A Multi-Satellite Intelligent Mission Planning System and Method Based on a Large Language Model

By using a multi-satellite intelligent mission planning system based on a large language model, and employing greedy algorithms and heuristic algorithms optimized by the large language model, the speed and adaptability issues of satellite mission planning are solved, enabling rapid response and self-learning, thereby improving the accuracy and efficiency of planning.

CN119624025BActive Publication Date: 2025-10-28SHANGHAI JIAOTONG UNIV
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Patent Information

Application Number
CN202411785646.5
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-12-06
Publication Date
2025-10-28
Estimated Expiration
2044-12-06

AI Technical Summary

Technical Problem

Existing satellite mission planning technologies are slow, lack flexibility and adaptability, struggle to meet dynamically changing mission requirements, and are prone to getting stuck in local optima, lacking broad adaptability and optimization capabilities.

Method used

A multi-satellite intelligent mission planning system based on a large language model is adopted, including a heuristic algorithm module, an optimization module, a mission generation module, and a mission execution module. A heuristic algorithm is constructed using a greedy algorithm and then deeply analyzed and optimized using a large language model to generate mission plans and guide satellites to execute missions.

Benefits of technology

It improves the processing speed and adaptability of task planning, avoids the limitations of optimization, achieves rapid response and self-learning capabilities, and enhances the accuracy and efficiency of planning.

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Abstract

This invention discloses a multi-satellite intelligent mission planning system and method based on a large language model, comprising: a heuristic algorithm module construction module for constructing heuristic algorithm modules based on a greedy algorithm; a large model optimization module for performing in-depth analysis and optimization of key functions in the heuristic algorithm modules using a large language model to obtain optimized heuristic algorithm modules; a mission generation module for generating mission plans using the optimized heuristic algorithm modules; and a mission execution module for guiding satellites to execute missions according to the mission plans. This invention utilizes heuristic algorithms to quickly generate initial mission planning schemes and applies a large language model to perform in-depth optimization of key functions (such as mission sequencing and stripe selection), improving the accuracy and efficiency of the planning.
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Description

Technical Field

[0001] This invention belongs to the field of satellite mission planning, and in particular relates to a multi-satellite intelligent mission planning system and method based on a large language model. Background Technology

[0002] Satellite mission planning refers to the process of arranging satellite orbits, observation targets, and timing to accomplish specific observation tasks. This process is crucial for the effective use of satellite resources, improving observation efficiency and data quality, and plays a key role, especially in fields such as land resource surveys, environmental monitoring, and disaster prevention and mitigation.

[0003] With the increasing number of satellites and the diversification of application needs, the amount of information that needs to be processed for mission planning has increased significantly, making it urgent to develop new satellite mission planning technologies.

[0004] While existing satellite mission planning technologies are effective to some extent, they still have the following main drawbacks:

[0005] Slow processing speed: The large number of tasks and complex constraints make traditional algorithms (such as genetic algorithms and particle swarm optimization) slow and not agile enough for sudden events that require rapid response.

[0006] Insufficient flexibility and adaptability: Traditional algorithms are often designed for static problems. They are difficult to make effective adjustments quickly for dynamically changing task requirements (such as the insertion of emergency tasks), and they lack learning ability and continuous optimization ability. They cannot cope with different task backgrounds and lack broad adaptability.

[0007] Limitations of optimization: Many traditional algorithms (such as simulated annealing and genetic algorithms) are prone to getting stuck in local optima and are not easy to reach the global optimum. Furthermore, parameter settings depend on experience and are complex to adjust, which affects the versatility and efficiency of the algorithm. Summary of the Invention

[0008] To address the aforementioned technical problems, this invention proposes a multi-satellite intelligent mission planning system and method based on a large language model, thereby resolving the issues present in the prior art.

[0009] To achieve the above objectives, this invention provides a multi-satellite intelligent mission planning system based on a large language model, comprising:

[0010] The heuristic algorithm module building module is used to build heuristic algorithm modules based on greedy algorithms;

[0011] The large model optimization module is used to perform in-depth analysis and optimization of the key functions in the heuristic algorithm module through a large language model, so as to obtain an optimized heuristic algorithm module.

