Improved NSGA-II-based power transmission line inspection unmanned aerial vehicle task allocation method

Abstract

The invention discloses a power transmission line inspection unmanned aerial vehicle task allocation method based on improved NSGA-II, and the method is characterized in that a mixed integer programming multi-objective optimization scheduling model is provided based on two optimization objectives: (1) the sum of total path lengths of unmanned aerial vehicles is shortest, and (2) the longest working time of the unmanned aerial vehicles is minimized; an improved non-dominated sorting genetic algorithm (AE-NSGAII) is constructed, the crossover mutation rate can be adaptively adjusted, repeated individuals are prevented from being generated to enhance search, and more solutions which are better in two target directions can be found. According to the method, one solution can be finally selected from a plurality of pareto optimal solutions as an unmanned aerial vehicle distribution scheme according to different actual conditions, so that the cooperative inspection working efficiency of a plurality of unmanned aerial vehicles at a certain parking point is improved, the cost is reduced, and the inspection time is shortened.

Description

Technical Field

[0001] The present invention relates to the field of unmanned aerial vehicle (UAV) mission assignment and scheduling, and specifically to a method for assigning missions to UAVs for power transmission line inspection based on improved NSGA-II. Background Art

[0002] The main method of traditional power inspection is manual inspection, which has high labor intensity, high cost, low efficiency and lack of safety. By using UAVs equipped with cameras and lidar, power inspection of large areas, under harsh weather or terrain can be achieved efficiently, safely and flexibly. When multiple UAVs conduct joint inspections, it is necessary to determine the sequence of power transmission towers that each UAV needs to inspect. How to determine these sequences is crucial for improving inspection efficiency and reducing inspection costs. The definition of the Multiple Traveling Salesman Problem (MTSP) is as follows: There are n cities and m traveling salesmen. Each traveling salesman starts from the starting city, visits some cities and then returns to the ending city. It is required that except for the starting and ending cities, each city is visited by exactly one traveling salesman, and a distribution plan that meets the above requirements and has the minimum cost is required. Multi-objective optimization refers to making an optimal decision by weighing among multiple objectives to make the overall situation as optimal as possible. There are conflicts among these objectives: the optimization of one objective often leads to the deterioration of other objectives. The problem of optimizing multiple objectives while solving MTSP is called the Multi-Objective MTSP (MOMTSP). The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is an improved genetic algorithm and is currently widely used in multi-objective optimization scenarios. This algorithm uses fast non-dominated sorting and crowding distance calculation to reduce the computational complexity of the algorithm and maintain the diversity of the population. Summary of the Invention

[0003] In the mission scenario of UAV power inspection, a vehicle carries several UAVs and stops at a parking point. All the power transmission towers to be inspected at this parking point will be assigned to these UAVs, and these UAVs will ultimately complete the inspection of all the power transmission towers. Since all UAVs start simultaneously at the beginning of the inspection, after the UAV that takes the longest time to complete all tasks returns to the parking point, the inspection task corresponding to this parking point is considered completed, and the vehicle can leave. In order to complete all the inspection tasks at this parking point as soon as possible, the longest UAV mission execution time should be minimized during mission assignment. Moreover, the total path length of all UAV inspections should also be minimized during mission assignment. Since the above mission scenario aims to minimize two objectives, the UAV mission assignment problem to be solved by the present invention is a MOMTSP problem.

