Unmanned aerial vehicle path planning method based on multi-objective self-organizing squirrel foraging mechanism

Abstract

The application provides a kind of unmanned aerial vehicle path planning method based on multi-objective self-organizing squirrel foraging mechanism, aims to establish the confrontation environment model in three-dimensional space, and comprehensively considers the influence of terrain and threat area.For the problem of large space for solving three-dimensional model, a segmented squirrel foraging mechanism is designed, and different position updating methods are designed for squirrel populations with different sorting positions to improve the convergence performance.For the requirement of path planning for the diversity of multi-objective Pareto solution set, a multi-membrane multi-objective evolution framework is designed, each membrane has its own optimal solution set in the iteration process, and different membranes are prioritized according to a specific non-dominated sorting method, to improve the diversity of algorithm solution set.

Description

Technical Field

[0001] This invention relates to a path planning method for unmanned aerial vehicles (UAVs) based on the multi-target membrane squirrel foraging mechanism, belonging to the field of UAV trajectory planning. Background Technology

[0002] With the development of information technology, unmanned operation, and intelligence in aviation, unmanned aerial vehicles (UAVs) are gaining increasing advantages in adversarial environments. They are not only low-cost and can be controlled unmanned to reduce casualties, but also capable of sustained high-intensity combat. Path planning is one of the key technologies for achieving UAV autonomy and intelligence. UAV path planning involves using one or more optimization algorithms to plan one or more safe and effective paths from the starting point to the target point, while satisfying constraints such as the UAV's own performance and various threats. Most UAV path planning research only considers a single target or transforms multiple targets into a single target through a weighted sum method. Research on path planning that considers multiple targets is relatively rare. Furthermore, the former method can only plan one path per algorithm run, making it difficult to meet the diverse needs of decision-makers, and setting weights is also challenging. This is especially true in adversarial systems where each path may correspond to different strategic decisions.

[0003] Compared to traditional single-objective path planning methods, multi-objective path planning methods, due to their algorithm optimization mechanism, perform non-dominated optimization on different objective functions of an engineering problem, ultimately obtaining a set of non-dominated optimal solutions. In the UAV flight environment, three types of flight costs need to be considered: path cost, threat cost, and concealment cost. The selection of UAV paths requires a comprehensive consideration of these three costs. Therefore, to improve decision-making efficiency, designing effective multi-objective path planning algorithms is crucial for modern UAV adversarial decision-making technology.

[0004] A literature search in relevant fields revealed that in the paper "Multi-target UAV Path Planning Based on Improved NSGA-II Algorithm" published in *Fire Command and Control* (2022, 47(02): 43-55), Fan Jiao et al. designed different evolutionary operators for the characteristics of path planning as an engineering problem based on the original NSGA-II algorithm, ultimately obtaining a set of Pareto optimal paths. However, their environmental modeling method was two-dimensional, only considering the threat zone and not the influence of terrain on the trajectory. Secondly, the path planning model proposed in this paper had fewer intermediate nodes, resulting in fewer Pareto optimal results, which is not conducive to path selection for adversarial decision-making. In their paper "Multi-UAV Cooperative Path Planning Based on Multi-Objective Optimization Algorithm" published in *Systems Engineering and Electronics Technology* (2017, 39(04): 782-787), Zhou Deyun et al. proposed the CO-NSGA-II algorithm. Addressing the engineering problem of cooperative multi-UAV path planning, the algorithm improves cooperative ranking by replacing congestion distance ranking with congestion distance ranking during the non-dominated ranking process. This allows for the acquisition of a set of Pareto optimal paths while meeting the requirements of multi-UAV cooperation. However, their improved congestion ranking method does not consider that different paths may correspond to similar Pareto solutions in the solution space, resulting in low diversity of the final results. Furthermore, the environmental modeling is also a two-dimensional spatial model, leading to poor practicality. Summary of the Invention

[0005] This invention aims to establish an adversarial environment model in three-dimensional space, comprehensively considering the influence of terrain and threat zones. To address the large solution space of the three-dimensional model, a segmented squirrel foraging mechanism is designed, employing different position update methods for squirrel groups at different ranking positions to improve convergence performance. To address the requirement for diverse Pareto solution sets in path planning, a multi-membrane multi-objective evolutionary framework is designed. During iteration, each membrane has its own optimal solution set, and different membranes are prioritized according to a specific non-dominated sorting method, further enhancing the diversity of the algorithm's solution set.