[0012] The task generation module is used to generate task plans through an optimized heuristic algorithm module;

[0013] The mission execution module is used to guide the satellite to perform its mission according to the mission plan.

[0014] Preferably, the heuristic algorithm module includes a first building unit, a second building unit, and a modular unit;

[0015] The first construction unit is used to construct the dataset for implementing the plan and the evaluation indicators for evaluating the planning scheme;

[0016] The second building unit is used to build the basic algorithm based on the greedy algorithm;

[0017] The modular unit is used to modularize the basic algorithm to obtain a modular algorithm.

[0018] Preferably, the large model optimization module includes a labeling unit, an optimization unit, and an evaluation unit;

[0019] The marking unit is used to construct an evaluation function based on the evaluation index, and to mark the evaluation function and the function to be optimized in the modular algorithm through decorators to obtain a specification file;

[0020] The optimization unit is used to optimize the function to be optimized in the specification file based on the dataset to obtain a preliminary heuristic algorithm module;

[0021] The evaluation unit is used to evaluate the preliminary heuristic algorithm module based on the dataset and evaluation metrics. When the evaluation is qualified, the optimized heuristic algorithm module is obtained.

[0022] Preferably, the multi-satellite intelligent mission planning system further includes a feedback module, which is used to evaluate the effectiveness of the satellites in performing their missions and feed the results back to the large model optimization module to participate in the in-depth analysis and optimization of key functions.

[0023] This invention also provides a multi-satellite intelligent mission planning method based on a large language model, comprising the following steps:

[0024] A heuristic algorithm module is constructed based on a greedy algorithm.

[0025] The key functions in the heuristic algorithm module are analyzed and optimized using a large language model to obtain an optimized heuristic algorithm module.

[0026] Task planning is generated using an optimized heuristic algorithm module;

[0027] The mission plan guides the satellite in carrying out its mission.

[0028] Preferably, before constructing the heuristic algorithm module, the method further includes: constructing a dataset for implementing the plan and evaluation metrics for evaluating the plan scheme, wherein the dataset includes a target dataset and a satellite dataset.

[0029] Preferably, the method for constructing a heuristic algorithm module includes: constructing a basic algorithm based on a greedy algorithm, and modularizing the basic algorithm to obtain a heuristic algorithm module.

[0030] Preferably, the method for obtaining the optimized heuristic algorithm module includes:

[0031] Based on the evaluation metrics, an evaluation function is constructed. The evaluation function and the function to be optimized in the modular algorithm are marked with decorators to obtain the specification file.

[0032] Based on the dataset, the function to be optimized in the specification file is optimized to obtain a preliminary heuristic algorithm module;

[0033] The initial heuristic algorithm module is evaluated based on the dataset and evaluation metrics. When the evaluation is satisfactory, the optimized heuristic algorithm module is obtained.

[0034] Preferably, the present invention also evaluates the effectiveness of the satellite in performing its mission and feeds the evaluation results back to the large model optimization module to participate in the in-depth analysis and optimization of key functions.

[0035] Compared with the prior art, the present invention has the following advantages and technical effects:

[0036] This invention discloses a multi-satellite intelligent mission planning system and method based on a large language model, comprising: constructing a heuristic algorithm module based on a greedy algorithm; performing in-depth analysis and optimization of key functions in the heuristic algorithm module using a large language model to obtain an optimized heuristic algorithm module; generating a mission plan using the optimized heuristic algorithm module; and guiding satellites to execute missions according to the mission plan. This invention utilizes a heuristic algorithm to quickly generate an initial mission planning scheme and applies a large language model to deeply optimize key functions (such as mission sequencing and stripe selection), improving the accuracy and efficiency of the planning, avoiding optimization limitations, and making the invention more adaptable. Attached Figure Description

[0037] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0038] Figure 1 This is a schematic diagram of the multi-satellite intelligent mission planning system architecture according to an embodiment of the present invention;

[0039] Figure 2 This is a flowchart of the multi-satellite intelligent mission planning method according to an embodiment of the present invention;

[0040] Figure 3 This is a flowchart illustrating the implementation process of the large model optimization module in this embodiment of the invention.