[0004] The present invention models the UAV mission assignment as a multi-objective multi-traveling salesman problem (MOMTSP), and comprehensively optimizes two objectives (total path length, longest UAV mission execution time). Since the NSGA-II algorithm has the problems of too fast convergence and poor global search ability in the mission scenario of the present invention, an improved non-dominated sorting genetic algorithm (AE-NSGA-II) is proposed. The AE-NSGA-II algorithm can find more solutions that are better in both objectives. The improvement measures are as follows: ① When generating the offspring population, for two randomly selected individuals, they are crossed and mutated with a certain probability. The obtained individuals are not directly put into the offspring population like NSGA-II, but are checked: whether the chromosome encoding is repeated with an individual in the parent population. If it is repeated, the new individual is further processed: both crossed and mutated until the obtained new individual is no longer repeated with the individuals in the parent population. This measure can ensure the diversity of individuals in the population and avoid the reduction of the search space due to the existence of too many repeated individuals. ② On the basis of ①, since in the NSGA-II algorithm, the non-dominated rank can reflect the quality of individuals to a certain extent, different individuals in different non-dominated ranks in the parent population are given different crossover and mutation probabilities to make the final actual crossover probability stable at a relatively high level (about 0.95), and the actual mutation probability increases with the improvement of the non-dominated rank, realizing that the more excellent the individual, the higher the probability of its mutation, and jumping out of the local optimum of the current optimal solution. Prevent the population from being trapped in a certain hyperplane in the search space during evolution and unable to get rid of it only by crossover. The mutation operation can help to get rid of this situation. The specific implementation process of the UAV mission assignment algorithm is as follows:

[0005] Step 1: Adopt the two-part chromosome technique, initialize the population and set the number of generations of evolution Gen = 1, and the termination condition k = 0.

[0006] Step 2: Judge whether the first-generation offspring population has been generated. If it has been generated, let the number of generations of evolution Gen = 2. Otherwise, perform non-dominated sorting on the initial population, and generate the first-generation offspring population through selection, crossover, and mutation (here add ①: avoid generating repeated individuals. Add ②: set different crossover probabilities and mutation probabilities for different individuals according to different non-dominated ranks), and make the number of generations of evolution Gen = 2.

[0007] Step 3: Merge the parent population and the offspring population into a new population.

[0008] Step 4: Judge whether a new parent population has been generated. If not, calculate the objective function of the individuals in the new population, and perform operations such as fast non-dominated sorting, calculation of crowding degree, and elite strategy to generate a new parent population; otherwise, go to Step 5.

[0009] Step 5: Perform selection, crossover, and mutation operations on the generated parental population (add ① here: avoid generating duplicate individuals. Add ②: set different crossover probabilities and mutation probabilities for different individuals according to different non-dominated levels) to generate the offspring population.

[0010] Step 6: Determine whether the similarity between the Pareto optimal solutions obtained in this iteration and the previous iteration reaches 85%. If it reaches, then k = k + 1. Determine whether the iteration end condition is satisfied: If k < 15, then the generation number Gen = Gen + 1 and return to Step 3; otherwise, go to Step 7.

[0011] Step 7: Select one solution from the Pareto optimal solutions according to the actual situation as the final UAV allocation plan to obtain the task sequences of each UAV. Description of the Drawings

[0012] Figure 1 Schematic diagram of the two-part chromosome representation of ten towers and four UAVs in the present invention

[0013] Figure 2 Schematic diagram of the Pareto front in the present invention

[0014] Figure 3 Schematic diagram of the Pareto optimal solution obtained by AE-NSGA-II in the present invention

[0015] Figure 4 Route map of UAV task allocation in the present invention Detailed Implementation Modes

[0016] I. Problem Description

[0017] In the UAV inspection scenario, a vehicle carrying multiple UAVs stops at a certain parking point. All UAVs will start from this parking point simultaneously, complete the inspection tasks of the towers assigned to them respectively, and then return to the parking point. A set of task allocation plans should be found to ensure that all towers are inspected and only inspected once, and that: 1) the total path length of all UAVs is the shortest, 2) the task execution time of the longest UAV is the shortest, so as to minimize the cost and time of the entire inspection process. The model assumptions, symbol definitions, objective functions, and constraints are as follows:

[0018] 1. Model Assumptions

[0019] The model of the present invention has the following assumptions:

[0020] 1) Use exactly the same UAVs

[0021] 2) Neglect the inspection time of the UAVs at the towers

[0022] 3) The path length between the UAV and the pole tower is the straight-line distance between the two.

