Satellite task scheduling method and system

Abstract

The invention provides a satellite task scheduling method and system, and relates to the technical field of satellite task scheduling, and the method comprises the following steps: obtaining a satellite and a satellite task set, and determining a decision variable of satellite task scheduling according to the satellite and the satellite task set; constructing a satellite task scheduling model based on the decision variable of satellite task scheduling; solving the satellite task scheduling model by adopting a multi-target genetic algorithm to obtain a satellite task scheduling solution; and generating a scheduling instruction based on the satellite task scheduling solution, and performing task scheduling on the satellite according to the scheduling instruction. According to the method, a multi-population coevolution mechanism, an active auxiliary population selection mechanism and a dynamic Epsilon constraint relaxation mechanism are embedded in a traditional constraint multi-objective evolutionary algorithm framework, and the optimization efficiency, solution set quality and scheme feasibility of satellite task scheduling under complex constraints are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of satellite mission scheduling technology, and in particular to a satellite mission scheduling method and system. Background Technology

[0002] Satellite mission scheduling is a core component in aerospace engineering, bridging satellite resources and mission requirements. Its core objective is to achieve coordinated optimization of multiple objectives, including mission completion rate and time expenditure, under constraints such as satellite storage capacity, visible time windows, and maximum operating time. With the widespread application of low-Earth orbit satellite constellations and multi-mission payload satellites, satellite missions are characterized by "numerous numbers, significant differences in priorities, and complex intertwined constraints." Traditional scheduling techniques are no longer adequate for practical needs, driving multi-objective optimization algorithms to become the mainstream solution in this field.

[0003] Existing satellite mission scheduling technology has evolved from early single-objective optimization (such as maximizing mission completion rate) to multi-objective collaborative optimization. Solution algorithms have also transitioned from deterministic methods such as greedy algorithms and integer programming to intelligent optimization algorithms such as genetic algorithms and particle swarm optimization. Among these, multi-objective optimization algorithms, represented by the Non-Dominated Sorting Genetic Algorithm (NSGA-II), have become a research hotspot due to their ability to generate non-dominated solution sets covering multiple optimization objectives. These algorithms, through mechanisms such as fast non-dominated sorting and crowding calculation, balance the quality and distribution of solution sets to a certain extent, and have been applied in satellite mission scheduling scenarios of low to medium complexity.

[0004] However, when faced with the complex satellite scheduling problem involving multiple constraints and expanding mission scale, existing technologies still have significant bottlenecks, specifically in the following aspects: 1. The initial population generation strategy is simplistic, resulting in low constraint adaptability and resource utilization: Existing algorithms mostly use global uniform sampling to generate the initial population without specifically designing it to take into account the constraints of satellite scheduling. This leads to a large number of individuals in the initial population becoming invalid solutions due to severe violations of constraints such as time windows and storage capacity, requiring the algorithm to incur significant iterative costs to screen for feasible solutions. Furthermore, the number and size of auxiliary populations are often fixed and cannot be dynamically adjusted according to the number of constraints. This results in insufficient exploration capability when constraints are complex, and waste of computational resources when constraints are simple.

[0005] 2. Rigid constraint handling mechanisms and an imbalance between exploration and development: In existing technologies, constraint relaxation coefficients are mostly fixed values ​​or linearly adjusted, which cannot adapt to the needs of different evolutionary stages of the algorithm. If the constraints are too strict in the early stages of optimization, the algorithm is easily confined to a local feasible region, leading to premature convergence; if the constraints are too loose in the later stages of optimization, it is difficult to guarantee the feasibility of the final solution set. Some algorithms lack evolutionary stagnation detection mechanisms, and cannot actively adjust the constraint strategy when the population gets stuck in a local optimum, further reducing the quality of the solution set.

[0006] 3. Uneven resource allocation in constraint optimization leads to low efficiency in solving core problems: Satellite scheduling involves multiple constraints such as task allocation uniqueness and temporal mutual exclusion. Existing algorithms often adopt an equal treatment strategy for all constraints, failing to dynamically allocate computational resources based on the real-time violation rate of constraints. When some constraints become major obstacles to population evolution, the algorithm cannot concentrate computing power to prioritize breakthroughs, resulting in delays in solving key constraint problems. Conversely, when some constraints are largely satisfied, a large amount of resources are still allocated for redundant optimization, reducing overall solution efficiency.