[0041] Figure 4 This is a graph showing the optimization score of the selection function in an embodiment of the present invention.

[0042] Figure 5 The graph shows the optimization curve of the sorting function in an embodiment of the present invention. Detailed Implementation

[0043] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0044] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0045] Example 1

[0046] like Figure 1 As shown, this embodiment provides a multi-satellite intelligent mission planning system based on a large language model, including:

[0047] The heuristic algorithm module building module is used to build heuristic algorithm modules based on greedy algorithms;

[0048] The large model optimization module is used to perform in-depth analysis and optimization of key functions in the heuristic algorithm module through a large language model, so as to obtain an optimized heuristic algorithm module.

[0049] The task generation module is used to generate task plans through an optimized heuristic algorithm module;

[0050] The mission execution module is used to guide the satellite in performing its mission according to the mission plan.

[0051] Furthermore, the heuristic algorithm module includes a first building unit, a second building unit, and a modular unit;

[0052] The first building unit is used to build the dataset for implementing the plan and the evaluation indicators for evaluating the plan scheme;

[0053] The second building unit is used to build the basic algorithm based on the greedy algorithm;

[0054] Modular units are used to modularize basic algorithms to obtain modular algorithms.

[0055] Furthermore, the large model optimization module includes a labeling unit, an optimization unit, and an evaluation unit;

[0056] The labeling unit is used to construct the evaluation function based on the evaluation index, and to label the evaluation function and the function to be optimized in the modular algorithm through the decorator to obtain the specification file;

[0057] The optimization unit is used to optimize the function to be optimized in the specification file based on the dataset to obtain a preliminary heuristic algorithm module;

[0058] The evaluation unit is used to evaluate the initial heuristic algorithm module based on the dataset and evaluation metrics. When the evaluation is qualified, the optimized heuristic algorithm module is obtained.

[0059] Furthermore, the multi-satellite intelligent mission planning system also includes a feedback module, which is used to evaluate the effectiveness of satellite mission execution and feed the results back to the large model optimization module for in-depth analysis and optimization of key functions.

[0060] The heuristic algorithm module uses a greedy algorithm as its foundation to quickly generate a preliminary task plan based on task urgency and resource availability.

[0061] The large model optimization module utilizes well-trained large language models (such as GPT) to further analyze and optimize key functions in the heuristic algorithm. It primarily optimizes task ranking and stripe selection—functions that significantly impact the final planning result—enhancing the accuracy and efficiency of decision-making through model inference. It also performs self-learning, continuously learning from new task execution results and adjusting its optimization strategies accordingly.

[0062] The mission execution module guides the satellite in carrying out specific missions based on the final optimized mission plan, including the scheduling, management, and resource allocation of observation missions. It monitors the mission execution status, updates the mission progress in real time, and provides feedback to the optimization module as needed to adjust the plan.

[0063] like Figure 2 As shown, this embodiment also provides a multi-satellite intelligent mission planning method based on a large language model, including the following steps:

[0064] A heuristic algorithm module is constructed based on a greedy algorithm.

[0065] By conducting in-depth analysis and optimization of key functions in the heuristic algorithm module using a large language model, an optimized heuristic algorithm module is obtained.

[0066] Task planning is generated using an optimized heuristic algorithm module;

[0067] The satellite is guided to perform its mission according to the mission plan.

[0068] The specific implementation steps are shown in Table 1:

[0069] Table 1

[0070]

[0071]

[0072] In step 1.1, the required dataset should consist of two parts: the target dataset and the satellite dataset.

[0073] The target dataset should contain geographic information for all targets, including their coordinates, altitude, boundaries, and area (if any) in a specified coordinate system, as well as constraints such as the number of observations required, the required resolution, the solar altitude angle for observation, the available observation window, and the time interval between observations. This data should be saved in CSV or PKL (recommended) format for later retrieval.

[0074] The satellite dataset should include motion information for all satellites, including their nadir trajectories, orbital altitudes, and Earth orbit periods, as well as constraints such as resolution and maximum cumulative operating time per orbit. This data should be saved in CSV or PKL format (recommended) for later retrieval.