[0023] 4) The UAV flies at a constant speed throughout the flight.

[0024] 5) The flight path length of the UAV is used to approximate the time for the UAV to perform the task.

[0025] 6) Ignore the takeoff and landing time of the UAV.

[0026] 2. Symbol Definitions

[0027] (1) Parameters

[0028] The following definitions are used when formulating the objectives and constraints:

[0029] m: The number of UAVs

[0030] n: The number of pole towers to be inspected

[0031] C ijk : The path length experienced by UAV k flying from pole tower i to pole tower j

[0032] (2) Decision Variables

[0033]

[0034] Decision variable X ijk Indicates whether UAV k will fly from pole tower i to pole tower j. This decision variable is binary. Tower 0 represents the parking point.

[0035] 3. Objective Function and Constraints

[0036] This model aims to find the Pareto optimal solution that minimizes the total path length of the UAVs and the longest UAV mission time, which belongs to a multi-objective optimization problem (MOP). Therefore, the objective function is:

[0037] minZ total (2)

[0038] minZ max (3)

[0039]

[0040] Z max =max(t k );k=1,...,m (5)

[0041]

[0042] The objective function (2) represents minimizing the total path length of the UAVs, and the objective function (3) represents minimizing the maximum value of the path lengths of each UAV. The constraints include:

[0043]

[0044]

[0045]

[0046]

[0047]

[0048] Constraints (7) and (8) ensure that each tower is reached by only one UAV and is visited only once. (9) and (10) ensure that each UAV must start from and return to the parking point. (11) is a connectivity constraint to avoid generating subcircuits in the final solution.

[0049] II. Specific solution steps

[0050] According to the characteristics of the model of the present invention, a chromosome coding method, a crossover operator, and a mutation operator are designed. Two improvement measures are introduced into the NSGA-II algorithm, namely, an adaptive crossover rate and mutation rate, and enhancing the exploration of different individuals, to solve the model. These improvements aim to enhance the search ability and diversity of the algorithm to obtain better solutions.

[0051] 1. Initial chromosome coding

[0052] The present invention uses a two-part chromosome technique, which can generate solutions with better fitness values. The coding method uses real number coding. Each chromosome is divided into two parts. The first part is a permutation including n towers. The second part has m - 1 genes, where m is the number of UAVs. Each gene value in the second part is between 1 and n, and each gene value represents a segmentation point for the first part of the chromosome. The m - 1 segmentation points can divide the tower sequence in the first part of the chromosome into m parts, and each segment represents the entire tower sequence that a UAV needs to inspect. The gene values in the second part of the chromosome are non-repeating and sorted in ascending order. For example, Figure 1A two-part chromosome representation of ten poles and four UAVs is given. The first part of the chromosome is: 6-5-3-2-9-7-8-1-4-10. The second part of the chromosome is: 2-6-8, representing the split points for the first part of the chromosome. The task sequences of the first and second UAVs are divided at index 2, those of the second and third UAVs are divided at index 6, and those of the third and fourth UAVs are divided at index 8. In addition, we represent the parking point as pole No. 0. Each UAV will leave the parking point and return to the parking point after completing all assigned tasks. Therefore, a 0 is added at the beginning and end of the task sequence of each UAV. Thus, the task sequence of UAV1 is: 0-6-5-0, that of UAV2 is: 0-3-2-9-7-0, that of UAV3 is: 0-8-1-0, and that of UAV4 is: 0-4-10-0.

