches the preset precision or the maximum iteration number, if yes, output the position of the alpha wolf, i.e. the position of the target, if not, return to step 2.

[0012] In step 1, the hierarchical system of the wolf pack is modified in the ROWPA optimization algorithm, the hierarchical system in the wolf pack is the alpha wolf and the hunting wolf, the generation rule of the alpha wolf is changed, the definitions of the scout wolf and the wolf are integrated, the scout wolf and the wolf are temporarily eliminated, the functions of the two are integrated, and the hunting wolf is generated, in the case that the alpha wolf is not generated, all the wolves in the wolf pack are hunting wolves, so as to improve the utilization rate of the wolf pack and improve the aggregation efficiency of the wolf pack.

[0013] In step 1, the process of initializing the wolf pack specifically comprises the following steps:

[0014] Step 101: suppose the number of all the wolves in the wolf pack is A, and the maximum iteration number is V max Since it is in a two-dimensional space, the total number of directions of the wolf pack in the hunting activity is 2, and the maximum search number of the hunting wolf is T max , the hunting step is set as Step X , and the optimal position of the target in the solution space is solved.

[0015] Step 102: Assuming that the odor concentration factor of a certain wolf at position P is C, the odor concentration factor of the i-th wolf at position P is C i , the determination value of the optimal odor concentration factor is C lead , the odor concentration factor at the obstacle is 0, and the calculation formula of the odor concentration factor is:

[0016]

[0017] Wherein, C is the odor concentration factor, and P is the position vector;

[0018] Step 103: The position of each wolf is represented by a vector P, which is defined in a two-dimensional space P=(P1, P2), P1 is its component in one-dimensional space, and P2 is its component in two-dimensional space, then the expression of the position of the i-th wolf in the wolf pack is:

[0019] P i =(P i1 ,P i2 ),1≤i≤A

[0020] Wherein, A is the total number of the wolf pack, P i is the position vector of the i-th wolf, P i1 is the component of the i-th wolf in one-dimensional space, and P i2 is the component of the i-th wolf in two-dimensional space;

[0021] Step 104: Let the initial iteration number t=0, initialize the position of the wolf pack, randomly generate the initial position of the i-th wolf in the wolf pack, and the formula for initializing the position of the wolf pack is:

[0022] P i 0 =P min +(P max -P min )rand(·)

[0023] Wherein, P i 0 is the position vector of the initial position of the i-th wolf, P min is the lower limit of the value of the wolf pack in two-dimensional space, i.e. the minimum value, P max is the upper limit of the value of the wolf pack in two-dimensional space, i.e. the maximum value, and rand(·) is a random function that generates a random number in the range of [0, 1].

[0024] In step 2, the process of walking search of the wolf pack in the solution space specifically includes the following steps:

[0025] Step 201: If no individual wolf reaches the judgment condition to become the leader wolf to initiate the call after the wolf pack is initialized, the hunting wolf starts to perform the wandering search in the solution space to find the target, and the wandering stage is in a dynamic search state due to the unknown position of the optimal solution;

[0026] Step 202: A feedback adjustment mechanism is added to the wandering formula, and an adaptive wandering step formula is proposed. In the case of a known maximum wandering search number T max , the adaptive control formula of the wandering stage is:

[0027]

[0028] Wherein, β is used to provide multiple direction choices for the search, so that the wandering step Step X is not limited to one direction, and the surrounding environment can be more comprehensively searched, so as to ensure that the robot adjusts the attack step through the perception of external changes in the search process, is the position vector of the i-th wolf after moving in the n-dimensional space, is the position vector of the i-th wolf after moving in the n-dimensional space, and r is the number of space dimensions;

[0029] Step 203: Judge whether there is a wolf reaching the concentration judgment factor C lead , if yes, the wolf pack hunting stage ends and turns into the raid stage, if not, a new round of wandering behavior is continued until a hunting wolf first perceives the odor concentration factor C n ≥ C lead or the hunting number T reaches the maximum wandering search number T max .

[0030] In step 2, the process of generating the leader wolf is specifically:

[0031] The odor concentration factor of the prey at the position of each wolf is calculated, and an odor concentration factor set C is formed, the odor concentration factor at the position of the i-th wolf is C i , the odor concentration factor at the position of the leader wolf is C lead , a judgment value C lead of the optimal odor concentration factor, that is, the concentration judgment factor, is set, according to the size of the odor concentration factor C, whether the largest odor concentration factor in the odor concentration factor set C is greater than or equal to C lead , if yes, the wolf becomes the leader wolf, and the position is recorded as P best .

[0032] The leader wolf in step 2 is variable, and in the iteration process of the wolf pack, the wolf with the optimal odor concentration factor in each evolution is compared with the odor concentration factor of the current leader wolf, if the odor concentration factor of this wolf is better, it becomes the new leader wolf, the leader wolf does not need to perform the three intelligent behaviors of hunting, raiding and surrounding in the hunting activity, only triggers the calling function, becomes the symbol of the hunting activity of the wolf pack, and the leader wolf generation rule has a constraint condition to solve the disorder of repeated transformation of the leader wolf among several hunting wolves, the constraint condition includes:

[0033] The first constraint condition: it is stipulated that in each surrounding process of the wolf pack, a wolf has only one opportunity to become a leader wolf, that is, a wolf can only emit a calling behavior once in a surrounding;

[0034] The second constraint condition: a historical leader wolf set H is established, the serial number of the wolf that has become a leader wolf in the past is counted into the historical leader wolf set H, the prerequisite for the i-th wolf to become a leader wolf is that the i-th wolf does not belong to the historical leader wolf set H;

[0035] The third constraint condition: after each calling behavior, the concentration judgment factor C lead changes, that is, after each calling behavior initiated in the wolf pack, the new optimal solution is 1.5 times the original C lead , the condition for initiating the calling behavior again will be more stringent, so as to greatly reduce the disorder of the algorithm in the running process and ensure the quality of the optimal solution.