[0075] Furthermore, the evaluation indicators in step 1.1 should be designed based on the type of task to be performed, should have the characteristic of quantitative comparison of controlled variables, and should have a high degree of discrimination to clearly distinguish the advantages and disadvantages of different solutions. For example, if the task completion level is used as the evaluation indicator, a time range T can be specified, and scores can be assigned based on the number of effective observations or the observed area completed within time T (the higher the completion level, the higher the score); at the same time, the task completion time can also be used as the evaluation indicator, specifying the time required to complete a certain number or all of the required observations or the observed area, and assigning scores based on the length of time (the shorter the time required, the higher the score).

[0076] In step 1.2, the constructed basic algorithm should meet the following requirements:

[0077] The algorithm input should be the dataset from step 1.1;

[0078] The algorithm output should be a satellite scheduling plan, stored in CSV format, and used as input for subsequent evaluation;

[0079] The basic algorithm constructed does not require the following:

[0080] There are no specific language requirements for the algorithm, but Python is recommended.

[0081] There are no requirements regarding the content, form, or complexity of the algorithm, but for ease of subsequent operations, it is recommended to use an algorithm with relatively simple logic.

[0082] In step 1.3, "modularizing the algorithm" refers to abstracting and decomposing some functionalities of the main program into multiple sub-functions by defining functions. Each sub-function is responsible for a single function and collaborates through data transfer to ultimately complete the overall program output. Each sub-function should have a clearly defined responsibility, and its function, input parameters, and output results should be explained in detail with comments. This method not only makes the program structure clearer and easier to maintain and modify, but also provides a solid foundation for the subsequent learning and optimization of larger models.

[0083] Furthermore, before constructing the heuristic algorithm module, the following steps are included: constructing a dataset to implement the planning and evaluation metrics to evaluate the planning scheme. The dataset includes the target dataset and the satellite dataset.

[0084] Furthermore, the method for constructing heuristic algorithm modules includes: building basic algorithms based on greedy algorithms, and modularizing the basic algorithms to obtain heuristic algorithm modules.

[0085] Furthermore, methods for obtaining the optimized heuristic algorithm module include:

[0086] An evaluation function is constructed based on the evaluation metrics. The evaluation function and the function to be optimized in the modular algorithm are marked with decorators to obtain the specification file.

[0087] Based on the dataset, the function to be optimized in the specification file is optimized to obtain a preliminary heuristic algorithm module;

[0088] The initial heuristic algorithm module is evaluated based on the dataset and evaluation metrics. When the evaluation is satisfactory, the optimized heuristic algorithm module is obtained.

[0089] Furthermore, this invention will also evaluate the effectiveness of the satellite in performing its missions and feed the evaluation results back into the large model optimization module to participate in the in-depth analysis and optimization of key functions.

[0090] Example 2

[0091] The above methods are illustrated with examples as follows:

[0092] First, define the point objectives and the area objectives.

[0093] Point target: refers to a target object whose area is not considered, only its location coordinates are available, and there is a requirement for the number of observations. The score is calculated based on the ratio of the number of observations to the required number of observations.

[0094] Regional targets: Target objects with an area, defined by the coordinate information of the regional boundary, and scores are calculated based on the ratio of the observed area to the target area.

[0095] Consider a task planning problem, T a T represents the set of regional targets. p Let T represent the set of point targets. Each target t∈T in the target set... a or t∈T p It has complex constraints and priority weights. The mission execution object (satellite) is a set of execution units S, and the accessibility of each execution unit s∈S to the target t depends on the mission planning time and its constraints.

[0096] The completion of a task objective depends on the effective coverage of the objective by multiple execution units s∈S. Different objective types have different evaluation criteria:

[0097] For point target t∈T p The evaluation criteria depend on the relationship between the number of effective coverages and the number of coverages required.

[0098] For the regional target t∈T a The evaluation criteria depend on the ratio between the effective coverage area and its total area.

[0099] set up:

[0100] n is the number of point targets, n = |T p |,

[0101] m is the number of targets in the region, m = |T a |,

[0102] f i This represents the number of times the target at point i is effectively covered.

[0103] F i The number of times the target point i is covered is required.