[0007] 4. Insufficient inter-population information exchange and evolutionary vitality: In existing multi-population algorithms, the main population and auxiliary populations often evolve independently, lacking an effective individual migration mechanism. Although the main population possesses global search capabilities, the proportion of individuals with excellent constraint fit is low; while the auxiliary population focuses on specific constraints, it is prone to getting trapped in local searches due to limited genetic information. Information barriers between populations prevent the effective transfer of high-quality genes, resulting in insufficient overall evolutionary vitality of the algorithm and difficulty in generating scheduling schemes that balance global optimization and constraint satisfaction.

[0008] How to solve the above-mentioned technical problems is the challenge facing this invention. Summary of the Invention

[0009] To address the shortcomings of existing technologies, this invention provides a satellite mission scheduling method and system that embeds a multi-population co-evolution mechanism, an active auxiliary population selection mechanism, and a dynamic Epsilon constraint relaxation mechanism into the traditional constrained multi-objective evolutionary algorithm framework. This effectively improves the optimization efficiency, solution set quality, and scheme feasibility of satellite mission scheduling under complex constraints.

[0010] The technical solution adopted by this invention to solve its technical problem is as follows: This invention provides a satellite mission scheduling method, comprising the following steps: Obtain the set of satellites and satellite missions, and determine the decision variables for satellite mission scheduling based on the set of satellites and satellite missions; Construct a satellite mission scheduling model based on decision variables for satellite mission scheduling; A multi-objective genetic algorithm is used to solve the satellite mission scheduling model to obtain the satellite mission scheduling solution; The system generates scheduling instructions based on satellite mission scheduling solutions and performs mission scheduling on satellites according to these instructions.

[0011] Preferably, the decision variables for satellite mission scheduling include:

[0012] in, For the task With satellite The distribution relationship, This is the actual start time of the satellite's mission. This refers to the actual end time of the satellite's mission. This represents the completion status of a task under the scheduling scheme. For satellite collection, For a set of tasks.

[0013] Preferably, the construction of the satellite mission scheduling model includes: Define the objective function for satellite mission scheduling and construct constraints for the decision variables of satellite mission scheduling; The objective function of satellite mission scheduling includes minimizing the negative value of the weighted mission completion rate, minimizing the total time expenditure of all satellites performing missions, minimizing the actual start time of all missions, and minimizing the proportion of incomplete missions. The constraints include task allocation uniqueness constraint, time window constraint, timing mutual exclusion constraint, visibility constraint, storage capacity constraint, and maximum working time constraint.

[0014] Preferably, the step of solving the satellite mission scheduling model using a multi-objective optimization algorithm includes: Based on the satellite mission scheduling model, an initial population is generated and an external elite set is constructed using a multi-population initialization strategy. The initial population includes a main population and several auxiliary populations. The external elite set is used to store the optimal solution during iteration. Define a dynamic Epsilon constraint relaxation mechanism and initialize the Epsilon value. Iteratively perform parallel evolution, population migration, environmental selection and external elite set update on the initial population. Repeat the iteration and update the Epsilon value according to the dynamic Epsilon constraint relaxation mechanism after each iteration until the iteration termination condition is met. Output the solution in the external elite set and use the solution in the external elite set as the satellite mission scheduling solution.

[0015] Preferably, generating the initial population includes uniformly generating a principal population of size N in the decision space using Latin hypercube sampling, based on the dimensions of the decision variables. The formula for calculating the size and number of the auxiliary population based on constraints is as follows:

[0016] in, To assist in population size, The maximum number of auxiliary populations is preset. The total number of constraints. For the first A secondary population, Main population size, This is a scale ratio coefficient; The auxiliary population is generated by initializing based on its quantity and size.

[0017] Preferably, the dynamic Epsilon mechanism includes: Define the maximum function evaluation number, and calculate the control generation of the dynamic Epsilon mechanism based on the maximum function evaluation number and the population size; In each iteration, the evolutionary stagnation detection function is called to calculate the stagnation index value and preset the stagnation threshold. The stagnation index value is compared with the stagnation threshold. If the stagnation index value exceeds the stagnation threshold, an adaptive adjustment strategy is used to increase the Epsilon value. If the stagnation index value does not exceed the stagnation threshold, it is determined whether the current iteration number exceeds the control generation of the dynamic Epsilon mechanism. If the current iteration number does not exceed the control generation of the dynamic Epsilon mechanism, the Epsilon value is updated using a nonlinear decay formula. If the current iteration number exceeds the control generation of the dynamic Epsilon mechanism, the Epsilon value is set to 0. The adaptive adjustment strategy is expressed as follows:

[0018] in, For the updated Epsilon value, For adjustment coefficients, The current Epsilon value, For indicators of stagnation; The nonlinear attenuation formula is expressed as follows:

[0019] in, For the updated Epsilon value, To control algebra, This is the curvature parameter.

