A Multi-Star Joint Region Coverage Planning Method Based on an Improved Multi-Objective Evolutionary Algorithm

Abstract

This invention relates to a multi-satellite joint regional coverage planning method based on an improved multi-objective evolutionary algorithm, comprising the following steps: decomposing the area to be covered into discrete strip sets of all remote sensing satellites based on the imaging conditions of each satellite; binary encoding the strips in the discrete strip sets, using all encoded individuals as input to the improved multi-objective evolutionary algorithm, which employs a combination of the NSGA-III and S-CDAS algorithms to achieve an extreme solution preservation mechanism; constructing a multi-objective optimization model composed of multiple objective functions, and solving the multi-objective optimization model using the improved multi-objective evolutionary algorithm to obtain the regional coverage result. The improved multi-objective evolutionary algorithm in this invention can preserve extreme solutions, thus achieving satisfactory regional coverage results, and can also optimize the rationality of the regional coverage scheme from other objective dimensions.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of remote sensing satellite imaging task planning, and particularly relates to a multi-satellite joint regional coverage planning method based on an improved multi-objective evolutionary algorithm, which is used for formulating an optimal regional coverage scheme for a remote sensing satellite constellation. BACKGROUND

[0002] The multi-satellite joint regional coverage process aims to select an optimal combination of satellites from all available satellite resources, so that they can maximize the acquisition of images of the region to be covered while meeting various constraints. At the same time, according to actual task requirements, the regional coverage task often needs to optimize multiple objectives such as image quality, timeliness, cost, etc. while maximizing coverage. Therefore, the regional coverage problem can be transformed into a typical multi-objective combination optimization problem.

[0003] Currently popular multi-objective evolutionary algorithms such as NSGA-II, NSGA-III, etc. have a serious performance decline when solving multi-objective optimization problems with more than three objective functions. The main reason is that the selection pressure based on Pareto dominance will be severely reduced with the increase in the number of objectives, causing all candidate solutions to concentrate on the same Pareto front in one iteration, making them incomparable, thereby causing the optimal solution in each objective dimension (hereinafter referred to as extreme solution) to be unable to be retained in the algorithm iteration process. The improvement work of multi-objective evolutionary algorithms mostly focuses on improving the convergence and diversity of the algorithm, and rarely considers the extreme solution retention problem, thereby causing existing multi-objective evolutionary algorithms to be difficult to effectively apply to the field of satellite regional coverage. In most cases, coverage is the most important task objective, and users always want to optimize other objectives on the premise of maximizing coverage. However, the inability to retain extreme solutions not only reduces the efficiency of genetic operations in the algorithm, but more importantly, it cannot provide users with satisfactory regional coverage planning schemes. Therefore, an improved multi-objective evolutionary algorithm is needed to retain extreme solutions while ensuring algorithm performance to solve the multi-satellite joint regional coverage problem. SUMMARY

[0004] In order to solve the problem that existing multi-objective evolutionary algorithms cannot retain extreme solutions, resulting in the difficulty of obtaining satisfactory regional coverage planning schemes for multi-satellite joint regional coverage, the present application provides a multi-satellite joint regional coverage planning method based on an improved multi-objective evolutionary algorithm.

[0005] To solve the above problems, the present application adopts the following technical scheme:

[0006] A multi-satellite joint regional coverage planning method based on an improved multi-objective evolutionary algorithm, comprising the following steps:

[0007] Step 1: Based on the imaging conditions of each remote sensing satellite, decompose the area to be covered into discrete strip sets of all remote sensing satellites.

[0008] Step 2: Perform binary encoding on the stripes in the discrete stripe set. All individuals obtained after encoding are used as input to the improved multi-objective evolutionary algorithm. The binary encoding method is as follows:

[0009] A set of stripes for a remote sensing satellite is represented by a vector of length k, with k stripes in total. Each element in the vector can only be 1 or 0, where 1 indicates that the corresponding strip is selected and 0 indicates that the strip is not selected. The matrix composed of all the vectors is a single entity.