[0036] The expressions of the second constraint condition and the third constraint condition are:

[0037]

[0038] Wherein, C' lead is the current concentration judgment factor, C lead is the concentration judgment factor before the change, P i is the position vector of the i-th wolf, P best is the position vector of the leader wolf, N is the number of hunting wolves in the wolf pack, and H is the historical leader wolf set.

[0039] In step 3, the path planning process of the other hunting wolves in the wolf pack according to the A* algorithm and the leader wolf replacement mechanism includes the following steps:

[0040] Step 301: the leader wolf initiates calling, at this time the position of the leader wolf is the target position and remains unchanged, and the remaining N hunting wolves in the wolf pack initiate raiding towards the target, this process is actually a path planning problem with each hunting wolf as the starting point and the target as the endpoint, the heuristic A* algorithm after corner optimization is used for path optimization, and the total cost dynamic measurement calculation formula of the A* algorithm is:

[0041] f(p) = g(p) + w(p) * h(p), w(p) ≥ 1

[0042] Wherein, w(p) is the adjustment function of the impact evaluation value, that is, the greater w(p) is, the closer the A* algorithm is to the BFS algorithm, and the smaller w(p) is, the closer the A* algorithm is to the Dijkstra algorithm;

[0043] Step 302: In the process of the hunting wolf rushing to the leader wolf, if the smell concentration factor C i of the i-th wolf is greater than the smell concentration factor C lead of the current leader wolf, the hunting wolf will become the new leader wolf, and the original leader wolf will become a hunting wolf. With the new leader wolf issuing a call, each hunting wolf rushes to the new target position again. If the smell concentration factor possessed by each hunting wolf is always less than C lead during the rushing process, the hunting wolf will continue to rush to the target position until the distance between the hunting wolf and the target position is less than a set distance threshold D limited , the hunting wolf stops rushing and enters a hunting stage, and the distance threshold D limited is calculated by the following formula:

[0044]

[0045] Wherein, ω is a distance judgment factor, P nmin is the lower limit of the value of the wolf pack in the n-dimensional space, and P nmax is the upper limit of the value of the wolf pack in the n-dimensional space.

[0046] The step 4 of implementing the hunting process on the target specifically includes the following steps:

[0047] Step 401: After the distance between all hunting wolves and the leader wolf satisfies the condition of being less than or equal to the threshold D limited , each hunting wolf cooperates to hunt the target;

[0048] Step 402: Under the condition that the maximum iteration number is V max , an adaptive control formula of the hunting stage is constructed and obtained, so that the hunting behavior has a feedback adjustment mechanism to the environment, and the adaptive control formula of the hunting stage is:

[0049]

[0050] Wherein, is the position vector of the s-th wolf after the n-dimensional space is expected to move at the iteration number t, is the position vector of the s-th wolf in the n-dimensional space at the iteration number t, is the position vector of the leader wolf at the iteration number t, V is the current iteration number, t is the iteration number, is set according to the hunting step Step3, is a random number from 0 to 1, so as to avoid that the iteration number t tends to the maximum iteration number V max When the algorithm optimization changes are not obvious, is used to provide multiple direction selection for the search, so that the hunting step Step3 is not limited to one direction, and the surrounding environment can be searched more comprehensively, and it is ensured that the intelligent agent can perceive external changes to adjust the hunting step in the hunting process.

[0051] Step 403: Based on the obstacle avoidance problem caused by the fact that the hunting wolves do not exchange information with each other, information exchange is carried out after each execution of the hunting step, and the search efficiency of the hunting wolves in the space is improved, and the formula of the information exchange is:

[0052]

[0053] Wherein, P in is the position vector of the i-th wolf in the n-dimensional space before moving, P i ' n is the position vector of the i-th wolf in the n-dimensional space at this time, is the influence factor of the i-th wolf in the n-dimensional space to the k-th wolf and the g-th wolf adjacent to the i-th wolf and maintaining a safe distance, is an influence factor of the i-th wolf in the n-dimensional space to the leader wolf and maintaining a safe distance; in

[0054] Step 404: If the hunting wolf encounters an obstacle, the formation obstacle avoidance is carried out, and if there is no obstacle, the formation configuration is carried out, and the formation is maintained.

[0055] Step 405: When the iteration number t reaches the maximum iteration number V max of the wolf group or the obtained optimal individual reaches the preset precision, the hunting stage is ended.

[0056] In step 5, the process of updating the wolf group based on the elimination update mechanism is specifically:

[0057] After one hunting stage is ended, B wolves with the minimum odor concentration factor, i.e. the B wolves with the worst fitness value, are eliminated, and B artificial wolves are randomly generated, and the population optimization formula of the elimination update mechanism is:

[0058]

[0059] Wherein, B is the number of eliminated wolves, is an evolution proportion factor of the wolf group, A is the number of all wolves in the wolf group, and N is the number of hunting wolves in the wolf group.