[0020] Preferably, the parallel evolution includes primary population evolution and active auxiliary population evolution; The main population evolves by performing tournament selection and genetic operations on the main population to obtain the main offspring population; The evolution of the active auxiliary population includes calculating the average positive violation of constraints for the auxiliary population and sorting the average positive violation scores in descending order to obtain the constraint average positive violation score ranking; the formula for calculating the constraint average positive violation score is expressed as follows:

[0021] in, The degree to which an individual violates constraints. The number of individuals in the population that violate the constraints; Based on the average positive violation rate of the constraints and the average positive violation rate of the constraints, the top few auxiliary populations in the ranking are selected as active auxiliary populations; Selective and genetic operations are performed on the active auxiliary population to obtain the auxiliary offspring population.

[0022] Preferably, the population migration includes: Define the migration generation interval. At each iteration, determine whether the current iteration number meets the migration generation interval. If it does, calculate the average Euclidean distance between each individual in the main population and other individuals and sort them in descending order. Select the top few individuals and distribute them to the auxiliary population. At the same time, calculate the constraint violation degree of the individuals in the auxiliary population and sort them in ascending order. Select the top few individuals and add them to the main offspring population.

[0023] Preferably, the environment selection and external elite group update include: The main population, the main offspring population, and the auxiliary offspring population are merged to obtain the merged population. A rapid non-dominated sorting and crowding calculation is performed on the merged population to obtain the non-dominated hierarchy and individual density. Based on the non-dominated hierarchy and individual density, a new generation of dominant population of size N is obtained from the merged population, and the non-dominated solutions in the new generation of dominant population of size N are used to update the external elite set.

[0024] The present invention also provides a satellite mission scheduling system, comprising: The data acquisition module is used to acquire a set of satellites and satellite missions, and to determine the decision variables for satellite mission scheduling based on the set of satellites and satellite missions. The model building module is used to build a satellite mission scheduling model based on the decision variables of satellite mission scheduling; The model solving module is used to solve the satellite mission scheduling model using a multi-objective genetic algorithm to obtain the satellite mission scheduling solution; The scheduling execution module is used to generate scheduling instructions based on the satellite mission scheduling solution and to schedule satellite missions according to the scheduling instructions.

[0025] The beneficial effects of this invention are as follows: It embeds a multi-population co-evolutionary mechanism, an active auxiliary population selection mechanism, and a dynamic Epsilon constraint relaxation mechanism into the traditional constrained multi-objective evolutionary algorithm framework, effectively improving the optimization efficiency, solution set quality, and scheme feasibility of satellite mission scheduling under complex constraints. By using uniform sampling across the entire space for the main population and constraint-specific initialization for the auxiliary population, an initial solution set with both global diversity and local feasibility can be quickly generated in the early stages of evolution, avoiding the predicament of traditional single initialization strategies struggling to quickly locate feasible regions in complex constraint spaces. The defined dynamic Epsilon constraint relaxation mechanism allows for mild constraint violations in the early stages of optimization to enhance global exploration capabilities, and then strictly converges to a fully feasible solution in the later stages, achieving a dynamic balance between the exploration and development phases. The introduced nonlinear decay and stagnation detection-based adaptive adjustment strategy intelligently help the algorithm escape local optima, significantly improving its robustness under strong constraints and nonlinear environments, ultimately ensuring that the obtained scheduling scheme strictly satisfies all constraints. By calculating and ranking the average positive violation degree of each constraint in real time, computational resources are dynamically concentrated on the constraint with the most severe violation. This adaptive resource allocation strategy overcomes the inefficiency caused by the average processing of all constraints in traditional algorithms. By establishing a bidirectional, periodic individual exchange channel between the main population and the auxiliary population, it effectively integrates "global exploration information" with "local constraint optimization expertise." Injecting diverse individuals into the auxiliary population broadens its search scope, while elite individuals from the auxiliary population are fed back to the main population, accelerating global convergence. Combining fast non-dominated sorting with environment selection based on crowding calculation, it effectively maintains the breadth and uniformity of the solution set's distribution in the target space while ensuring convergence towards the Pareto front. Attached Figure Description

[0026] Figure 1 This is a diagram illustrating the method steps of the present invention.

[0027] Figure 2 This is a system module diagram of the present invention.