[0010] Step 3: Construct a multi-objective optimization model consisting of multiple objective functions, and solve the multi-objective optimization model using the improved multi-objective evolutionary algorithm to obtain the region coverage result. The specific steps of the improved multi-objective evolutionary algorithm are as follows:

[0011] Step 1: Population initialization, the initial population size is N;

[0012] Step 2: Perform selection, crossover, and mutation genetic operations on the population to generate offspring populations;

[0013] Step 3: Merge the parent and offspring populations to form a population R of size 2N. t ;

[0014] Step 4: Use the Pareto-dominated non-dominated sorting method to sort population R t The individuals in the population are divided into different frontal planes F = {F1, F2, ...}, and starting from F1, all individuals within the frontal plane are placed into a new population S. t Until the new population S t The size of the first step is greater than N, assuming the maximum frontier surface is F at this point. l Determine the maximum frontier surface F l If the sequence number l is greater than 1, proceed to step 5; otherwise, proceed to step 6.

[0015] Step 5, S t \F l Individuals in the process directly proceed to the next iteration, and the maximum frontier F is then processed. l Individuals on the network perform the environment selection operation of the NSGA-III algorithm to select the remaining N-|S t \F l Each individual proceeds to the next iteration, then jumps to step 7;

[0016] Step 6: For population R tAll individuals are subjected to S-CDAS non-dominated sorting, and the specific sorting process is as follows:

[0017] (1) Move the origin of the coordinate system to O = (O1, O2, ..., O2) i ,…,O M ), in Let M be the minimum value of the i-th objective function, and M be the total number of objective functions;

[0018] (2) Create a landmark vector L = {p1, p2, ..., p...} M},in It is the maximum value of the i-th objective function, δ = 10 -6 ;

[0019] (3) For population R t Repeat the following steps for all individuals:

[0020] For an individual x, calculate according to formula (1) in For x and p i Determined included angle:

[0021]

[0022] Where r(x) is the objective function F(x) = (f1(x), f2(x), ..., f i (x),…,f M The second norm of (x)), f i (x) is the value of the objective function for individual x at the i-th time, ω i (x) is F(x) and f i The angle between (x) and l i (x) is x and p i The Euclidean distance between them;

[0023] Modify the objective function values ​​of other individuals' y according to formula (2):

[0024]

[0025] Where r(y) is the objective function F(y) = (f1(y), f2(y), ..., f i (y),…,f M The second norm of (y)), f i (y) is the value of individual y in the objective function at the i-th time, ω i (y) is F(y) and f i The angle between (y) and (y);

[0026] (4) Compare the modified objective functions F'(x) and F'(y). If F'(x) < F'(y), it is considered that individual y is dominated by individual x, and all individuals determine their front based on the number of times they are dominated.

[0027] (5) Divide all individuals into two parts according to their fronts. The first part consists of n individuals with smaller fronts and directly enters the next iteration. The second part is the remaining individuals, which enter the environmental selection operation of the NSGA-III algorithm to select the remaining N - n individuals to enter the next iteration, and then jump to step 7.

[0028] Step 7: Form a new population.

[0029] Step 8: Determine whether the maximum number of iterations has been reached. If not, jump to step 2 and repeat steps 2 to 7 until the maximum number of iterations is reached, and the algorithm ends.

[0030] The beneficial effects of the present invention are as follows:

[0031] (1) By improving the traditional NSGA-III algorithm, the present invention utilizes the combination of the NSGA-III algorithm and the S-CDAS algorithm to implement an extreme solution retention mechanism, enabling extreme solutions to always remain undominated by other solutions and thus be retained, thereby obtaining a satisfactory regional coverage result. Moreover, the rationality of the regional coverage plan can be optimized from other objective dimensions.