[0060] Compared with the prior art, the present application has the following advantages: ​

[0061] 1、The application improves the utilization rate of the wolf pack and enhances the aggregation efficiency of the wolf pack by modifying the hierarchy of the wolf pack in the WPA algorithm, in the ROWPA optimization algorithm, the hierarchy of the wolf pack is simplified to the leader wolf and the hunting wolf, the definition of the leader wolf is unchanged, that is, the wolf with the optimal prey odor concentration factor C lead is able to gather the surrounding wolves to surround and capture the prey by the calling function, the generation rule of the leader wolf is changed, that is, C lead is no longer the optimal value selected from the wolf pack, but a predetermined judgment value, only the hunting wolf that reaches the judgment value can become the leader wolf and initiate the call, so that the generation of the leader wolf is more objective, and the hunting wolf is the wolf that can complete the search target task and the surrounding target prey task, and has the behavior functions of the scout wolf and the fierce wolf in the existing WPA algorithm, the application also optimizes the parameter configuration by reducing some parameter settings such as the step factor involved in the WPA algorithm, relaxes the restrictions on the movement of the wolf pack, and improves the running efficiency of the WPA algorithm to a certain extent, and improves the rate of multi-agent swarm path optimization;

[0062] 2、The application combines the dynamic weight heuristic A* algorithm optimized by the corner, in the ROWPA optimization algorithm, the path planning problem implied in the existing WPA algorithm process is studied after being refined, when one of the hunting wolves has the optimal odor concentration factor C lead , changes to the leader wolf, initiates the call, and under the condition that the default leader wolf is equal to the target, for other hunting wolves in the space, the position of the known solution is known, the problem can be converted into a path planning problem with known start and end points in a static space, the heuristic A* algorithm optimized by the corner is used for path optimization to speed up the speed of the unmanned agent gathering to attack the target and reduce the response time of the target;

[0063] 3、The application sets the constraint condition so that the condition for initiating the calling behavior again will be more stringent, solves the disorder problem that may be caused by position mutation, greatly reduces the disorder of the algorithm in the algorithm running process, also ensures the quality of the optimal solution, effectively avoids falling into a local optimal solution in the path planning of multi-agent cooperative control, and improves the optimization precision;

[0064] 4、The application sets the information exchange mechanism and the adaptive distributed control strategy in the ROWPA optimization algorithm, effectively prevents the collision and information sharing problem of the unmanned agent in the surrounding process when the multi-agent cooperates to surround, and multiple unmanned agents can efficiently and conflict-free surround the target in the environment. BRIEF DESCRIPTION OF DRAWINGS

[0065] Figure 1 is the research framework diagram of the embodiment in the application.

[0066] Figure 2 A schematic diagram of the ROWPA wolf pack hierarchy of the present application.

[0067] Figure 3 A flowchart of the method of the present application.

[0068] Figure 4 A detailed flowchart of the encirclement of the present application.

[0069] Figure 5 A schematic diagram of the classification results of the WPA and ROWPA on the wine set of the present application.

[0070] Figure 6 A schematic diagram of the optimization process of the WPA and ROWPA on the parameter c of the present application.

[0071] Figure 7 A schematic diagram of the optimization process of the WPA and ROWPA on the parameter g of the present application.

[0072] Figure 8 A schematic diagram of the two-dimensional plane encirclement environment of the present application.

[0073] Figure 9 A four-time solving effect diagram for the MCST problem of the present application, wherein, Fig. (9a) is a first-time solving effect diagram for the MCST problem of the present application, Fig. (9b) is a second-time solving effect diagram for the MCST problem of the present application, Fig. (9c) is a third-time solving effect diagram for the MCST problem of the present application, and Fig. (9d) is a fourth-time solving effect diagram for the MCST problem of the present application.

[0074] Figure 10 A four-time experimental output result schematic diagram for the MCST problem of the present application, wherein, Fig. (10a) is a first-time experimental output result schematic diagram for the MCST problem of the present application, Fig. (10b) is a second-time experimental output result schematic diagram for the MCST problem of the present application, Fig. (10c) is a third-time experimental output result schematic diagram for the MCST problem of the present application, and Fig. (10d) is a fourth-time experimental output result schematic diagram for the MCST problem of the present application.

[0075] Figure 11 A four-time experimental wolf pack raid original path reproduction diagram for the MCST problem of the present application, wherein, Fig. (11a) is a first-time experimental wolf pack raid original path reproduction diagram for the MCST problem of the present application, Fig. (11b) is a second-time experimental wolf pack raid original path reproduction diagram for the MCST problem of the present application, Fig. (11c) is a third-time experimental wolf pack raid original path reproduction diagram for the MCST problem of the present application, and Fig. (11d) is a fourth-time experimental wolf pack raid original path reproduction diagram for the MCST problem of the present application.

[0076] Figure 12 Fig. (12a) is a reproduction graph of the corner optimization path of the wolf pack raid for the first time experiment of the MCST problem of the present application, Fig. (12b) is a reproduction graph of the corner optimization path of the wolf pack raid for the second time experiment of the MCST problem of the present application, Fig. (12c) is a reproduction graph of the corner optimization path of the wolf pack raid for the third time experiment of the MCST problem of the present application, and Fig. (12d) is a reproduction graph of the corner optimization path of the wolf pack raid for the fourth time experiment of the MCST problem of the present application.

[0077] Figure 13 Fig. (13) is a schematic diagram of the case of the wolf pack raid twice in the MCST problem of the present application. DETAILED DESCRIPTION

[0078] The present application will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0079] EMBODIMENT

[0080] As shown in the drawings, the present application provides a multi-agent cluster path optimization method based on the ROWPA optimization algorithm, which comprises the following steps: Figure 1

[0081] Step 1: Initialize the wolf pack, assuming that the total number of wolf packs is A, A∈{3,4,5}, and the maximum number of iterations is V max Since it is in a two-dimensional space, the total number of directions of the wolf pack in the hunting activity is 2, and the maximum search number of the hunting wolf is T max , and the hunting step is set to Step X , the optimal position of the target prey in the solution space is solved, assuming that the smell concentration factor of the prey smelled by a wolf at position P is C, then the smell concentration factor of the position of the ith wolf is C i , the optimal smell concentration factor is C lead , the smell concentration factor at the obstacle is 0, and the calculation formula of the smell concentration factor is:

[0082]

[0083] Where C is the smell concentration factor, and P is the position vector.