[0028] Figure 3 This is a schematic diagram of simulation results for different scenarios in Embodiment 3 of the present invention. Detailed Implementation

[0029] To clearly illustrate the technical features of this solution, the following detailed implementation method will be used to explain the solution.

[0030] Example 1: See Figure 1 As shown, this embodiment is a satellite mission scheduling method, including the following steps: S1. Obtain the set of satellites and satellite missions, and determine the decision variables for satellite mission scheduling based on the set of satellites and satellite missions; Based on satellite mission and resource classification, this embodiment takes the mission-satellite allocation relationship and the temporal relationship of mission execution as the core decision content of satellite mission scheduling, and uniformly represents the decision variables of the satellite mission scheduling problem as:

[0031] in, For the task With satellite The allocation relationship is the basis for the spatial resource allocation of the scheduling scheme; This is the actual start time of the satellite's mission. The actual end time of the satellite's mission, along with the other two factors, jointly determine the mission. In satellite The execution time interval is the core of the time resource allocation in the scheduling scheme; This represents the completion status of a task under the scheduling scheme. For satellite collection, For a set of tasks.

[0032] The decision variables fully define the solution space of the satellite mission scheduling problem, determining not only the matching relationship between missions and satellite resources, the order and timing of mission execution, but also the overall benefit of the scheduling scheme. This provides a unified decision basis for the subsequent construction of multi-objective optimization models and the design of solution algorithms.

[0033] S2. Construct a satellite mission scheduling model based on decision variables for satellite mission scheduling; Define the objective function for satellite mission scheduling and construct constraints for the decision variables of satellite mission scheduling; The objective function for satellite mission scheduling includes minimizing the negative weighted mission completion rate, minimizing the total time spent by all satellites performing missions, minimizing the actual start time of all missions, and minimizing the proportion of incomplete missions; the formula is expressed as follows:

[0034] in, As task priority weight, This represents the total number of tasks.

[0035] The constraints include task allocation uniqueness constraints, time window constraints, timing mutual exclusion constraints, visibility constraints, storage capacity constraints, and maximum working time constraints, expressed by the following formulas:

[0036] in, For the task Whether by satellite solve, The earliest start time of the task. The latest start time for the task. Service time for the task and They represent satellites For the task The The start and end times of a visible time window. For the amount of data in the task, For the satellite's storage capacity, For satellite Maximum working hours.

[0037] S3. A multi-objective genetic algorithm is used to solve the satellite mission scheduling model to obtain the satellite mission scheduling solution; Based on the satellite mission scheduling model, an initial population is generated using a multi-population initialization strategy, and an external elite set is constructed to store the optimal solution during iteration; the initial population includes a main population and several auxiliary populations. Based on the dimensions of the decision variables, Latin hypercube sampling is used to uniformly generate a principal population of size N in the decision space; The formula for calculating the size and number of the auxiliary population based on constraints is as follows:

[0038] in, To assist in population size, The maximum number of auxiliary populations is preset. The total number of constraints. For the first A secondary population, Main population size, This is a scale ratio coefficient; The auxiliary population is generated by initializing based on its quantity and size.

[0039] It should be noted that traditional constrained multi-objective optimization algorithms typically employ a single uniform initialization strategy, which struggles to quickly locate feasible regions and maintain population diversity in complex constraint spaces. To address this, this invention designs a multi-population collaborative initialization mechanism. The main population is generated using a standard initialization method, ensuring uniform distribution in the decision space, while the auxiliary populations are initialized specifically for particular constraints, aiming to enhance the ability to explore constraint boundaries. Within this multi-population initialization framework, population combinations with different search focuses are constructed, and an adaptive allocation method for the auxiliary population based on the number of constraints is proposed. The problem interface is dynamically invoked to obtain constraint quantity information, accurately identifying the total number of equality and inequality constraints in the optimization problem, providing an accurate basis for the reasonable allocation of the auxiliary populations. When the number of constraints is large, multiple auxiliary populations are created to specifically optimize different constraints; when the number of constraints is small, computational resources are concentrated on in-depth processing of key constraints. Furthermore, the algorithm adaptively adjusts the size of the auxiliary populations according to problem characteristics, enhancing exploration capabilities for complex problems and optimizing computational efficiency for simple problems.