[0104] P i,p Let be the priority score for the i-th target point.

[0105] a j This represents the effective coverage area of ​​the target in the j-th region.

[0106] A j Let j be the total area of ​​the target region.

[0107] Pj,a Let be the priority score of the target in the j-th region.

[0108] The goal of task planning is to maximize an evaluation metric P, which is defined as the weighted sum of all point objectives and area objectives:

[0109]

[0110] in:

[0111] The first summation term represents the coverage contribution of each point target, reflecting the ratio of the effective coverage of each point target to the number of times it is required to be covered, multiplied by the corresponding priority score;

[0112] The second summation term represents the coverage contribution of regional targets, reflecting the ratio of the effective coverage area of ​​each regional target to its total area, multiplied by the corresponding priority score.

[0113] The availability of execution units s∈S and their access to targets may be affected by various complex constraints, such as time, resources, and geometric location. These constraints will affect the effective coverage of targets, thereby affecting the maximization process of the overall task planning evaluation index P.

[0114] Next, consider a specific case. In this embodiment, we hypothesize that mission planning will be performed on 450 point targets and 50 regional targets (a total of 500 initial targets) scattered across different regions of the globe, as well as a total of 60 targets dynamically added over time (50 point targets and 10 regional targets). The execution targets are a total of 200 satellites. Both the mission targets and the satellites have complex constraints, and different mission targets have different priorities (manifested as different scores). The dataset used is the satellite access information for each target. The evaluation index P for a certain planning scheme is calculated as follows:

[0115]

[0116] Where n and m are the total number of point targets and area targets, respectively, and f i With F i P represents the effective coverage count and the required coverage count for the i-th target point, respectively. i,p Let a be the score for the i-th target point. i With A i P represents the effective coverage area of ​​the i-th target region and the total area of ​​the target region, respectively. i,a Let be the score for the target in the i-th region.

[0117] After completing the heuristic algorithm module, the task ranking and strip selection functions were selected as the optimization targets for the large language model. The large model used was GPT-3.5-turbo, accessible and interactive via API. Each round of prompts used four previously generated algorithm samples. The optimization process was recorded using TensorBoard. Six different scenarios were selected to form the training set, and the total score was calculated by weighting the difficulty of the scenario scores. The computing environment was Windows 11 operating system, Python 3.11, and an 8-core 4GB processor. First, the strip selection function was optimized, and the resulting optimization curve is shown below. Figure 4 As shown.

[0118] The initial score represents the score of the original basic heuristic algorithm on the test set, reaching its maximum value after 1.35 hours of iteration. In the early to mid-stages, the optimization score improves rapidly. This indicates that the function has a relatively large optimization space, and further improvements are possible through measures such as extending the number of iterations. The final generated result of the stripe selection function is as follows:

[0119]

[0120]

[0121] It can be observed that the optimized function primarily adjusts the point target selection strategy, favoring SAR satellites with smaller swaths and higher resolution. This aligns with practical logic, as there is no area determination for point targets, thus prioritizing smaller swath satellites and reserving larger swath satellite resources for regional targets. However, some unreasonable aspects exist, such as simply summing the solar elevation angle and deflection angle, and prioritizing strips with longer durations, indicating that the function still has room for improvement.

[0122] After evolving the stripe selection function, the task ranking function was further evolved and iterated, using the same configuration as before. The resulting optimization curve is shown below. Figure 5 As shown.

[0123] The initial score, representing the final result of the optimized selection function, reached its maximum value after 0.86 hours. The task ranking function also showed significant improvement, representing a major breakthrough. The final result of the task ranking function is as follows:

[0124]

[0125]

[0126]

[0127] It can be seen that the generated strategy tends to first arrange point objectives, then select effective but unplanned information from the access information of each task, calculate their potential scoring ability, and finally rank all tasks according to the product of potential scoring ability and scoring factor. This strategy is a modification of the original strategy and has achieved good improvement results.