[0006] The objective of this invention is achieved as follows: Step 1: Establish an adversarial environment model; the mountain peak modeling function is: Where z(x,y) is the elevation of the mountain peak at the location with x as the horizontal coordinate and y as the vertical coordinate, and (x0,y0) is the coordinate of the center point of the mountain peak. s and y s , representing the inclination of the mountain peaks along the x-axis and y-axis respectively, with h being the summit height. The final 3D mountain model is composed of the superposition of multiple mountain peak functions; the radar-target distance modeling function is... Where R(x,y,z) is the distance from the target to the radar center point within the radar range, R maxThe maximum range monitored by radar; since anti-aircraft guns have a maximum elevation angle, their attack range is modeled using a cylinder, with the modeling function being the cylinder G(x,y,z), which satisfies the constraints. Where h max G is the height of the cylinder. max Let θ be the radius of the base of the cylinder, and θ be the maximum elevation angle of the anti-aircraft gun. max For θ max =arctan(h max / G max );

[0007] Step 2: Determine the multi-objective function for the three objectives;

[0008] Step 3: Squirrel population initialization, calculating the initial objective function value;

[0009] Step 4: Sort the non-dominated solutions of the squirrel population to obtain the Pareto solution set for this iteration;

[0010] Step 5: Calculate congestion distance and sort congestion distances within the same level;

[0011] Step Six: Submembrane Division, for the non-dominated squirrel population after sorting in generation t. Let the radius of the submembrane be R. Select the squirrel individual p1, which is in the undivided state and ranks first in the current population to be divided, as the leader of the current submembrane. Iterate through the current population and calculate the distance between the q-th individual and the leader individual p1. if Then, add this squirrel individual to the submembrane of the current leader individual, and mark this individual as having been assigned to a submembrane in the original population; repeat this step until all individuals in the original population have been assigned to the leader individual's submembrane. The set of individuals in the k-th submembrane is then represented as...

[0012]

[0013] Step 7: Evolution of each squirrel subpopulation within the membrane, selecting the first m subpopulations within the membrane of the k-th subpopulation. k Each individual is a hickory tree squirrel, and the mth individual... k +1 individuals up to the nth k One individual was an oak squirrel, and the rest were squirrels in ordinary trees;

[0014] Step 8: Determine if the final iteration count has been reached. If yes, output the multi-objective Pareto solution set for this terrain environment. If no, increment the iteration count t by 1, go to step 4, and iterate again.

[0015] Compared with existing technologies, the advantages of this invention are as follows: Most current multi-objective optimization algorithms applied to UAV trajectory planning involve two-dimensional environment modeling, but actual adversarial situations involve complex three-dimensional models, thus requiring comprehensive consideration of the impact of terrain, threats, and other factors on UAV trajectory planning. Secondly, when classic multi-objective optimization algorithms such as NSGA-II are applied to path planning, their congestion distance calculation method only considers the congestion degree of the target space, and their evolutionary method is overall population evolution, which easily leads to congested trajectory planning results and poor diversity. Furthermore, during the evolutionary process, the evolutionary method of classic multi-objective optimization algorithms is prone to getting trapped in local optima, resulting in poor convergence performance. The advantages of this invention are: the congestion distance calculation method considers both the target space and the decision space simultaneously, comparing the ratio of congestion distances within their respective spaces and retaining the larger ratio (i.e., the one with the greater influence) as the final congestion distance. Secondly, this invention designs a multi-objective, multi-membrane evolutionary method. After non-dominated sorting, different sub-membranes evolve in different directions, minimizing the possibility of the entire population evolving in the same direction and improving the diversity of path planning. Furthermore, this invention improves the classic squirrel foraging optimization algorithm as an evolutionary algorithm, designing different evolutionary methods for different squirrel groups to improve the convergence of the Pareto optimal path solution set for path planning. Attached Figure Description

[0016] Figure 1 This is a flowchart of the algorithm of the present invention.

[0017] Figure 2 This is a three-dimensional environment modeling diagram for the present invention.

[0018] Figure 3 This is the path planning result of the multi-objective algorithm proposed in this invention.

[0019] Figure 4 The results are shown in the classical multi-objective algorithm NSGA-II path planning results compared with the present invention. Detailed Implementation

[0020] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0021] This invention specifically relates to a UAV trajectory planning method based on an improved multi-objective squirrel foraging optimization algorithm. First, an adversarial 3D environment model is performed. Then, an improved multi-objective squirrel foraging optimization algorithm is proposed to iterate the path planning process, ultimately yielding path planning results with high diversity and strong convergence.