[0040] Define a dynamic Epsilon constraint relaxation mechanism and initialize the Epsilon value. Iteratively perform parallel evolution, population migration, environmental selection and external elite set update on the initial population. The dynamic Epsilon mechanism includes: Define the maximum function evaluation number, and calculate the control generation of the dynamic Epsilon mechanism based on the maximum function evaluation number and the population size; In each iteration, the evolutionary stagnation detection function is called to calculate the stagnation index value and preset the stagnation threshold. The stagnation index value is compared with the stagnation threshold. If the stagnation index value exceeds the stagnation threshold, an adaptive adjustment strategy is used to increase the Epsilon value. If the stagnation index value does not exceed the stagnation threshold, it is determined whether the current iteration number exceeds the control generation of the dynamic Epsilon mechanism. If the current iteration number does not exceed the control generation of the dynamic Epsilon mechanism, the Epsilon value is updated using a nonlinear decay formula. If the current iteration number exceeds the control generation of the dynamic Epsilon mechanism, the Epsilon value is set to 0. The adaptive adjustment strategy formula is expressed as follows:

[0041] in, For the updated Epsilon value, For adjustment coefficients, The current Epsilon value, For indicators of stagnation;

[0042]

[0043] in, For the first Stagnation count of generations, This is the stagnation tolerance threshold (usually 10). For the first The feasibility rate of the generation, To improve tolerance, For the first Stagnation count of generations.

[0044]

[0045] in, For the first The number of feasible solutions. For the first Total population size.

[0046] It should be noted that in this embodiment, the feasible solution is the one where the constraint violation degree is less than the violation degree tolerance threshold.

[0047] The nonlinear attenuation formula is expressed as follows:

[0048] in, For the updated Epsilon value, To control algebra, This is the curvature parameter.

[0049] It should be noted that calling the evolutionary stagnation detection function to analyze the improvement of the current population and historical populations, and calculating the stagnation index value, quantifies the evolutionary process by comparing the quality improvement of populations across multiple generations. This provides a basis for subsequent adaptive adjustments, ensuring the algorithm can respond promptly to stagnation states. When significant evolutionary stagnation is detected, an adaptive adjustment strategy is adopted, appropriately increasing the Epsilon value according to the degree of stagnation. This treatment provides additional exploration space for the algorithm by temporarily relaxing constraints, helping the population escape local optima and reactivate the evolutionary process. In the early and mid-stages of optimization, a new Epsilon value is calculated according to a nonlinear decay formula. This calculation is based on the ratio between the current generation and the control generation, and the decay rate is adjusted through curvature parameters to achieve a gradual tightening of constraints.

[0050] To address the problem that traditional constrained multi-objective optimization algorithms are prone to getting trapped in local feasible regions or converging prematurely when dealing with complex constrained problems, this invention proposes a dynamic Epsilon constraint relaxation mechanism. The core idea of ​​this mechanism is to achieve a balance between exploration and development during the optimization process by dynamically adjusting the constraint tolerance (Epsilon value). In the early stages of optimization, a larger Epsilon value is used to allow for minor constraint violations and to allow crossing infeasible regions (barriers), enhancing the algorithm's exploration capabilities. As the optimization progresses, the constraints are gradually tightened, and the Epsilon value approaches zero, eventually converging to a strictly feasible solution. This ensures that the final solution set strictly satisfies all constraints, guaranteeing the quality and practical feasibility of the solution.

[0051] Parallel evolution includes the evolution of the main population and the evolution of the active auxiliary population; The main population evolves into a tournament selection and genetic operation performed on the main population to obtain the main offspring population; The evolution of active auxiliary populations includes calculating the average positive violation rate of constraints for the auxiliary populations and sorting the average positive violation rates in descending order to obtain the constraint average positive violation rate ranking; the formula for calculating the average positive violation rate is expressed as follows:

[0052] in, The degree to which an individual violates constraints. The number of individuals in the population that violate the constraints; Based on the average positive violation rate of the constraints and the average positive violation rate of the constraints, the top few auxiliary populations in the ranking are selected as active auxiliary populations; Selective and genetic operations are performed on the active auxiliary population to obtain the auxiliary offspring population.