[0032] (2) Similar to other multi-objective evolutionary algorithms, the improved multi-objective evolutionary algorithm can provide different solutions to meet different task requirements. For example, when the user wants the highest quality image and allows a slight reduction in the coverage rate, we can directly select a corresponding solution from multiple solutions without having to re-run the algorithm after changing the objective function, greatly improving the planning efficiency.

[0033] (3) The regional coverage plan obtained by the multi-satellite joint regional coverage planning method based on the improved multi-objective evolutionary algorithm according to the present invention can significantly reduce the imaging cost and improve the utilization efficiency of satellite resources. In addition, the average resolution and average swing angle are also smaller than those of the single-objective genetic algorithm, indicating that the regional coverage plan of the present invention can obtain higher image quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a flowchart of the multi-satellite joint regional coverage planning method based on the improved multi-objective evolutionary algorithm described in the embodiments of the present invention;

[0035] Figure 2 is a schematic diagram of the regional decomposition and strip selection process;

[0036] Figure 3 is a schematic diagram of the genetic operation design;

[0037] Figure 4 This is a flowchart of the improved multi-objective evolutionary algorithm in this invention;

[0038] Figure 5 A comparison chart of the trends in maximum coverage;

[0039] Figure 6 A comparison chart of regional coverage results;

[0040] Figure 7 This is a radar chart comparing the target values ​​of the improved multi-objective evolutionary algorithm and the single-objective genetic algorithm in this invention. Detailed Implementation

[0041] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings and preferred embodiments.

[0042] like Figure 1 As shown, this embodiment of the invention provides a multi-satellite joint region coverage planning method based on an improved multi-objective evolutionary algorithm. The method specifically includes the following steps:

[0043] Step 1: Based on the imaging conditions of each remote sensing satellite (including the visible time window, satellite swath width, and maximum side sway angle, etc.), the area to be covered is decomposed into a discrete strip set of all remote sensing satellites.

[0044] Given that the area to be covered is much larger than the single observation range of any remote sensing satellite, it is necessary to decompose the area to be covered into discrete strips before formulating a regional coverage plan. Figure 2 The process of region decomposition and strip selection is shown. Figure 2 (a) is the area to be covered. Figure 2 (b) The rectangle represents the maximum coverage area of ​​the remote sensing satellite, determined by its swath width and maximum lateral tilt angle. The lines within the rectangle represent the nadir trajectory of the satellite. Since the lateral tilt angle is a continuous variable, a single remote sensing satellite can actually produce an infinite number of corresponding stripes. Therefore, considering the computational complexity of the problem, such as... Figure 2 As shown in (c), the side sway angle is divided into a set of discrete values ​​with a step size of 0.5 km. This allows the remote sensing satellite to obtain a limited number of stripes in each imaging opportunity, which is the strip set generated by the remote sensing satellite. The stripes generated by all remote sensing satellites participating in the regional coverage planning task together form the discrete strip set of the area to be covered. This completes the decomposition of the area to be covered into the discrete strip set of all remote sensing satellites.

[0045] Step 2: Encode the strips in the discrete stripe set into binary form. All individuals obtained after encoding are used as input to the improved multi-objective evolutionary algorithm.

[0046] Due to the specific nature of the practical problem, this invention employs a binary encoding method different from the traditional NSGA-III. Specifically, the binary encoding method used in this invention is as follows: a vector of length k represents the stripe set of a remote sensing satellite, with k stripes. Each element in the vector can only be 1 or 0; 1 indicates that the corresponding stripe is selected, and 0 indicates that the stripe is not selected. Since the number of stripes varies among different satellites, each individual satellite is a matrix composed of vectors of different lengths, i.e. Figure 3 Each rectangle in the diagram represents an individual.

[0047] Step 3: Construct a multi-objective optimization model consisting of multiple objective functions, and solve the multi-objective optimization model using an improved multi-objective evolutionary algorithm to obtain the region coverage result.