[0022] Figure 1 The algorithm flowchart of this invention is introduced, and the detailed process is as follows:

[0023] Step 1: Adversarial Environment Modeling. Since the adversarial environment typically includes mountains, radar threat zones, and anti-aircraft artillery threat zones, the mountain modeling function is as follows: Where z(x,y) is the elevation of the mountain peak at the location with x as the horizontal coordinate and y as the vertical coordinate, and (x0,y0) is the coordinate of the center point of the mountain peak. s and y s Here, represents the inclination of the mountain peak along the x-axis and y-axis, respectively, and h represents the height of the mountain peak. The final 3D mountain model is composed of the superposition of multiple mountain peak functions. The radar-target distance modeling function is... Where R(x,y,z) is the distance from the target to the radar center point within the radar range, R max The maximum radar detection range is given by the formula, indicating that the radar detection range is spherical; any target entering the radar range will be detected. Since anti-aircraft guns have a maximum elevation angle, their attack range can be approximated by modeling it as a cylinder. The modeling function is a cylinder G(x,y,z), which satisfies the constraints... Where h max G is the height of the cylinder. max Let θ be the radius of the base of the cylinder, and θ be the maximum elevation angle of the anti-aircraft gun. max For θ max =arctan(h max / G max ).

[0024] Step Two: Determine the multi-objective function for the three objectives. The multi-objective optimization model designed in this invention performs joint optimization of multiple objectives using three objective functions: minimizing path length cost, minimizing path threat cost, and minimizing path concealment cost. The total path length cost is calculated as follows: Where L is the total path length and N is the total number of path nodes. These are the three-dimensional coordinates of the path nodes. The path threat cost is calculated as follows: Where M is the total number of threat points. Let the threat weight be the j1th threat point. Let i be the coordinates of the i2th node on the path. Let J be the coordinates of the j1th threat point. To ensure the UAV maintains a certain level of stealth during its movement, the total path stealth cost is calculated as follows: Where H is the total concealment cost. h is the height of the i3th node in the path. safe This is a defined upper limit for the security height of the system; exceeding this limit increases the risk of exposure.

[0025] Step 3: Squirrel population initialization and calculation of the initial objective function value. Let the total number of squirrels in the population be L1, and the squirrel population matrix for generation t be... in The path node matrix representing each individual. With [x1,x2,...,xN ]correspond, With [y1,y2,...,y N ]correspond, With [z1,z2,...,z] N Corresponding to, (x) l ,y l ,z l Let l = 1, 2, ..., N be the coordinates of the l-th node in the path represented by each individual. Therefore, P is an L1×3N matrix. The objective function value is calculated for the initialized squirrel population matrix, yielding the objective function value matrix for the t-th generation. in Let m be the objective function value of the o-th squirrel in generation t under the m-th objective function. The path length cost vector represents the path length cost of the L1-th squirrel in generation t. Let L1 represent the path threat cost vector, which is composed of the path threat generation value of the L1-th generation of the t-th squirrel. Let L1 be the path concealment cost vector, which represents the path concealment cost of the L1th squirrel in generation t. For the Oth squirrel, ... Mapping to a path node matrix, calculating L, T, and H, then... The multi-target vector of the o-th squirrel is Let t = 1 initially.

[0026] Step 4: Sort the non-dominated solutions of the squirrel population to obtain the Pareto solution set for this iteration. First, for the i-th squirrel individual in the population, i = 1, 2, ..., L1, iterate through all other squirrel individuals in the population and determine the non-dominated relationship between them. The non-dominated relationship is determined as follows: for individuals a and b, the three objective function values ​​of individual a are... and The three objective function values ​​for individual b are and If for any All This indicates that individual a dominates individual b. If the i-th squirrel individual is not dominated by any of the other individuals (i = 1, 2, ..., L1), then the i-th individual is added to the subpopulation with the highest priority and removed from the original population. This process is repeated until the number of individuals in the original population is zero, meaning that all squirrel individuals have undergone a non-dominant hierarchy, and ultimately K sorted populations with different priorities are obtained.