[0053] 2. Crossover operator, mutation operator

[0054] In the genetic algorithm, the crossover operator is a key operator that determines the global search ability of the algorithm. It generates new individuals by simulating the crossover of genes on chromosomes in nature, which can increase population diversity and accelerate the search process. Since the present invention adopts a two-part chromosome technique, and the first part of the chromosome is a full permutation of 1 to n (n is the number of poles), the partially-matched crossover (PMX) operator is used to perform crossover on the first part of the chromosome. This operator can ensure that there are no duplicate genes among the genes in the first part of the chromosome. Because the second part is m - 1 genes (m is the number of UAVs), and each gene value is an integer from 1 to n, increasing and non-repeating, the uniform crossover operator is used to perform crossover on the second part of the chromosome (if a gene position is repeated after crossover, the gene at that position is not crossed).

[0055] The mutation operation determines the local search ability of the algorithm and generates new individuals by simulating the mutation of genes on chromosomes in nature. It can expand the search space, accelerate the convergence to the optimal solution, and enhance population diversity. It can introduce new genes into the population to avoid premature convergence of the algorithm and falling into local optima. In the task scenario of the present invention, the position-based mutation operator is used for the first part of the chromosome, which ensures that there are no duplicate genes in the first part of the chromosome. For the second part of the chromosome, simple mutation is used, and each gene value is converted to binary for simple mutation (if a gene position is repeated after mutation, it is mutated again).

[0056] 3. Fast non-dominated sorting

[0057] Fast non-dominated sorting is a concept proposed based on Pareto domination. In the present invention, there are two objective functions: Z total and Z max . If individual x 1 and individual x 2 satisfy the conditions of Z total (x 1 ) < Z total (x 2 ) and Z max (x 1 ) < Z max (x 2 ), then individual x 1 is considered to dominate individual x 2 , and x 2 is a dominated solution. If x 1 is not dominated by any other solution, then x1 is considered a non-dominated solution (also known as a Pareto solution).

[0058] The main task of fast non-dominated sorting is to find all Pareto solutions in the solution space. As Figure 2 shown, each black point represents a Pareto-optimal solution. All Pareto-optimal solutions together form the Pareto-optimal solution set, and these solutions are not dominated by any other solution. It can be considered that these solutions are the optimal solutions for UAV task allocation. After being mapped by the objective function, these solutions form the Pareto front of the UAV task allocation problem.

[0059] 4. Enhanced exploration idea

[0060] In the NSGA-II algorithm, there are likely to be too many duplicate solutions in the population, resulting in being trapped in local optimal solutions and difficult to jump out.

[0061] To strengthen exploration during the generation of the offspring population, a measure of "preventing the generation of duplicate individuals" is added. In the NSGA-II algorithm, during the generation of the offspring population, two parent individuals are randomly selected multiple times, and they are cross-mutated with a certain probability to obtain two new individuals. These new individuals are added to the offspring population and then merged with the parent population. After non-dominated sorting and calculating the crowding degree of the merged population, screening is performed to obtain a new parent population. However, this method has certain defects. Suppose a new individual X new already has the same chromosome encoding as an individual X old in the population. Adding this individual to the offspring population will cause a waste of resources, and the existence of duplicate individuals in the population will narrow the search space.

[0062] Therefore, after obtaining a new individual, it should be determined whether the new individual needs to be improved. The criterion for improvement set here is: there is a duplication of chromosomes with the population obtained in the previous iteration. If satisfied, it needs to be improved: re - perform the operations of both crossover and mutation using the operator until the newly obtained individual is different from the existing individuals.

[0063] 5. Adaptive Mutation Rate

[0064] The crossover operation randomly exchanges parts of the genes of two individuals, and this operation can pass excellent genes to the next generation. The mutation operation causes some changes in the chromosomal genes, thus introducing new gene combinations. Both crossover and mutation can increase the diversity of the population, but the crossover operation mainly conducts global search, while the mutation operation conducts local search. Premature convergence to a local optimum may occur during the evolutionary process, leading to premature termination of evolution. The mutation operation can prevent this phenomenon and help escape from the local optimum.