[0128] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A multi-satellite intelligent mission planning system based on a large language model, characterized in that, include: The heuristic algorithm module building module is used to build heuristic algorithm modules based on greedy algorithms; The large model optimization module is used to perform in-depth analysis and optimization of the key functions in the heuristic algorithm module through a large language model, so as to obtain an optimized heuristic algorithm module. The large model optimization module includes a labeling unit, an optimization unit, and an evaluation unit; The marking unit is used to construct an evaluation function based on the evaluation index, and to mark the evaluation function and the function to be optimized in the modular algorithm through decorators to obtain a specification file; The optimization unit is used to optimize the function to be optimized in the specification file based on the dataset to obtain a preliminary heuristic algorithm module; The evaluation unit is used to evaluate the preliminary heuristic algorithm module based on the dataset and evaluation indicators. When the evaluation is qualified, the optimized heuristic algorithm module is obtained. Specifically, the specification file is passed to the local LLM or LLM API for learning and to generate the required functions. The generated functions are then passed to the evaluator, which evaluates them on the test data in the dataset. Functions that pass the evaluator, along with their scores, are entered into the program pool. The program pool performs clustering based on the scores of different functions and distinguishes between functions generated in different iteration rounds. Before entering the next iteration, in addition to the previous specification file, a new set of prompts is automatically generated, which presents the functions generated in previous iterations. This process is repeated iteratively, and the function with the highest score at the end constitutes the new optimized algorithm. The task generation module is used to generate task plans through an optimized heuristic algorithm module; The mission execution module is used to guide the satellite to perform its mission according to the mission plan.

2. The multi-satellite intelligent mission planning system based on a large language model according to claim 1, characterized in that, The heuristic algorithm module includes a first building unit, a second building unit, and a modular unit; The first construction unit is used to construct the dataset for implementing the plan and the evaluation indicators for evaluating the planning scheme; The second building unit is used to build the basic algorithm based on the greedy algorithm; The modular unit is used to modularize the basic algorithm to obtain a modular algorithm.

3. The multi-satellite intelligent mission planning system based on a large language model according to claim 1, characterized in that, The multi-satellite intelligent mission planning system also includes a feedback module, which is used to evaluate the effectiveness of satellite mission execution and feed the results back to the large model optimization module for in-depth analysis and optimization of key functions.

4. A multi-satellite intelligent mission planning method based on a large language model, characterized in that, Includes the following steps: A heuristic algorithm module is constructed based on a greedy algorithm. The key functions in the heuristic algorithm module are analyzed and optimized using a large language model to obtain an optimized heuristic algorithm module. The method for obtaining the optimized heuristic algorithm module includes: Based on the evaluation metrics, an evaluation function is constructed. The evaluation function and the function to be optimized in the modular algorithm are marked with decorators to obtain the specification file. Based on the dataset, the functions to be optimized in the specification file are optimized to obtain a preliminary heuristic algorithm module. The functions to be optimized include a strip selection function and a task sorting function. The initial heuristic algorithm module is evaluated based on the dataset and evaluation metrics. When the evaluation is satisfactory, the optimized heuristic algorithm module is obtained. Specifically, the specification file is passed to the local LLM or LLM API for learning and to generate the required functions. The generated functions are then passed to the evaluator, which evaluates them on the test data in the dataset. Functions that pass the evaluator, along with their scores, are entered into the program pool. The program pool performs clustering based on the scores of different functions and distinguishes between functions generated in different iteration rounds. Before entering the next iteration, in addition to the previous specification file, a new set of prompts is automatically generated, which presents the functions generated in previous iterations. This process is repeated iteratively, and the function with the highest score at the end constitutes the new optimized algorithm. Task planning is generated using an optimized heuristic algorithm module; The mission plan guides the satellite in carrying out its mission.

5. The multi-satellite intelligent mission planning method based on a large language model according to claim 4, characterized in that, Before building the heuristic algorithm module, the following steps are also included: building a dataset to implement the planning and evaluation metrics to evaluate the planning scheme, wherein the dataset includes a target dataset and a satellite dataset.

6. The multi-satellite intelligent mission planning method based on a large language model according to claim 4, characterized in that, The method for constructing heuristic algorithm modules includes: constructing a basic algorithm based on a greedy algorithm, and modularizing the basic algorithm to obtain a heuristic algorithm module.

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