[0048] The objective functions constituting the multi-objective optimization model can be selected according to the user's actual needs, including but not limited to the following five objective functions: The first objective is to maximize coverage (equivalent to maximizing total benefit), which is the most important objective function in the regional coverage problem; the second objective is to minimize the overlap rate of the selected strips; the third objective is to minimize the number of selected strips. These two objectives are beneficial to improving satellite utilization efficiency and reducing imaging costs. The overlap rate is defined as the ratio of the overlapping area of ​​the strips within the target area to the total coverage area; the fourth objective is to minimize the average resolution; and the fifth objective is to minimize the average side tilt angle. These two objectives are for improving image quality. The five objectives are defined as follows:

[0049] (1) Maximize coverage:

[0050]

[0051] Among them, area T The area is the region to be covered. ijk For being x ijk The area covered, x ijk It is a variable with a value of 0 or 1, indicating whether the k-th stripe of the i-th remote sensing satellite is selected when the j-th orbit passes overhead, N ij Let S be the number of stripes into which the target area is divided by the i-th remote sensing satellite when it passes over on orbit j, and let T be the set of remote sensing satellites. i For the set of transit orbits.

[0052] (2) Minimize the strip overlap rate:

[0053]

[0054] The overlap() function is used to calculate the overlapping area of ​​the stripes.

[0055] (3) Minimize the number of stripes:

[0056]

[0057] Where, n s This represents the number of stripes in the final area coverage scheme.

[0058] (4) Minimize the average resolution:

[0059]

[0060] Where, r i Let be the resolution of the i-th remote sensing satellite.

[0061] (5) Minimize the average lateral swing angle:

[0062]

[0063] Among them, sa ijk SA is the lateral sway angle of the k-th strip when the i-th remote sensing satellite passes over the j-th orbit. i Let be the maximum side-swing angle of the i-th remote sensing satellite.

[0064] This invention improves upon the traditional NSGA-III algorithm, enabling the improved multi-objective evolutionary algorithm to preserve extreme solutions in the population and enhance the diversity of the original algorithm. This improved multi-objective evolutionary algorithm is named ESP-NSGA-III. The algorithm flow is as follows: Figure 4 As shown, the specific steps are as follows:

[0065] Step 1: Population initialization, with a size of N, meaning the initial population has N individuals;

[0066] Step 2: Perform genetic operations (selection, crossover, mutation) on the population to generate offspring populations;

[0067] The genetic manipulation design diagram is shown below. Figure 3 As shown, when performing genetic operations, the crossover operator uses random multi-point crossover, such as... Figure 3 As shown in (a). Specifically, for two individuals, if the random number is less than the crossover probability, then m rows of the two individuals are randomly selected and swapped to generate a new individual.

[0068] The mutation operator employs a random single-point mutation operation, such as... Figure 3 As shown in (b). Specifically, for an individual, if the random number is less than the mutation probability, then c rows are randomly selected. For each row, if there is an element with a value of 1, then 1 is changed to 0; if all elements are 0, then an element is randomly selected and its value is set to 1.

[0069] Step 3: Merge the parent and offspring populations to form a population R of size 2N. t ;

[0070] Step 4: Use the Pareto-dominated non-dominated sorting method to sort population R t The individuals in the population are divided into different frontal planes F = {F1, F2, ...}, and starting from frontal plane F1, all individuals within the frontal plane are placed into the new population S. t Until the new population S t The size of the first step is greater than N, assuming the maximum frontier surface is F at this point. l Determine the maximum frontier surface F l If the sequence number l is greater than 1, proceed to step 5; otherwise, proceed to step 6.