[0084] The position of each wolf is represented by a vector P, which is defined in a two-dimensional space P=(P1,P2), P1 is its component in one-dimensional space, and P2 is its component in two-dimensional space, then the expression of the position of the ith wolf in the wolf pack is:

[0085] P i =(P i1 ,P i2 ​), 1≤i≤A

[0086] where A is the total number of wolves, P i is the position vector of the i-th wolf, P i1 is the component of the i-th wolf in one-dimensional space, P i2 is the component of the i-th wolf in two-dimensional space;

[0087] Then, let the initial iteration number t = 0, initialize the position of the wolf pack, generate a random initial position of the i-th wolf in the wolf pack, and the formula for initializing the position of the wolf pack is:

[0088] P i 0 = P min + (P max - P min )rand(·)

[0089] where P i 0 is the position vector of the initial position of the i-th wolf, P min is the lower limit of the value of the wolf pack in two-dimensional space, i.e. the minimum value, P max is the upper limit of the value of the wolf pack in two-dimensional space, i.e. the maximum value, and rand(·) is a random function for generating a random number in the range [0, 1] to ensure that each wolf is randomly dispersed in the environment, which is conducive to fully searching the solution space;

[0090] Step 2: wandering phase. If no individual wolf reaches the judgment condition after the wolf pack is initialized and changes to the leader wolf, the hunting wolves start to wander and search in the solution space to find the target. In the wandering phase, the wolf pack is in a dynamic search state because the position of the optimal solution is unknown. In order to give the wolf pack better flexibility and freedom in the wandering phase, a feedback adjustment mechanism is added to the executed wandering formula, and a step formula for adaptive wandering is proposed. Under the condition that the maximum wandering search number is T max , the adaptive control formula for the wandering phase is:

[0091]

[0092] where β is used to provide multiple direction choices for the search, so that the wandering step Step X is not limited to one direction, which can more comprehensively search the surrounding environment and ensure that the robot adjusts the siege step by sensing external changes in the search process, is the position vector of the i-th wolf after moving in the n-th dimensional space, is the position vector of the i-th wolf after moving in the n-th dimensional space, and r is the number of spatial dimensions.

[0093] Once a wolf reaches C lead, the leader wolf initiates a call, the wandering phase ends, and the raid phase begins, otherwise, a new round of wandering behavior is executed until a wolf first perceives the odor concentration factor C n ≥ C lead or the number of hunting times T reaches the maximum limit T max ;

[0094] Step 3: Wolf pack call and raid phase, the leader wolf triggers the call function, at this time the leader wolf and the target are by default in the same position and remain unchanged, the remaining N-1 hunting wolves in the wolf pack launch a raid on the target position, this process is actually a path planning problem with a known starting point for each hunting wolf and a target endpoint. To improve the raid speed of the hunting wolves and reduce the response time of the leader wolf, a heuristic A* algorithm optimized for corners can be used for path optimization. According to the dynamic measurement formula of the total cost of A* algorithm:

[0095] f(p) = g(p) + w(p) * h(p), w(p) ≥ 1

[0096] Where w(p) is the adjustment function that affects the evaluation value, that is, the larger w(p) is, the closer the A* algorithm is to the BFS algorithm, and the smaller w(p) is, the closer the A* algorithm is to the Dijkstra algorithm.

[0097] During the raid of the hunting wolves to the leader wolf, if the odor concentration factor C i of the i-th wolf is better than the current leader wolf, then this hunting wolf becomes the new leader wolf, and the original leader wolf returns to the hunting wolf state. With the new leader wolf initiating a call, each hunting wolf re-raids towards the new optimal position, otherwise, if the odor concentration factor of each hunting wolf is always less than C lead during the raid, the hunting wolves will continue to raid the target position until the distance between them and the target is less than the set distance threshold D limited , at which point the wolves stop raiding and enter the hunting phase. The calculation formula for the distance threshold is:

[0098]

[0099] Where ω is the distance judgment factor, P nmin is the lower limit of the value of the wolf pack in the n-dimensional space, and P nmax is the upper limit of the value of the wolf pack in the n-dimensional space.

[0100] Step 4: Wolf pack hunting phase, the hunting process is shown in Figure 4 After all the hunting wolves are within a distance less than or equal to the threshold D limited from the leader wolf, the wolf pack cooperates to hunt the prey until the iteration number t of the algorithm reaches the maximum iteration number V maxOr the optimal individual obtained in the algorithm running reaches the preset accuracy, the algorithm ends.