[0065] In NSGA - II, the non - dominated rank of an individual to some extent reflects the quality of this individual in the entire population. The higher the non - dominated rank, the better the performance of this individual in the two objectives, and vice versa for a lower non - dominated rank. The more excellent an individual is, the more its mutation probability should be increased to jump out of the local optimum of the current optimal solution and prevent the population from being trapped in a certain hyperplane in the search space during evolution and unable to escape only by crossover. The mutation operation can help with this escape.

[0066] For the individual i selected from the parent population Pop, calculate the crossover probability pc i and the mutation probability pm i The formulas are as follows:

[0067]

[0068]

[0069]

[0070] where i.rank represents the non - dominated rank of individual i, rank avg represents the average non - dominated rank of all individuals in the current parent population, popnum represents the size of the parent population Pop, and l is the minimum non - dominated rank value (1 is the highest non - dominated rank value, and the higher the non - dominated rank, the lower the non - dominated rank value).

[0071] Introduce "enhanced exploration" and "adaptive crossover and mutation rates" to ASGA-II, which we call the AE-NSGA-II algorithm. When generating the offspring population, this algorithm will avoid the newly generated individuals being the same as those in the parent population. Therefore, for the two selected parent individuals, there can only be the following behaviors: only crossover, only mutation, both crossover and mutation. It is impossible for two individuals to neither hybridize nor mutate. Therefore, the actual crossover rate and mutation rate of the two selected individuals are not equal to the pc and pm calculated by (12) and (13). In fact, when "enhanced exploration" and "adaptive crossover and mutation rates" are introduced simultaneously, the actual crossover probability can be maintained above 0.9, and the actual mutation probability increases with the increase of the non-dominated rank. The reasons are as follows. The calculation formulas (12) and (13) can keep the probability of "only mutation" below 0.1, thus maintaining the probability of actual crossover above 0.9. These formulas can significantly reduce the probability of "only crossover" as the non-dominated rank increases, resulting in a significant increase in the probability of "both crossover and mutation", thereby increasing the actual mutation probability.

[0072] p 仅交叉 = pc × (1 - pm) (15)

[0073] p 仅变异 = pm × (1 - pc) (16)

[0074] p 既交叉又变异 = 1 - p 仅交叉 - p 仅变异 (17)

[0075] p 实际交叉 = p 仅交叉 + p 既交叉又变异 (18)

[0076] p 实际变异 = p 仅变异 + p 既交叉又变异 (19)

[0077] Taking the current parent population divided into 10 non-dominated ranks, with the average non-dominated rank rank avg being 6.04 as an example, as shown in Table 1, based on (12) and (13), the pc and pm for each non-dominated rank can be obtained, as shown in the second and third columns of Table 1. Use formulas (15) to (19) to calculate the probabilities and fill them in the fourth to eighth columns of the table respectively. Although pc and pm decrease as the non-dominated rank of the individual increases, the analysis shows that the probability of "actual crossover" for all individuals remains around 0.95, and the probability of "actual mutation" increases with the increase of the non-dominated rank.

[0078] Therefore, AE-NSGA-II stabilizes the crossover probability of all individuals at around 0.95. Moreover, the more excellent the individual is, the greater the possibility of mutation, preventing them from falling into local optimal solutions.

[0079] Table 1 Probabilities of individuals performing various operations after introducing adaptive crossover and mutation rates and enhanced search measures

[0080]

[0081] 6. Setting for the end of iteration

[0082] In the present invention, the similarity between the Pareto optimal solutions obtained in the current iteration and the Pareto optimal solutions of the previous iteration is calculated each time. The similarity is defined as follows:

[0083]

[0084] S 1 、S 2 are respectively: the sets of Pareto optimal solutions after the completion of the previous and current iterations, A = S 1 ∩S 2 , where max(S 1 .size - A.size, S 2 .size - A.size) represents the number of individuals that have changed in the two optimal solution sets. When the similarity between the Pareto optimal solutions obtained in the previous round and the Pareto optimal solutions of this round reaches 85% for 15 consecutive times, it is considered that convergence has been achieved and the iteration is stopped.