[0071] Step 5, S t \F l (representing S) t Remove F l The remaining individuals directly enter the next iteration, and the maximum frontier F is then processed. l Individuals on the network perform environment selection operations (including normalization, association, and niche preservation) using the NSGA-III algorithm to select the remaining N-|S t \F l Each individual proceeds to the next iteration, then jumps to step 7;

[0072] Step 6: For population R t All individuals are subjected to S-CDAS non-dominated sorting, and the specific sorting process is as follows:

[0073] (1) Move the origin of the coordinate system to O = (O1, O2, ..., O2) i ,…,O M ), in Let M be the minimum value of the i-th objective function, and M be the total number of objective functions;

[0074] (2) Create a landmark vector L = {p1, p2, ..., p...} M},in It is the maximum value of the i-th objective function, δ = 10 -6 ;

[0075] (3) For population R t Repeat the following steps for all individuals:

[0076] For an individual x, calculate according to formula (1) in For x and p i Determined included angle:

[0077]

[0078] Among them, r(x) is the two-norm of the objective function F(x) = (f1(x), f2(x), …, f i (x), …, f M (x)), and f i (x) is the value of the individual x in the i-th objective function, ω i (x) is the included angle between the objective function F(x) and f i (x), and l i (x) is the Euclidean distance between x and p i ;

[0079] Next, modify the objective function values of other individuals y according to formula (2):

[0080]

[0081] Among them, r(y) is the two-norm of the objective function F(y) = (f1(y), f2(y), …, f i (y), …, f M (y)), and f i (y) is the value of the individual y in the i-th objective function, ω i (y) is the included angle between the objective function F(y) and f i (y);

[0082] (4) Compare the modified objective functions F'(x) and F'(y). If F'(x) < F'(y), it is considered that the individual y is dominated by the individual x, and all individuals determine their positions on the front surface according to the number of times they are dominated;

[0083] (5) Divide all individuals into two parts according to their front surfaces. The first part is n individuals with smaller front surfaces, which directly enter the next iteration. The second part is the remaining individuals, which enter the environmental selection operation to select the remaining N - n individuals to enter the next iteration, and then jump to step 7;

[0084] Step 7: Form a new population;

[0085] Step 8: Determine whether the maximum number of iterations has been reached. If not, jump to step 2 and repeat steps 2 to 7 until the maximum number of iterations is reached, and the algorithm ends, obtaining multiple solutions of the multi-objective optimization model, and each solution corresponds to a regional coverage result.

[0086] The improved multi-objective evolutionary algorithm of this invention adds a process to determine whether the index l of the maximum frontier Fl is greater than 1. If the index l is greater than 1, it is the same as the original NSGA-III algorithm; if the index l is equal to 1, the S-CDAS non-dominated sorting is introduced, but the introduced S-CDAS non-dominated sorting process is different from the original S-CDAS process. Extreme solution preservation is also reflected in S-CDAS. The S-CDAS non-dominated sorting uses the objective function value of the extreme solution to modify the objective function values ​​of other solutions, ensuring that the extreme solution can never be dominated by other solutions, thus preserving it.

[0087] This invention improves the traditional NSGA-III algorithm by combining the NSGA-III algorithm and the S-CDAS algorithm to achieve an extreme solution retention mechanism. This ensures that extreme solutions are never dominated by other solutions and are thus retained, thereby obtaining satisfactory region coverage results. Furthermore, it can optimize the rationality of the region coverage scheme from other objective dimensions.

[0088] The following simulation experiment illustrates the implementation method and effects of the present invention.

[0089] (I) Problem Simplification and Setting

[0090] (1) The satellite camera can only swing back and forth;

[0091] (2) The imaging mission cannot be interrupted once it begins, until the mission ends;

[0092] (3) Each satellite can select a maximum of one stripe per transit, i.e.:

[0093] (4) After taking into account various constraints, the length of all strips is limited to between the minimum imaging length and the maximum imaging length;

[0094] (5) Satellite storage space and energy limitations are not considered.

[0095] This simulation experiment uses five objective functions—maximizing coverage, minimizing the overlap rate of selected strips, minimizing the number of selected strips, minimizing the average resolution, and minimizing the average side sway angle—to construct a multi-objective optimization model.