[0027] Step 5: Calculate congestion distance and sort congestion distances within the same level. In multi-objective path planning, the calculation of congestion distance includes the calculation of congestion distance in the target space and congestion distance in the decision space, and the impact of both on the solution space needs to be considered comprehensively. The calculation method for congestion distance in the target space is as follows: For the i-4th individual at the k-th level in generation t, k = 1, 2, ..., K, its congestion distance in the target space is: in and It is the objective function value of the m-th objective function of the i4+1-th and i4-1-th individuals after sorting. and Let be the maximum and minimum values ​​of the objective function at the k-th level and the m-th level, respectively. The crowding distance in the decision space for the i-4th individual at the k-th level in generation t is . in Let be the j-th decision vector of the (i4+1)-th squirrel individual, which is the three-dimensional coordinate of the j-th node on the path represented by the (i4+1)-th squirrel individual. Let be the j-th decision vector of the i-th (i4-1)-th individual, representing the three-dimensional coordinates of the j-th node on the path represented by the i-th (i4-1)-th squirrel individual. Also, calculate the average crowding distance in the target space at the k-th level of the t-th generation. Crowding distance of the decision space at the k-th level in generation t Where N k Let be the number of individuals contained in the k-th level. Then, the special crowding distance for the i4th squirrel individual in the k-th level of the t-th generation is calculated as follows: express The value depends on the target space crowding distance. distance from crowded decision-making space The degree of impact was then assessed. Finally, within each level, the levels were sorted from largest to smallest based on the calculated congestion distance.

[0028] Step Six: Submembrane Division. For the squirrel population after non-dominated sorting in generation t... Let the radius of the submembrane be R. Select the squirrel individual p1, which is in the undefined submembrane state and ranks first in the current population to be divided, as the leader of the current submembrane. Iterate through the current population and calculate the distance between the q-th individual and the leader p1. if Then, add this squirrel individual to the submembrane of the current leader individual, and mark this individual as having a submembrane assigned in the original population. Repeat this step until all individuals in the original population have been assigned to the leader individual's submembrane. The set of individuals in the k-th submembrane is then represented as...

[0029] Step 7: Evolution of each squirrel subpopulation within the membrane. Select the first m cells within the membrane of the k-th subpopulation. kEach individual is a hickory tree squirrel, and the mth individual... k +1 individuals up to the nth k One individual is an acorn squirrel, and the rest are squirrels in ordinary trees. For the pecan squirrels, an elite-guided strategy is implemented, and the specific update method for the c-th dimension position of the i-th squirrel is as follows: in Let c be the c-th dimension variable of the i5th pecan individual within the k-th submembrane of the (t+1)-th generation. Let be the c-th dimension variable of the i5th squirrel individual in the t-th generation, s1 be the weighting factor with a uniform random number in the range [0,1], and s2 be the sine and cosine influence factors with a value in the range [0,π]. Let be the c-th dimension variable representing the historical best individual up to the k-th submembrane in the t-th generation.

[0030] For the oak squirrel individual within the k-th submembrane, the position of the i-th 6th oak squirrel individual... Transformed into quantum position Executing a quantum update strategy, we evolve towards the pecan squirrel individual, and the c-th dimension position of the i6th oak individual in the t-th generation. and its quantum position The mapping relationship is The quantum rotation angle of the c-th dimension position of the i6th oak tree individual in the t-th generation is Where δ t It is the inertia coefficient, used to balance the algorithm's global and local optimization capabilities during evolution. The calculation formula is δ. t =l1+l2×(g max -t) / g max , where g max The maximum number of iterations is set for the algorithm, and l1 and l2 are two constants. Let be the c-th dimension quantum variable of the optimal hickory tree individual in the t-th generation of the k-th submembrane. The specific update method for the c-th dimension variable of the i-th individual of the t-th generation of the oak squirrel in the k-th submembrane is as follows: in and Let be the c-th quantum variable of the i6th oak squirrel individual before and after the t-th generation update. After evolution, the quantum position is determined according to the mapping relationship. Transform into the corresponding position

[0031] For ordinary tree squirrel individuals, a perturbation update strategy is implemented, where each squirrel individual is randomly perturbed within a defined range. The specific update method for the position of an ordinary tree squirrel individual within the k-th submembrane is as follows: in and Let randa and randb be the c-th dimension variable of the i7th ordinary tree squirrel individual before and after the t-th generation update, respectively. randa and randb are the random individual indices among the ordinary tree squirrel individuals, w1 is a random value between -1 and 1, and w2 is a weighting factor representing the individual's... and For individuals The extent of the impact.

[0032] Step 8: Determine if the final iteration count has been reached. If yes, output the multi-objective Pareto solution set for this terrain environment. If not, increment the iteration count t by 1 and return to Step 4 to iterate again.