[0053] It should be noted that determining the actual number of constraints to be processed, taking the minimum value between the preset auxiliary population size and the actual number of constraints in the problem, avoids wasting computational resources and ensures that the algorithm can effectively handle all important constraints in the actual problem, laying the foundation for subsequent constraint violation analysis. An initialization of the average positive violation array records the average violation degree of each constraint in the current population. This is a key data structure for determining which constraints need to be prioritized; its size is consistent with the actual number of constraints to ensure data integrity and accuracy. For each constraint, the violation vector of the current population for that constraint is extracted. This step obtains the violation status of all individuals for a specific constraint by accessing the corresponding column of the constraint violation matrix, ensuring that the selection decision is based on complete population state information. The positive violation degree of each constraint is calculated to determine whether there is a positive violation of the current constraint. Checking whether there are elements greater than zero in the positive violation degree vector determines whether the constraint has been violated by individuals in the population, directly affecting whether the constraint will be selected as an active constraint. For constraints that are violated, their average positive violation score is calculated. The average of all positive violation values ​​quantifies the overall impact of the constraint on the population. This metric reflects the severity and prevalence of constraint violations and is the core basis for subsequent ranking and selection decisions. For constraints without violations, their average positive violation score is set to zero, explicitly indicating that this constraint is not currently a focus of optimization and does not require additional computational resources. Constraints are ranked in descending order based on their average positive violation scores. The auxiliary populations corresponding to the top K constraints with the highest violation scores are selected as the active population. This ranking and selection process achieves intelligent allocation of computational resources, ensuring that the algorithm always prioritizes constraints that have the greatest impact on the current population's evolution.

[0054] Traditional multi-constraint optimization algorithms typically treat all constraints equally, neglecting the dynamic importance and varying degrees of violation of different constraints during the optimization process. This leads to fragmented computational resources and low optimization efficiency. To address this, this invention dynamically selects auxiliary populations corresponding to the most critical constraints for activation and optimization by analyzing the violation degree of each constraint in real time. When the average violation degree of some constraints is significantly higher than others, it indicates that these constraints are the main obstacles to the current optimization. In this case, the algorithm prioritizes activating the auxiliary populations corresponding to these constraints, concentrating computational resources to solve the key constraint problem. When the average violation degrees of multiple constraints are similar, it indicates that multiple constraints simultaneously affect the population evolution. In this case, the algorithm simultaneously activates multiple auxiliary populations, processing multiple important constraints in parallel. When the average violation degree of all constraints is close to zero, it indicates that the population has basically satisfied all constraints. At this point, the algorithm reduces the number of active auxiliary populations, redirecting computational resources to improving the quality and distribution of the solution set. This mechanism dynamically adjusts the auxiliary population activation strategy by evaluating the degree of violation of each constraint in real time. This enables the algorithm to intelligently allocate computing resources according to the current optimization state and prioritize the constraints that have the greatest impact on population evolution, thereby significantly improving the solution efficiency of complex constraint optimization problems.

[0055] Population migration includes: Define the migration generation interval. At each iteration, determine whether the current iteration number meets the migration generation interval. If it does, calculate the average Euclidean distance between each individual in the main population and other individuals and sort them in descending order. Select the top few individuals and distribute them to the auxiliary population. At the same time, calculate the constraint violation degree of the individuals in the auxiliary population and sort them in ascending order. Select the top few individuals and add them to the main offspring population.

[0056] Environmental selection and updates to the external elite group include: The main population, the main offspring population, and the auxiliary offspring population are merged to obtain the merged population. A rapid non-dominated sorting and crowding calculation is performed on the merged population to obtain the non-dominated hierarchy and individual density. Based on the non-dominated hierarchy and individual density, a new generation of dominant population of size N is obtained from the merged population, and the non-dominated solutions in the new generation of dominant population of size N are used to update the external elite set.

[0057] Repeat the iteration and update the Epsilon value according to the dynamic Epsilon constraint relaxation mechanism after each iteration until the iteration termination condition is met. Output the solution in the external elite set and use the solution in the external elite set as the satellite mission scheduling solution.

[0058] S4. Generate scheduling instructions based on satellite mission scheduling solutions, and perform mission scheduling for satellites according to the scheduling instructions.

[0059] Example 2: See Figure 2 As shown, this embodiment is a satellite mission scheduling system, including: The data acquisition module is used to acquire a set of satellites and satellite missions, and to determine the decision variables for satellite mission scheduling based on the set of satellites and satellite missions. The model building module is used to build a satellite mission scheduling model based on the decision variables of satellite mission scheduling; The model solving module is used to solve the satellite mission scheduling model using a multi-objective genetic algorithm to obtain the satellite mission scheduling solution; The scheduling execution module is used to generate scheduling instructions based on the satellite mission scheduling solution and to schedule satellite missions according to the scheduling instructions.

[0060] Example 3: To verify the effectiveness of the satellite mission scheduling method proposed in this invention, this embodiment conducts comparative experiments on satellite mission scheduling scenarios with different complexities, using the method of this invention (hereinafter referred to as A-NSGA-II) and satellite mission scheduling methods based on NSGA-III, MOEA / D, SPEA2 and NSGA-II algorithms, for scenarios with 3 satellites and 8 missions, 4 satellites and 10 missions, and 5 satellites and 15 missions.