[0096] Three types of satellites independently developed and in orbit by Changguang Satellite Technology Co., Ltd. were selected for simulation experiments. Some satellite information is shown in Table 1. The entire area of ​​a certain province was selected as the base map to be covered, with an area of ​​approximately 480,000 square kilometers.

[0097] Table 1. Satellite Parameters

[0098]

[0099] (II) Methodology for Joint Regional Coverage Planning by Remote Sensing Satellites

[0100] A five-objective optimization model was constructed and solved using the aforementioned ESP-NSGA-III algorithm. The experimental parameters were set as follows: population size 2^10, number of iterations 500, crossover probability 0.8, mutation probability 0.1, parameter m randomly generated between 1 and 15, parameter c set to 5, and parameter n set to 180. Comparison algorithms included NSGA-III, S-CDAS, Fuzzy-NSGA-II, Fuzzy-NSGA-III, SDR-NSGA-II, and SDR-NSGA-III.

[0101] (III) Simulation Results

[0102] (1) Analysis of algorithm convergence and diversity

[0103] Table 2. HV values ​​of 10 runs of 7 algorithms

[0104]

[0105] Table 3. PD values ​​of 7 algorithms after 10 runs

[0106]

[0107]

[0108] The overall performance of the algorithm was evaluated using hypervolume (HV), and the algorithm diversity was evaluated using pure diversity (PD). The results are shown in Tables 2 and 3, respectively. The numbers in parentheses in the tables indicate the ranking of ESP-NSGA-III among the seven algorithms. "+", "-", and "≈" indicate a comparison of the results of the other six algorithms with the results of ESP-NSGA-III. From Table 2, we can see that the overall performance of the algorithm of this invention consistently ranks in the top half of the seven algorithms in 10 runs, with a maximum difference of only 0.073 compared to SDR-NSGA-III. On average, the performance of ESP-NSGA-III is slightly better than NSGA-III and S-CDAS, and close to that of SDR-NSGA-II.

[0109] Table 3 shows that ESP-NSGA-III significantly outperforms all other algorithms in terms of diversity, and is the only algorithm with a PD value exceeding 1e+07. Due to the introduction of an extreme solution preservation mechanism, ESP-NSGA-III shows a significant improvement in diversity compared to the original NSGA-III. In conclusion, ESP-NSGA-III is an effective algorithm for solving multi-objective optimization problems, improving the diversity of existing algorithms while maintaining good convergence.

[0110] (2) Extreme solution retention results

[0111] The ability of ESP-NSGA-III to preserve extreme solutions is the greatest innovation of this invention and the biggest improvement compared to most other algorithms. Figure 5 The comparison results of the maximum coverage change trends of various algorithms during 500 iterations are presented. Figure 5 In the diagram, the curves near the top represent the maximum coverage curves corresponding to ESP-NSGA-III, while the curves near the bottom represent the maximum coverage curves corresponding to other algorithms. Figure 5 In (a), we can see that the maximum coverage curve obtained by ESP-NSGA-III consistently shows an upward trend, proving that the algorithm can indeed preserve extreme solutions. Furthermore, the maximum coverage continues to increase after 447 iterations, indicating that the genetic operation designed in this invention is effective and almost prevents the algorithm from getting trapped in local optima. Conversely, from the NSGA-III curve, we can see that when the number of iterations is small, the curve shows an upward trend because the traditional Pareto dominance has not yet failed. However, as the algorithm iterates, all candidate solutions are distributed on the same Pareto front, causing extreme solutions to disappear from the population. Therefore, after 500 iterations, the maximum coverage is only 0.9117, far less than the 0.9980 obtained by ESP-NSGA-III. The same phenomenon also appears in fuzzy and SDR-based algorithms, such as... Figure 5 As shown in (b)-(e). Although these algorithms have been shown to achieve good convergence and diversity on standard test problems, they are not suitable for practical problems because they cannot provide users with satisfactory area coverage solutions. S-CDAS is another method that can preserve extreme solutions, such as... Figure 5 As shown in (f). However, the convergence of this algorithm is much worse than that of ESP-NSGA-III, with a maximum coverage of only 0.9547 at the 500th iteration. In addition, S-CDAS has poor diversity and cannot provide enough evolutionary space for the population, which also leads to a poor maximum coverage result.