[0101] In order to make the hunting behavior have feedback regulation mechanism to the environment, the maximum iteration number V max In the case, the adaptive control formula of the hunting stage is:

[0102]

[0103] Wherein, is the position vector of the s-th wolf after the expected movement in the n-dimensional space at the iteration number t, is the position vector of the s-th wolf in the n-dimensional space at the iteration number t, is the position vector of the leader wolf at the iteration number t, V is the current iteration number, α is a random number from 0 to 1, to avoid the algorithm optimization change is not obvious when the iteration number t tends to the maximum iteration number V max , β is used to provide multiple direction selection for search, so that the hunting step Step3 is not limited to one direction, and the surrounding environment can be searched more comprehensively, so that the agent can perceive the external changes to adjust the hunting step in the hunting process;

[0104] For the obstacle avoidance problem caused by no information exchange between each other, in order to improve the search efficiency of the scout wolf in space, taking the i-th scout wolf as an example, the information exchange behavior is added after each execution of the hunting step, and the formula of information exchange is:

[0105]

[0106] Wherein, P in is the position vector of the i-th wolf in the n-dimensional space before movement, P i ' n is the position vector of the i-th wolf in the n-dimensional space at this time, is the influence factor of the i-th wolf in the n-dimensional space to keep a safe distance from the k-th wolf and the g-th wolf adjacent to it, φ in ∈[-1,1] is the influence factor of the i-th wolf in the n-dimensional space to keep a safe distance from the leader wolf, this formula not only considers the information of the position of the adjacent wolf, but also depends on the information of the position of the leader wolf, which plays the role of information exchange between wolves;

[0107] Step 5: updating the wolf group based on the elimination update mechanism, the elimination update mechanism in the ROWPA optimization algorithm is actually a distribution system based on the principle of winner-takes-all and merit-based rewards, the principle is that individuals in the wolf group are allocated food in order from strong to weak, which will lead to the starvation of small wolves, the wolf group update mechanism in the ROWPA optimization algorithm of the application is to eliminate the B wolves with the smallest odor concentration factor, that is, the worst fitness value after each hunting activity, and randomly generate B artificial wolves, the wolf group optimization formula of the elimination update mechanism is:

[0108]

[0109] Wherein, B is the number of eliminated wolves, beta is the evolution ratio factor of the wolf group, A is the number of all wolves in the wolf group, and N is the number of hunting wolves in the wolf group.

[0110] The rule for generating the leader wolf is as follows:

[0111] The odor concentration factor of the prey at the position of each wolf is calculated, and an odor concentration factor set C is formed, the odor concentration factor at the position of the i-th wolf is C i , and the odor concentration factor at the position of the leader wolf is C lead However, unlike the existing WPA algorithm, the generation rule of the leader wolf is not based on the maximum value of each hunting wolf in the wolf group searching in the wandering stage, but a given judgment value C lead Therefore, the leader wolf is not necessarily generated immediately after initialization, and it may not appear during the hunting process, and according to the size of the odor concentration factor C, it is judged whether the wolf with the largest odor concentration factor in the odor concentration factor set C is greater than or equal to C lead If this condition is met, the wolf is changed into a leader wolf, and the position is recorded as P best , the calling function is initiated, and other hunting wolves start the raiding behavior, and after gathering, they start hunting the prey target, that is, the position of the leader wolf. The leader wolf also does not need to perform the three intelligent behaviors of hunting, raiding and hunting in the hunting activity, and only needs to trigger the calling function to become the symbol of the wolf hunting activity. The leader wolf is not fixed, and in the iteration process of the wolf group, the wolf with the optimal odor concentration factor in each evolution will be compared with the C lead of the current leader wolf, and if the odor concentration factor C of the wolf is better, the wolf will replace the current leader wolf.

[0112] However, it should be pointed out that the existing WPA algorithm has the defect that when the wolf group is closer to the leader wolf, other hunting wolves are more likely to perceive a better odor concentration factor C, thereby changing the leader wolf, which may cause the leader wolf to repeatedly change among several hunting wolves, resulting in disordered WPA algorithm running errors. In order to solve the disorder problem caused by position mutation, the following provisions are made:

[0113] The rule is that each wolf has only one chance to become the leader wolf in each hunting process, i.e. each robot can only send out one call behavior in one hunting process;

[0114] A historical leader wolf set H is established, and the serial numbers of the wolves that have been the leader wolf in the past are counted into the historical leader wolf set H, and the prerequisite for the i-th wolf to become the leader wolf is that i does not belong to the historical leader wolf set H;

[0115] Concentration determination factor C lead The change also occurs after each call behavior, i.e. after each call behavior initiated in the wolf group, the new optimal solution is 1.5 times the original C lead , and the condition for initiating the call behavior again will be more stringent, which can greatly reduce the disorder of the algorithm during operation and also ensure the quality of the optimal solution, and the expression of the constraint condition is:

[0116]

[0117] , wherein C lead is the concentration determination factor.

[0118] According to the above steps, a series of simulation experiments are carried out, the operating system is 64-bit Windows 10, the RAM is 4.00 GB, and the MATLAB version number is matlab-2019a.

[0119] Experiment 1 is a performance comparison test between the ROWPA optimization algorithm and the existing WPA algorithm:

[0120] The Wine (red wine) data set is a classic classification test data set in Matlab, and the total number of samples is 178, wherein each sample has 13 numerical attributes, and the samples are randomly divided into 3 categories, one of which is the test set, and the other two are the test set, and the number of samples in each category is different. Next, the Wine data set will be used as the experimental data object to complete the comparison simulation experiment of the ROWPA optimization algorithm and the WPA algorithm to analyze the performance of the ROWPA optimization algorithm.

[0121] The experiment adopts the support vector machine (SVM) algorithm, and the role of the wolf swarm algorithm in the SVM training model is to optimize the penalty parameter c and the parameter g in the kernel function, and select the optimal values of the two to help accurately classify the samples of the Wine data set, under the same classification conditions, the existing WPA algorithm and the ROWPA optimization algorithm proposed in the present application are used to optimize the penalty parameter c and the parameter g in the kernel function respectively, and the experimental results obtained by running the Matlab code are as follows: Figure 5As shown in the figure, the classification accuracy is 100%, which proves that for the binary classification problem of the Wine dataset, the ROWPA optimization algorithm maintains the same high optimization accuracy as the WPA algorithm.