[0085] III. Selection of solutions

[0086] In the scenario of drone task allocation, our goal is to find a Pareto optimal solution set that performs well on both objectives and decide which solution to choose based on the actual situation. For example, in the case of natural disasters such as heavy rain or earthquakes, when emergency inspections of power poles are required, we should give priority to the solution with the shortest drone execution time and reduce the weight of the total path length of the drone. Assume that there are 20 pole towers that need to be inspected at the parking point and there are 4 drones. The coordinates of the parking point are (500, 500), and the coordinates of the pole towers are: (0, 0), (600, 999), (776, 739), (835, 251), (974, 971), (759, 661), (815, 2), (566, 898), (760, 310), (880, 990), (923, 679), (200, 964), (356, 48), (889, 38), (269, 854), (603, 772), (799, 821), (897, 131), (699, 87), (163, 682). The Pareto optimal solution obtained using the AE-NSGA-II algorithm is as follows Figure 3 As shown in Figure 2, there are 4 Pareto optimal solutions. If we consider emergency inspections, the shorter the stay time, the better. Therefore, the shorter the maximum path length, the better. We take the Pareto optimal solution in the lower right corner. The two fitness function values ​​of this individual are total path length: 6025.27, maximum path length: 1645.17. The chromosome corresponding to this individual is [1, 13, 19, 7, 14, 18, 4, 9, 6, 3, 17, 10, 5, 11, 16, 8, 2, 12, 15, 20, 2, 8, 14]. The task sequence of the four drones is shown in Table 2. The drone task allocation roadmap is shown in Figure 2. Figure 4 shown.

[0087] Table 2 Mission sequences of each UAV

[0088] Drone number Task sequence Travel length 0 0-1-13-0 1540.71 1 0-19-7-14-18-4-9 1330.4 2 0-6-3-17-10-5-11 1508.99 3 0-16-8-2-12-15-20 1645.17

Claims

1. An Unmanned Aerial Vehicle (UAV) Mission Assignment Method for Transmission Line Inspection Based on Improved NSGA-II ； This method models the UAV mission assignment as a Multi-Objective Multiple Traveling Salesman Problem (MOMTSP), comprehensively optimizing two objectives (total path length, longest UAV mission execution time); this method proposes an improved non-dominated sorting genetic algorithm (AE-NSGA-II), and the AE-NSGA-II algorithm can find more solutions that are superior in both objectives; the improvement measures of the algorithm are as follows: ①: When generating the offspring population, for two randomly selected individuals, they are crossed and mutated with a certain probability. The obtained individuals are not directly put into the offspring population like NSGA-II, but are checked: whether the chromosome encoding is repeated with an individual in the parent population. If it is repeated, the new individual is further processed: both crossed and mutated until the obtained new individual is no longer repeated with the individuals in the parent population. This measure can ensure the diversity of individuals in the population and avoid the reduction of the search space due to the existence of too many repeated individuals; ②: On the basis of ①, since in the NSGA-II algorithm, the non-dominated rank can to some extent reflect the quality of individuals, different individuals in different non-dominated ranks in the parent population are given different crossover and mutation probabilities to achieve that the final actual crossover probability is stabilized at a relatively high level (about 0.95), and the actual mutation probability increases with the improvement of the non-dominated rank, realizing: the more excellent the individual, the greater the probability of enhancing its mutation, jumping out of the local optimum of the current optimal solution; preventing the population from being trapped in a certain hyperplane in the search space during evolution and being unable to get rid of it only by crossover. The mutation operation can help with this getting rid of; the specific implementation process of this method is as follows: Step 1: Adopt the two-part chromosome technique, initialize the population and set the number of generations of evolution Gen = 1, and the termination condition k = 0; Step 2: Judge whether the first-generation offspring population has been generated. If it has been generated, then set the number of generations of evolution Gen = 2. Otherwise, perform non-dominated sorting on the initial population, and through selection, crossover, and mutation (add ① here: avoid generating duplicate individuals; Add ②: Set different crossover probabilities and mutation probabilities for different individuals according to different non-dominated ranks) to generate the first-generation offspring population and set the number of generations of evolution Gen = 2, Step 3: Merge the parent population and the offspring population into a new population; Step 4: Judge whether a new parent population has been generated. If not, calculate the objective functions of the individuals in the new population, and perform operations such as fast non-dominated sorting, calculation of crowding degree, and elitist strategy to generate a new parent population; otherwise, go to Step 5; Step 5: Perform selection, crossover, and mutation operations on the generated parent population (add ① here: avoid generating duplicate individuals; add ②: set different crossover probabilities and mutation probabilities for different individuals according to different non-dominated ranks) to generate the offspring population; Step 6: Determine whether the similarity between the Pareto optimal solutions obtained in this iteration and the previous iteration reaches 85%. If it reaches, then k = k + 1; determine whether the iteration end condition is satisfied: if k < 15, then the generation number Gen = Gen + 1 and return to Step 3; Otherwise, go to Step 7; Step 7: Select one solution from the Pareto optimal solutions as the final UAV allocation plan according to the actual situation, and obtain the task sequences of each UAV.