[0112] (3) Results of the regional coverage plan formulation

[0113] To verify the superiority of this invention in multi-objective optimization problems, a single-objective genetic algorithm was also used for result comparison. The objective function of the single-objective genetic algorithm is to maximize coverage, and other parameter settings such as population size, number of iterations, and genetic operations are the same as ESP-NSGA-III. After the algorithm runs, the single-objective genetic algorithm can only obtain one solution with the maximum coverage, while ESP-NSGA-III can provide 210 solutions for decision-makers to choose from according to different task requirements. Here, we selected the solution with the maximum coverage and compared it with the single-objective genetic algorithm. The visualization of the two region coverage schemes is shown below. Figure 6 As shown, Figure 6 (a) shows the coverage results for the ESP-NSGA-III region. Figure 6 (b) shows the region coverage results of the single-objective genetic algorithm. Each gray rectangle represents a strip selected to maximize the overall coverage. Figure 7 The radar charts provide a comparison of the five target values ​​for the two algorithms. The coverage achieved by ESP-NSGA-III (0.9980) is slightly lower than that of the genetic algorithm (0.9998), but still satisfactory. Most importantly, ESP-NSGA-III can simultaneously optimize the other four targets while maintaining similar coverage. Compared to the single-target genetic algorithm, ESP-NSGA-III reduces the overlap between strips by approximately 30% and uses six fewer satellites. These results demonstrate that the regional coverage scheme obtained by ESP-NSGA-III in this invention can significantly reduce imaging costs and improve the utilization efficiency of satellite resources. Furthermore, the average resolution and average swivel angle are also lower than those of the genetic algorithm, indicating that the regional coverage scheme of ESP-NSGA-III can achieve higher image quality.

[0114] In summary, all simulation results demonstrate that this invention not only achieves a satisfactory region coverage scheme by introducing an extreme solution preservation mechanism, but also optimizes the scheme's rationality from other objective dimensions. This proves the excellent performance of this invention in solving practical multi-objective optimization problems. Furthermore, like other multi-objective evolutionary algorithms, ESP-NSGA-III can provide different solutions to meet different task requirements. For example, when a user wants the highest quality image but allows for a slight reduction in coverage, we can directly select a corresponding solution from the 210 solutions instead of changing the objective function and rerunning the algorithm.