[0122] Observe the specific parameter optimization process. The solid curve represents the ROWPA optimization algorithm, while the dotted curve represents the WPA algorithm. Figure 6 and Figure 7 The experimental results lead to the following conclusions:

[0123] (1) From the perspective of convergence speed, the ROWPA optimization algorithm is significantly faster than the WPA algorithm in the optimization process of the penalty parameter c and the parameter g in the kernel function. In addition, under the same 5-iteration cycle, the ROWPA optimization algorithm can search near the global optimal value more quickly and has better inspiration. At the same time, from the optimization process of the parameter g, it can be seen that the ROWPA optimization algorithm has a stronger ability than the existing wolf pack algorithm in avoiding falling into the trap of local optimal solutions.

[0124] (2) From the perspective of convergence accuracy, the ROWPA optimization algorithm and the existing WPA algorithm can eventually converge to the optimal value, proving that the ROWPA optimization algorithm maintains the same high level of convergence accuracy as the WPA algorithm; and the convergence situation is also relatively stable, indicating that the ROWPA optimization algorithm also has a more obvious global optimization feature.

[0125] Experiment 2 is a simulation solution to the MCST problem using the ROWPA optimization algorithm:

[0126] like Figure 8 As shown in the figure, the MCST problem is solved so that wolves can efficiently and conflict-free capture their target. When the distance between the roaming wolf and the target (i.e., the leader) falls below the maximum capture radius, the roaming wolf stops approaching the target, indicating a successful capture. Based on the theoretical optimization and simulation work described above, we will apply this theoretical knowledge to the MCST problem generated by wolf pack hunting behavior using MATLAB, verify its rationality and effectiveness, and analyze the results.

[0127] Depend on Figures 9 to 12 The experimental results lead to the following conclusions:

[0128] (1) The code written by using the ROWPA optimization algorithm and the hunting strategy can effectively solve the MCST problem. In the four hunting activities, the wolf group and the target position are relatively dispersed, the search process of the wolf group covers most of the solution space as much as possible, and successful solutions are obtained. This first proves that the application has a strong application ability and is persuasive in solving the MCST problem. In addition, for a 50*50 two-dimensional space environment, in the face of a possible large search volume, the time spent by each hunting activity is 2.46, 2.43, 2.57 and 2.47 seconds, respectively, which is basically maintained at about 2.5 seconds. This proves that the search efficiency of the ROWPA optimization algorithm is efficient and stable, and also shows that the ROWPA optimization algorithm has strong convergence ability.

[0129] (2) The direction and process of the hunting wolf rushing to the target (i.e. the leader wolf) have strong purpose and heuristic. From the rushing path of the hunting wolf, the movement to the target point maintains a directional straight line in the absence of obstacles, which is a clear manifestation of the global optimization ability of the ROWPA optimization algorithm, and also proves that the heuristic of the WPA algorithm and the A* algorithm is well inherited by the ROWPA optimization algorithm.

[0130] (3) The corner optimization function of the ROWPA optimization algorithm is well embodied. By comparing Figure 11 and Figure 12 , we find that the rushing trajectory of the ROWPA optimization algorithm at the corner shows a smooth characteristic, and the output value of amend_count is 32, 58, 10 and 28, respectively, which proves that the corner optimization function effectively plays a role at the corner of each path optimization.

[0131] (4) In the search process, the requirements of efficient and conflict-free hunting of prey are realized. The four experiments all output the return value of "ROWPA optimization algorithm preyed successfully!", in fact, after repeated experiments, the success rate of the ROWPA optimization algorithm applied to the MCST problem of hunting the target by three unmanned agents is up to 100%, and the observation of the entire hunting path of the unmanned agent to the target prey does not appear the point of intersection with the obstacle. Combined with the output search time, this proves that the requirements of efficient and conflict-free hunting process are met.

[0132] In addition, during the experiment, the leader wolf replacement mechanism of the ROWPA optimization algorithm for the MCST problem is improved, and the new leader wolf must have a larger gap in the smell concentration factor compared to the current leader wolf. Therefore, the leader wolf is rarely replaced in multiple experiments, and the solution process is basically one-step, which improves the efficiency of the wolf algorithm to a certain extent. This also makes the leader wolf replacement and multiple raids in the search process occasional. In order to prove the effectiveness of the ROWPA optimization algorithm, a large number of repeated experiments are conducted, and the results with multiple raids are obtained, as shown in Figure 13 which proves that multiple raids have a certain negative impact on the WPA algorithm. The ROWPA optimization algorithm solves this problem by making relevant provisions, which proves that compared with the existing WPA algorithm, the ROWPA optimization algorithm has higher target search accuracy and the ability to jump out of local optimal solution. For example, in the process of multiple UAV cooperative hunting, the efficiency of the UAV swarm path optimization process is faster, the stability is stronger, the optimization accuracy is higher, the ability to jump out of local optimal solution is stronger, and the problem of collision and information sharing in the hunting process can be avoided.