2. A method for task allocation of transmission line inspection UAVs based on improved NSGA-II as claimed in claim 1, characterized in that, in Step 1, a two-part chromosome encoding technique is adopted; solutions with better fitness values can be generated; the encoding method adopts real number encoding; each chromosome is divided into two parts. The first part is an arrangement including n towers; the second part has m - 1 genes, where m is the number of UAVs; each gene value in the second part is between 1 and n, and each gene value represents a segmentation point for the first part of the chromosome; the m - 1 segmentation points can divide the tower sequence of the first part of the chromosome into m parts, and each segment represents the entire tower sequence that a UAV needs to inspect; the gene values in the second part of the chromosome are non-repeating and in ascending order; for example, the two-part chromosome of ten towers and four UAVs is represented as: 6-5-3-2-9-7-8-1-4-10-2-6-8. It can be obtained that the first part of the chromosome is: 6-5-3-2-9-7-8-1-4-10; the second part of the chromosome is: 2-6-8, representing the segmentation points for the first part of the chromosome; the task sequences of the first and second UAVs are divided at index 2, the task sequences of the second and third UAVs are divided at index 6, and the task sequences of the third and fourth UAVs are divided at index 8; in addition, we represent the parking point as tower No.

0. Each UAV will leave the parking point and return to the parking point after completing all assigned tasks; therefore, a 0 is added at the beginning and end of the task sequence of each UAV. Therefore, the task sequence of UAV1 is: 0-6-5-0, the task sequence of UAV2 is: 0-3-2-9-7-0, the task sequence of UAV3 is: 0-8-1-0, and the task sequence of UAV4 is: 0-4-10-0.

3. A method for task allocation of transmission line inspection UAVs based on improved NSGA-II as claimed in claim 1, characterized in that, in the crossover and mutation operations in Step 2 and Step 5, according to the different characteristics of the two parts of the chromosome, a partially matched crossover operator and a position-based mutation operator are adopted for the first part of the chromosome, and a uniform crossover operator and a basic bit mutation operator (converting each gene value to binary first) are adopted for the second part of the chromosome to prevent duplication in the first part of the chromosome, ensure that the second part of the chromosome is non-repeating and in ascending order, and can obtain better crossover and mutation effects.