[0115] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0116] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A multi-satellite joint regional coverage planning method based on an improved multi-objective evolutionary algorithm, characterized in that, The method comprises the following steps: Step 1: regionally decompose the to-be-covered region according to the imaging conditions of each remote sensing satellite, and decompose the to-be-covered region into a discrete strip set of all remote sensing satellites; Step 2: binary code the strips in the discrete strip set, and use all individuals obtained after coding as inputs of an improved multi-objective evolutionary algorithm, wherein the binary coding mode is as follows: A vector with a length of k is used to represent a strip set of a remote sensing satellite, the number of strips in the strip set is k, each element in the vector can only be 1 or 0, 1 represents selecting the corresponding strip, and 0 represents not selecting the strip, and a matrix composed of all vectors is an individual; Step 3: construct a multi-objective optimization model composed of multiple objective functions, solve the multi-objective optimization model by using the improved multi-objective evolutionary algorithm, and obtain a regional coverage result, wherein the specific steps of the improved multi-objective evolutionary algorithm are as follows: Step 1: population initialization, the number of individuals in the initial population is N; Step 2: perform selection, crossover, mutation and genetic operations on the population to generate a child population; Step 3, merging of parent and offspring populations to form a population of size 2N ; Step 4: Use the Pareto-dominated non-dominated sorting method to sort the population. Individuals are divided into different frontiers. and from Start sequentially, adding all individuals within the frontal plane to the new population. Until a new population The size of N is first greater than N, assuming the maximum frontier surface is at this time. Determine the maximum frontier surface If the sequence number l is greater than 1, proceed to step 5; otherwise, proceed to step 6. Step 5, The individuals in the set are directly entered into the next iteration, where The The individuals in the set are directly entered into the next iteration, where The remaining individuals, the set of individuals are subjected to the environmental selection operation of the NSGA-III algorithm on the maximum front to select the remaining The individuals in the set are directly entered into the next iteration, where The remaining individuals, the set of individuals are subjected to the environmental selection operation of the NSGA-III algorithm on the maximum front to select the remaining Step 6, S-CDAS non-dominated sorting of all individuals in the population is performed, in particular as follows: (1) move the coordinate origin to , where is the minimum value of the th objective function, is the total number of objective functions; (2) Create landmark vector where , is the maximum value of the th objective function, ; (3) For the population repeat the following for all individuals in the population: For an individual , calculated according to equation (1) , where is the included angle determined by and ​ （1） wherein, is the 2-norm of the objective function , is the value of the objective function for the individual , is the angle between , and , is the Euclidean distance between , and modify the objective function value of other individuals according to equation (2) : (2) wherein, is the objective function is the two-norm of is the individual is the value of the objective function is the angle between and and ​ (4) Comparing the modified objective function and if then the individual is dominated by the individual and all individuals determine their position on the front by the number of times they are dominated. (5) divide all individuals into two parts according to their front faces, the first part is n individuals with smaller front faces, which directly enter the next iteration, and the second part is the remaining individuals, which enter the environmental selection operation of the NSGA-III algorithm to select N-n individuals to enter the next iteration, and jump to step 7; Step 7: form a new population; Step 8: determine whether the maximum number of iterations is reached, if not, jump to step 2, and repeat steps 2 to 7 until the maximum number of iterations is reached, and the algorithm ends.

2. The multi-satellite joint regional coverage planning method based on the improved multi-objective evolutionary algorithm according to claim 1, characterized in that, When performing genetic operations, a random multi-point crossover is used for a crossover operator, and the specific mode is as follows: for two individuals, if the random number is less than the crossover probability, randomly select m rows of the two individuals to exchange; A random single-point mutation operation is used for a mutation operator, and the specific mode is as follows: for an individual, if the random number is less than the mutation probability, randomly select c rows, and for each row, if there is an element with a value of 1, change 1 to 0; if all elements are 0, randomly select an element and change its value to 1.

3. The multi-satellite joint regional coverage planning method based on the improved multi-objective evolutionary algorithm according to claim 2, characterized in that, The value of N is 210, the maximum number of iterations is 500, the crossover probability is 0.8, the mutation probability is 0.1, the parameter m is randomly generated between 1 and 15, the parameter c is 5, and the parameter n is 180.

4. The multi-satellite joint regional coverage planning method based on the improved multi-objective evolutionary algorithm according to claim 1, characterized in that, The multiple objective functions are as follows: (1) maximizing coverage rate: wherein, is the total area of the region to be covered, is the area of the region covered, is the area of the region covered, is a variable with value 0 or 1, indicating whether the kth strip of the ith remote sensing satellite is selected when the jth orbit is passing, is the number of strips into which the target region is divided by the ith remote sensing satellite when the jth orbit is passing, is a set of remote sensing satellites, is a set of passing orbits; (2) minimizing strip overlap rate: wherein overlap ( ) is a function for calculating the strip overlap area; (3) minimizing the number of strips: wherein, is the number of strips in the final regional coverage scheme; (4) minimizing the average resolution: wherein, Ri is the resolution of the i-th remote sensing satellite; (5) minimizing the average side swing angle: wherein, is the side-slip angle of the kth strip of the ith remote sensing satellite at the jth orbit transit, is the maximum side-slip angle of the ith remote sensing satellite.

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