[0033] like Figure 1 As shown, this invention performs 3D adversarial environment modeling, considering terrain influence, anti-aircraft artillery threats, and radar threats. A1 and A2 are radar threat zones, with center coordinates A1(35, 80, 0) and a radius of 10, and A2(70, 20, 0) and a radius of 13. B1 and B2 are anti-aircraft artillery threat zones, with center coordinates B1(30, 45, 0) and a radius of 10, and B2(80, 40, 0) and a radius of 10. The initial population size is L1 = 100, and the maximum number of iterations is g. max =500, weighting factors s1=0.63, s2=0.56, w2=0.68.

[0034] like Figure 2 and Figure 3 As shown, the improved multi-objective squirrel foraging algorithm proposed in this invention employs a special crowding distance calculation method and a multi-membrane evolution in different directions, resulting in a highly diverse Pareto optimal path set for path planning. In contrast, the classic multi-objective algorithm NSGA-II produces poorly diverse path planning results. Therefore, the algorithm proposed in this invention is particularly suitable for the engineering problem of UAV trajectory planning, capable of planning multiple different paths in complex adversarial environments, which is beneficial for decision-makers to select UAV trajectories according to strategic needs.

Claims

1. A UAV trajectory planning method based on a multi-objective self-organizing squirrel foraging mechanism, characterized in that, The steps are as follows: Step 1: Resume adversarial environment model, the mountain peak modeling function is: ,in The mountain peak is on the x-axis. The vertical axis is The elevation of the mountain peaks at that location The coordinates of the center point of the mountain peak are: and The mountain peaks are respectively axial direction and Inclination in the axial direction, The final 3D mountain model is composed of multiple mountain peak functions superimposed to represent the mountain peak height. The radar-target distance modeling function is ,in The distance from the target within radar range to the radar center point. The maximum range detected by radar; because anti-aircraft guns have a maximum elevation angle, their attack range is modeled using a cylinder, and the modeling function is a cylinder. It satisfies the constraints ,in The height of the cylinder The radius of the cylinder's base is the maximum elevation angle of the anti-aircraft gun. for ; Step 2: Determine the multi-objective function for the three objectives; Step 3: Squirrel population initialization, calculating the initial objective function value; Step 4: Sort the non-dominated solutions of the squirrel population to obtain the Pareto solution set for this iteration; Step 5: Calculate congestion distance and sort congestion distances within the same level; Step Six: Submembrane Division, the first For the squirrel population matrix after non-dominated sorting The radius of the submembrane is set to be Select the first squirrel individual in the current population to be divided that is in the undivided submembrane state. The leader of the current submembrane; traverse the current population and calculate the [number]th [unit]. Each individual squirrel and the current leader of the uterine membrane. distance ,if If the squirrel is added to the current leader's submembrane, it is marked as having a submembrane in the original population. This step is repeated until all individuals in the original population have been assigned to the leader's submembrane. The set of individual submembranes is represented as , ; Step 7: Evolution of each intramembranous squirrel population, selecting the [number]th [unit / group]. The inner membrane of the individual The individuals were hickory tree squirrels, the first... Individuals to the first One individual was an oak squirrel, and the rest were squirrels in ordinary trees; Step 8: Determine if the final iteration count has been reached. If yes, output the multi-objective Pareto solution set for this terrain environment; otherwise, set the iteration count to zero. Add 1, proceed to step four, and iterate again.

2. The UAV trajectory planning method based on the multi-objective self-organizing squirrel foraging mechanism according to claim 1, characterized in that, Step two specifically includes: The total path length cost is calculated as follows: in This is the total path length. This represents the total number of path nodes. The path node's three-dimensional coordinates are given; the path threat cost is calculated as follows: ,in The total number of threat points. For the first Threat weight of each threat point For path number The coordinates of each node, For the first The coordinates of each threat point, and the total concealment cost of the path are calculated as follows: ,in The total cost of concealment, It is the first in the path The height of each node This is a defined upper limit for the security height of the system; exceeding this limit increases the risk of exposure.