[0061] With 3 satellites and 8 missions, the number of decision variables reached 177, and the time window reached 59. The algorithm optimized the size of the main population and auxiliary population to 80 and 40 individuals respectively, evolving over 60 generations. Thirty independent experiments were conducted under the same experimental conditions. To assess statistical significance, a Friedman rank test with a significance level of 0.05 was performed. Table 1 lists the corresponding solution results.

[0062] Table 1. Comparison of Solution Results for 3 Satellites and 8 Mission Scenarios with Friedman's Mean Rank Test

[0063] A-NSGA-II achieved a Friedman composite score of 1.75, maintaining its top ranking in medium-complexity scenarios. SPEA2 and NSGA-III ranked second and third, respectively. The p-values ​​of the mean rank test for all algorithms were less than 0.05, indicating that A-NSGA-II maintains a significant advantage in medium-complexity scenarios. Regarding the objective function solution, A-NSGA-II exhibited the highest HV value and lowest IGD value in medium-complexity scenarios, with a relatively small standard deviation, demonstrating superior stability and solution quality in the 177-dimensional decision space. In terms of runtime, A-NSGA-II ran faster than other algorithms, reflecting the improvement in search efficiency brought about by parameter optimization, achieving a 48.1% improvement over NSGA-III. Within A-NSGA-II's co-evolutionary framework, the synergistic effect between the main population and auxiliary populations is more pronounced in medium-complexity search spaces. Through refined migration strategies and adaptive constraint handling, it effectively addresses complex constraints and multi-objective conflicts in medium-load scenarios, demonstrating the algorithm's good adaptability and robustness. To further compare the performance differences of the algorithms in moderately complex scenarios, the Pareto fronts obtained by each algorithm were analyzed, and the simulation results are as follows: Figure 3 As shown. Figure 3 (a) shows that in medium-complexity scenarios, the Pareto front obtained by the comparative algorithm has decreased quality and the solution set distribution is relatively sparse, while the Pareto front obtained by the A-NSGA-II algorithm still maintains good distribution uniformity and coverage, providing a comprehensive and high-quality trade-off between energy consumption and task completion rate, verifying the stable performance of the algorithm in medium-complexity scenarios. In the medium-load scenario of 3 satellites and 8 missions, the optimal solution exhibits obvious target conflict characteristics: the optimal completion rate solution achieves 100% completion of 8 tasks with zero latency, but requires the highest energy of 181.47; the optimal delay solution shows a large lead time but only completes 12.45% of the tasks; the optimal energy solution has an extremely low completion rate and extremely high latency. The Pareto solution set shows rich trade-off patterns, with completion rates ranging from 4.33% to 100%, and both positive and negative delays exist, with energy ranging from 1.33 to 181.47. In particular, several solutions with high completion rates and negative delays appear, providing decision-makers with sufficient flexibility to cope with medium-complexity scheduling requirements.

[0064] In the 4-satellite, 10-mission scenario, the number of decision variables increased to 336, and the time window reached 112. The algorithm adjusted the size of the main and auxiliary populations to 100 and 50 individuals respectively, evolving for 80 generations to cope with the higher-dimensional search space and more complex constraints. To verify the effectiveness of the A-NSGA-II algorithm in large-scale scenarios, it was further compared with NSGA-III, MOEA / D, SPEA2, and NSGA-II algorithms, with 30 independent experiments conducted under the same experimental conditions. To assess statistical significance, a Friedman rank test with a significance level of 0.05 was performed. Table 2 lists the corresponding solution results.

[0065] Table 2. Comparison of Solution Results for 4 Satellites 10 Mission Scenario and Friedman Mean Rank Test