[0133] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present application, and these modifications or replacements should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A multi-agent cluster path optimization method based on ROWPA optimization algorithm, characterized by: The method comprises the following steps: Step 1: Initialize the wolf pack, which is a group of unmanned agents, and preset the parameters of the ROWPA optimization algorithm; Step 2: The concentration determination factor determines whether any individual wolf meets the judgment condition of the leader wolf. If not, the wolf pack will wander around in the solution space, that is, the wolf pack enters the wandering stage. If so, the leader wolf, that is, the target, will be generated and the call will be initiated; Step 3: After the leader wolf initiates the call, the other hunting wolves in the pack plan their paths based on the A* algorithm and the leader wolf replacement mechanism, and gather towards the leader wolf's position; Step 4: The remaining hunting wolves, except the leader wolf, switch to siege behavior, encircle and capture the target, and obtain the target's location; Step 5: Update the wolf pack based on the elimination update mechanism and determine whether the wolf pack's optimization accuracy reaches the preset accuracy or the maximum number of iterations. If so, output the position of the leader wolf, that is, the target position. If not, return to step 2. In step 4, the process of encircling and capturing the target specifically includes the following steps: Step 401: The distance between all the roaming wolves and the leader wolf is less than or equal to the threshold D. limited Afterwards, the roaming wolves cooperated to round up the target; Step 402: When the maximum number of iterations is known to be V max Under this condition, the adaptive control formula of the roundup stage is constructed and obtained, so that the roundup behavior has a feedback adjustment mechanism to the environment. The adaptive control formula of the roundup stage is: in, is the position vector of the sth wolf after it moves in the n-dimensional space when the number of iterations is t, is the position vector of the sth wolf in the n-dimensional space when the number of iterations is t, is the position vector of the leader wolf when the iteration number is t, V is the current iteration number, t is the iteration number, set according to the capture step length Step3, α is a random number from 0 to 1 to avoid the iteration number t approaching the maximum iteration number V max When the algorithm optimization change is not obvious, β is used to provide multiple direction options for the search, so that the hunting step length Step3 is not limited to one direction, and the surrounding environment can be searched more comprehensively, ensuring that the agent can perceive external changes during the hunting process and adjust the hunting step length; Step 403: Based on the obstacle avoidance problem caused by the lack of information exchange between the roaming wolves, information exchange is performed after each round-up step to improve the roaming wolves' search efficiency in space. The formula for information exchange is: Among them, P in is the position vector of the i-th wolf in the n-dimensional space before it moves, P′ in is the position vector of the i-th wolf in the n-dimensional space at this time, is the influence factor for the i-th wolf to maintain a safe distance with its adjacent k-th and g-th wolves in the n-dimensional space, φ in ∈[-1,1] is the influence factor of the i-th wolf maintaining a safe distance from the leader wolf in the n-dimensional space; Step 404: If the wolves encounter an obstacle, they form a formation to avoid the obstacle. If there is no obstacle, they form a formation and maintain the formation. Step 405: When the number of iterations t reaches the maximum number of iterations V of the wolf pack max Or when the optimal individual obtained reaches the preset accuracy, the round-up phase ends.

2. A multi-agent cluster path optimization method based on ROWPA optimization algorithm according to claim 1, characterized in that: In the step 1, in the ROWPA optimization algorithm, the class system of the wolf pack is modified. The class system in the wolf pack is composed of leader wolves and hunting wolves. The rules for generating leader wolves are changed, the definitions of scout wolves and fierce wolves are integrated, scout wolves and fierce wolves are temporarily eliminated, and the functions of the two are integrated to generate hunting wolves. When the leader wolf is not generated, all wolves in the wolf pack are hunting wolves, so as to improve the utilization rate of the wolf pack and enhance the efficiency of wolf pack aggregation.

3. The multi-agent cluster path optimization method based on the ROWPA optimization algorithm according to claim 2 is characterized in that: In step 1, the process of initializing the wolf pack specifically includes the following steps: Step 101: Assume that the number of wolves in the wolf pack is A and the maximum number of iterations is V max Since it is in two-dimensional space, the total number of directions in which the wolf pack hunts is 2, and the maximum number of searches by the hunting wolf is T max , its hunting step length is set to Step X , solve the optimal position of the target in space; Step 102: Assuming that the concentration factor of the scent smelled by a wolf at position P is C, the concentration factor of the scent at the position of the i-th wolf is C i , the optimal odor concentration factor is C lead , the odor concentration factor at the obstacle is 0, and the calculation formula of the odor concentration factor is: Where C is the odor concentration factor, P is the position vector; Step 103: The position of each wolf is represented by a vector P, defined in two-dimensional space as P = (P1, P2), where P1 is its component in one-dimensional space and P2 is its component in two-dimensional space. The position of the i-th wolf in the pack is expressed as: P i =(P i1 ,P i2 ),1≤i≤A Among them, A is the total number of wolves, P i is the position vector of the i-th wolf, P i1 is the component of the i-th wolf in one-dimensional space, P i2 is the weight of the i-th wolf in two-dimensional space; Step 104: Assume that the initial iteration number t=0, initialize the position of the wolf pack, and randomly generate the initial position of the i-th wolf in the wolf pack. The formula for initializing the wolf pack position is: P i 0 =P min +(P max -P min )rand(·) Among them, P i 0 is the position vector of the initial position of the i-th wolf, P min is the lower limit of the wolf pack’s value in two-dimensional space, that is, the minimum value, P max is the upper limit of the wolf pack’s value in two-dimensional space, i.e., the maximum value, and rand(·) is a random function that generates random numbers in the range of [0,1].