3. The UAV trajectory planning method based on the multi-objective self-organizing squirrel foraging mechanism according to claim 2, characterized in that, Step three specifically includes: setting the total number of squirrel individuals in the population to be... , No. The squirrel population matrix is ,in The path node matrix representing each individual. and correspond, and correspond, and correspond, It is the first path represented by each individual. The coordinates of the nth node are obtained; the objective function value is calculated for the initialized squirrel population matrix to obtain the coordinates of the nth node. Substitute the objective function value matrix ,in For the first The generation The squirrel individual in the first The objective function value under each objective function, Indicates the first generation The path length cost vector is composed of the path length costs of each squirrel. Indicates the first generation The path threat cost vector is composed of the path threat cost of each squirrel. Indicates the first generation The path concealment cost vector, composed of the path concealment cost of the nth squirrel, is used for the nth squirrel. A squirrel, Mapped to a path node matrix, calculated , and ,but , , , No. The multi-target vector of the squirrel is Initial Order .

4. The UAV trajectory planning method based on the multi-objective self-organizing squirrel foraging mechanism according to claim 1, characterized in that, Step four specifically includes: First, for the first in the population... Individual squirrels Iterate through all squirrel individuals in the population except for this one, and determine the non-dominance relationship between them; the method for determining the non-dominance relationship is as follows: for each individual... and individuals , The three objective function values ​​of the individual are , and , The three objective function values ​​of the individual are , and If for any All This indicates that the individual Dominant Individual If the first Each individual squirrel is not dominated by any other individual. Then the first Each individual is added to the first-priority subpopulation and removed from the original population; this step is repeated until the number of individuals in the original population is zero, meaning all squirrel individuals have undergone non-dominant hierarchical division, and finally... Several populations have been sorted by different priorities.

5. The UAV trajectory planning method based on the multi-objective self-organizing squirrel foraging mechanism according to claim 1, characterized in that, Step five specifically includes: The method for calculating the target space congestion distance is as follows: For the first... The generation The first level Individual, The crowding distance in its target space is: ， in, and It is the number after sorting. The and the first The first individual The objective function value of each objective function; and The first The first level The maximum and minimum values ​​of the objective function; For the The generation The first level The crowding distance in the decision space for each individual is: in, For the first The first squirrel individual The decision vector, i.e. the decision vector... The path represented by each individual squirrel is the first The three-dimensional coordinates of each node, For the first The first individual The decision vector, i.e. the decision vector... The path represented by each individual squirrel is the first The three-dimensional coordinates of each node; Calculate the first one respectively The generation Average congestion distance of target spaces at each level , No. The generation Crowded decision-making spaces at each level ; in, For the first The number of individuals contained in each level; then for the first level... The generation The first level The specific crowding distance for an individual squirrel is calculated as follows: express The value depends on the target space crowding distance. distance from crowded decision-making space The degree of impact is then assessed; finally, within each level, the levels are sorted from largest to smallest according to the calculated congestion distance.

6. The UAV trajectory planning method based on the multi-objective self-organizing squirrel foraging mechanism according to claim 1, characterized in that, Step seven specifically includes: for individual pecan squirrels, implementing an elite guidance strategy, the first... The first individual hickory squirrel The specific method for updating the dimension position is as follows: in: For the first The generation The first one inside the membrane The first individual pecan squirrel dimensional variables, For the first The generation The first squirrel individual dimensional variables, This is the weighting influence factor, with a value range of [value range missing]. Uniform random numbers between The sine and cosine influence factors have a range of values. , As of the end of the The generation The historical best individual among the daughter membranes Dimensional variables; For the The oak squirrel individual within the membranous membrane, the first Location of individual oak squirrels Transformed into quantum position , ; Execute the quantum update strategy to evolve into a pecan individual, the first The generation The first oak individual Dimensional position and its quantum position The mapping relationship is: No. The generation The first oak individual The quantum rotation angle of the dimensional position is: in, It is the inertia coefficient, used to balance the algorithm's global and local optimization capabilities during evolution. The calculation formula is... ,in The maximum number of iterations set for the algorithm. and For two constants, For the first The first of the submembrane The first optimal hickory tree individual of the generation A quantum variable of dimension is used to update the position of an individual oak squirrel. The first sub-membrane The generation The first individual oak squirrel The specific update method for dimension variables is as follows: in, and The first Before and after the update The first individual oak squirrel 1D quantum variable; after evolution, the quantum position is determined according to the mapping relationship. Transform into the corresponding position ; For ordinary tree squirrel individuals, a perturbation update strategy is implemented, where each squirrel individual is randomly perturbed within a defined range; the... The specific method for updating the location of a common tree squirrel within the genus membrane is as follows: in, and For the first Before and after the update The first ordinary tree squirrel individual dimensional variables, and This is a random individual number among ordinary tree squirrels. To randomly select a value between -1 and 1, The weighting factor represents the individual and For individuals The extent of the impact.

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