4. A method for task allocation of transmission line inspection UAVs based on improved NSGA-II as claimed in claim 1, characterized in that, In Step 2 and Step 5, the improvement measure of "avoiding generating duplicate individuals" is added to the new individuals obtained after the crossover and mutation operations; In the NSGA-II algorithm, there are likely to be too many duplicate solutions in the population, resulting in being trapped in a local optimal solution and difficult to jump out; In order to strengthen exploration during the generation of the offspring population, a measure of "preventing the generation of duplicate individuals" is added; in the NSGA-II algorithm, during the generation of the offspring population, two parent individuals are randomly selected multiple times, and they are cross-mutated with a certain probability to obtain two new individuals; these new individuals are added to the offspring population and then merged with the parent population; after non-dominated sorting and calculation of crowding degree on the merged population, screening is performed to obtain a new parent population; however, this method has certain defects. Suppose a new individual X new has exactly the same chromosome encoding as an individual X old in the population, then adding this individual to the offspring population will cause waste of resources, and the existence of duplicate individuals in the population will reduce the search space; Therefore, after obtaining a new individual, it should be judged whether the new individual needs improvement. The criterion for improvement set here is: there is a duplication of chromosomes with the population obtained in the previous iteration; if it is satisfied, improvement is needed: re-perform the operations of both crossover and mutation using operators until the newly obtained individual is different from the existing individuals.

5. A method for task allocation of an inspection unmanned aerial vehicle for transmission lines based on improved NSGA-II as claimed in claim 1, characterized in that in Step 2 and Step 5, on the basis of adding the measure of "preventing the generation of duplicate individuals" to the NSGA-II algorithm, the improvement measure of "setting different crossover probabilities and mutation probabilities for different individuals according to different non-dominated ranks" is added; The crossover operation randomly exchanges some genes of two individuals, and this operation can transfer excellent genes to the next generation; the mutation operation makes some changes to the chromosome genes, thereby introducing new gene combinations; both crossover and mutation can increase the diversity of the population, but the crossover operation mainly performs global search, while the mutation operation performs local search; premature convergence to a local optimum may occur during the evolution process, resulting in premature termination of the evolution; the mutation operation can prevent this phenomenon and help escape from the local optimum; In NSGA-II, the non-dominated rank of an individual to a certain extent reflects the quality of this individual in the entire population; the higher the non-dominated rank, the better the performance of this individual in the two objectives, and vice versa for a lower non-dominated rank; the more excellent an individual is, the more the mutation probability should be increased to jump out of the local optimum of the current optimal solution and prevent the population from being trapped in a certain hyperplane in the search space during evolution and unable to get rid of it only by crossover. The mutation operation can help with this getting rid of; For the individual i selected from the parental population Pop, calculate the crossover probability pc i and the mutation probability pm i The formulas are as follows: where i.rank represents the non-dominated rank of individual i, and rank avg represents the average non-dominated rank of all individuals in the current parental population, popnum represents the size of the parental population Pop, and 1 is the minimum non-dominated rank value (1 is the highest non-dominated rank value, the higher the non-dominated rank, the lower the non-dominated rank value); the above three formulas stabilize the actual crossover probability of all individuals at about 0.95; moreover, the more excellent the individual, the greater the possibility of mutation, preventing them from falling into local optimal solutions.

6. A method for task allocation of an inspection unmanned aerial vehicle for transmission lines based on improved NSGA-II as claimed in claim 1, characterized in that the condition for judging whether to meet the end of iteration in Step 6 is: when the similarity between the Pareto optimal solution obtained in the previous round and the Pareto optimal solution in this round is as high as 85% for 15 consecutive times, it is considered that convergence has been reached and the iteration is stopped; in the algorithm, the similarity between the Pareto optimal solution obtained in each iteration and the Pareto optimal solution in the previous iteration is calculated each time; the similarity is defined as follows: S 1 and S 2 are respectively the sets of Pareto optimal solutions after the previous and current iterations. A = S 1 ∩S 2 , where max(S 1 .size - A.size, S 2 .size - A.size) represents the number of individuals that change in the two optimal solution sets.

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