4. The multi-agent cluster path optimization method based on the ROWPA optimization algorithm according to claim 1 is characterized in that: In step 2, the process of the wolf pack wandering and searching in the solution space specifically includes the following steps: Step 201: If no individual wolf meets the judgment condition to become the leader wolf and initiate the call after the wolf pack is initialized, the hunting wolf begins to wander in the solution space to search for the target. During the wandering stage, the wolf pack is in a dynamic search state because the location of the optimal solution is unknown. Step 202: Add the feedback adjustment mechanism to the walk formula and propose the step length formula of the adaptive walk. max In the case of , the adaptive control formula of the walking stage is: Among them, β is used to provide multiple direction options for search, making the walking step length Step X It is not limited to one direction and can search the surrounding environment more comprehensively, ensuring that the robot can adjust its siege step length by sensing external changes during the search process. is the position vector of the i-th wolf after moving in the n-dimensional space, is the position vector of the i-th wolf after moving in the n-dimensional space, and r is the number of spatial dimensions; Step 203: Determine whether there are wolves that have reached the concentration determination factor C lead If yes, it will transform into the leader wolf and initiate the call, the wolf pack hunting phase ends and enters the rush phase. If no, it will continue to execute a new round of wandering behavior until a hunting wolf first senses the odor concentration factor C. n ≥C lead Or the number of hunting times T reaches the maximum number of wandering searches T max .

5. The multi-agent cluster path optimization method based on the ROWPA optimization algorithm according to claim 1 is characterized in that: In step 2, the process of generating the leader wolf is specifically as follows: Calculate the odor concentration factor of the prey at each wolf's location and form the odor concentration factor set C. The odor concentration factor at the i-th wolf's location is C i , the odor concentration factor at the leader wolf's location is C lead , set a judgment value C of the optimal odor concentration factor lead , that is, the concentration judgment factor, according to the size of the odor concentration factor C, judge whether the largest odor concentration factor in the odor concentration factor set C is greater than or equal to C lead If so, the wolf becomes the leader wolf and its position is recorded as P best .

6. A multi-agent cluster path optimization method based on ROWPA optimization algorithm according to claim 5, characterized in that: In step 2, the leader wolf is variable. During the iterative process of the wolf pack, the wolf with the best odor concentration factor in each evolution is compared with the odor concentration factor of the current leader wolf. If the odor concentration factor of this wolf is better, it will become the new leader wolf. The leader wolf does not need to perform the three intelligent behaviors of hunting, rushing, and encircling during hunting activities. It only triggers the summoning function and becomes the symbol of the wolf pack's hunting activities. Constraints are set in the leader wolf generation rules to solve the disordered situation where the leader wolf repeatedly switches between several hunting wolves. The constraints include: The first constraint is that during each roundup, a wolf can only become the leader once, meaning it can only issue a single call. The second constraint is to establish a historical leader wolf set H. The serial numbers of wolves that have been leader wolves in the past will be included in the historical leader wolf set H. The prerequisite for the i-th wolf to become a leader wolf is that the i-th wolf does not belong to the historical leader wolf set H. The third constraint: After each summoning action, the concentration determination factor C lead Changes occur, that is, after each calling behavior initiated by the wolf pack, the new optimal solution is the original C lead The conditions for initiating the summoning behavior again will be more stringent, so as to greatly reduce the disorder of the algorithm during operation and ensure the quality of the optimal solution.

7. The multi-agent cluster path optimization method based on the ROWPA optimization algorithm according to claim 6 is characterized in that: The expressions of the second constraint and the third constraint are: Among them, C′ lead is the current concentration determination factor, C lead is the concentration determination factor before the change, P i is the position vector of the i-th wolf, P best is the location vector of the leader wolf, N is the number of hunting wolves in the wolf pack, and H is the set of historical leader wolves.

8. The multi-agent cluster path optimization method based on the ROWPA optimization algorithm according to claim 1 is characterized in that: In step 3, the process of path planning by other roaming wolves in the wolf pack according to the A* algorithm and the leader wolf replacement mechanism specifically includes the following steps: Step 301: The leader wolf initiates a call. At this point, the leader wolf's position is the target position and remains unchanged. The remaining N hunting wolves in the pack rush towards the target. This process is actually a path planning problem with each hunting wolf as the starting point and the target as the end point. The path optimization is performed based on the heuristic A* algorithm after corner optimization. The total cost dynamic measurement calculation formula of the A* algorithm is: f(p)=g(p)+w(p)*h(p),w(p)≥1 Among them, w(p) is the adjustment function that affects the evaluation value. That is, the larger w(p) is, the closer the A* algorithm is to the BFS algorithm, and the smaller w(p) is, the closer the A* algorithm is to the Dijkstra algorithm. Step 302: When the hunting wolf rushes towards the leader wolf, if there is a scent concentration factor C of the i-th wolf i Greater than the current leader wolf's scent concentration factor C lead , then the hunting wolf will become the new leader wolf, and the original leader wolf will become the hunting wolf. As the new leader wolf initiates the call, the hunting wolves will rush towards the new target location again. If during the rush, the odor concentration factor of each hunting wolf is always less than C lead , it will continue to rush towards the target position until the distance between it and the target position is less than the set distance threshold D limited , the hunting wolf stops running and enters the round-up phase, the distance threshold D limited The calculation formula is: Among them, ω is the distance determination factor, P nmin is the lower limit of the wolf pack’s value in the n-dimensional space, P nmax is the upper limit of the value of the wolf pack in the n-th dimension space.

9. The multi-agent cluster path optimization method based on the ROWPA optimization algorithm according to claim 1 is characterized in that: In step 5, the process of updating the wolf pack based on the elimination and update mechanism is specifically as follows: After a roundup phase, the B wolves with the smallest odor concentration factor, that is, the B wolves with the worst fitness value, are eliminated. At the same time, B artificial wolves are randomly generated. The population optimization formula of the elimination and update mechanism is: Among them, B is the number of wolves eliminated, β is the evolutionary scaling factor of the wolf pack, A is the number of all wolves in the wolf pack, and N is the number of hunting wolves in the wolf pack.

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