[0066] Table 2 shows that the Friedman composite score of A-NSGA-II further decreased to 1.65, maintaining its first-place ranking in large-scale scenarios. SPEA2 and NSGA-III ranked second and third, respectively. The p-values ​​of the mean rank test for each algorithm were all less than 0.05, indicating that A-NSGA-II still maintains a significant advantage in the most challenging large-scale scenarios. Regarding the objective function solution results, A-NSGA-II had the highest HV value and the lowest IGD value in large-scale scenarios, with a relatively small standard deviation, indicating that the algorithm maintains superior stability and solution quality in the 336-dimensional decision space. In terms of runtime, although the A-NSGA-II algorithm increased slightly compared to previous scenarios, it was still the most efficient among the compared algorithms, improving by 32.0% compared to NSGA-III. In the co-evolutionary framework of A-NSGA-II, the synergistic effect of the main population and auxiliary population in the ultra-high-dimensional search space is more crucial. Through refined migration strategies and adaptive constraint handling, it effectively addresses complex constraints and multi-objective conflicts in large-scale scenarios, demonstrating the algorithm's excellent scalability in large-scale optimization problems. To further compare the performance differences of the algorithms in large-scale scenarios, the Pareto fronts obtained by each algorithm were analyzed, and the simulation results are as follows: Figure 3 As shown. Figure 3(b) shows that, in the largest-scale scenario, the Pareto front obtained by the comparative algorithm is of significantly lower quality, with a sparse solution set and limited coverage. In contrast, the Pareto front obtained by the A-NSGA-II algorithm still maintains good distribution uniformity and wide coverage, providing a comprehensive and high-quality trade-off between energy consumption and task completion rate. This fully verifies the algorithm's superior performance and strong robustness in large-scale complex scenarios. In the high-load scenario of 4 satellites and 10 missions, the optimal solution exhibits more complex target conflict relationships: the optimal completion rate solution achieves 100% completion of 10 missions with zero latency, but requires high energy (151.34); the optimal latency solution shows a significant lead time (-3169.74 seconds) but the completion rate drops to 67.14%; the optimal energy solution has an extremely low completion rate (1.90%) and extremely high latency. The Pareto solution set exhibits a rich variety of trade-offs, with completion rates ranging from 1.90% to 100%, and includes both positive and negative delays. Its energy ranges from 3.63 to 151.34, providing decision-makers with ample flexibility to address complex multi-objective needs.

[0067] In the 5-satellite, 15-mission scenario, the number of decision variables surged to 642, and the time window reached 214. The algorithm significantly adjusted the size of the main and auxiliary populations to 120 and 60 individuals respectively, evolving for 100 generations to cope with the extremely high-dimensional search space and highly complex multi-objective constraints. To verify the effectiveness of the A-NSGA-II algorithm at the extreme scale, it was further compared with the NSGA-III, MOEA / D, SPEA2, and NSGA-II algorithms, with 30 independent experiments conducted under the same experimental conditions. To assess statistical significance, a Friedman rank test with a significance level of 0.05 was performed. Table 3 lists the corresponding solution results.

[0068] Table 3. Comparison of Solution Results for Scenario 15 of Satellite 5 and Friedman Mean Rank Test

[0069] Table 3 shows that the Friedman composite score of A-NSGA-II further decreased to 1.58, maintaining its first-place ranking in the extreme scale scenario. SPEA2 and NSGA-II ranked second and third, respectively. The p-values ​​of the mean rank test for each algorithm were all less than 0.05, indicating that A-NSGA-II still maintains a significant advantage in the most challenging extreme scale scenario. Regarding the objective function solution results, A-NSGA-II has the highest HV value and the lowest IGD value in the extreme scenario, with a relatively small standard deviation, indicating that the algorithm maintains superior stability and solution quality in the 642-dimensional ultra-high-dimensional decision space. In terms of runtime, although the A-NSGA-II algorithm significantly increased compared to previous scenarios, it was the most efficient among the compared algorithms, improving upon NSGA-III by 36.1%. Within the A-NSGA-II co-evolutionary framework, the synergistic effect between the main population and auxiliary populations in the extreme-dimensional search space is maximized. Through refined migration strategies and adaptive constraint handling, the algorithm effectively addresses complex constraints and multi-objective conflicts in ultra-large-scale scenarios, demonstrating its superior performance in extreme optimization problems. To further compare the performance differences of the algorithms at extreme scales, the Pareto fronts obtained by each algorithm are analyzed, and the simulation results are as follows: Figure 3 As shown. Figure 3 (c) shows that, under extreme scale scenarios, the quality of the Pareto front obtained by the comparative algorithm significantly decreases, with a sparse solution set distribution and limited coverage. In contrast, the Pareto front obtained by the A-NSGA-II algorithm maintains good distribution uniformity and broad coverage, providing a comprehensive and high-quality trade-off between energy consumption and task completion rate. This fully verifies the algorithm's superior performance and strong robustness under extreme complex scenarios. In the extreme load scenario of 5 satellites and 15 missions, the optimal solution exhibits unprecedented optimization characteristics: for the first time, it achieves unified optimality across all three objectives, completing 100% of the 15 missions with zero latency, consuming 299.99 kJ of energy, and achieving a utilization rate of 0.999%. The optimal energy solution achieves a completion rate of 20.55%, with extremely high latency and the lowest energy consumption of 7.46 kJ. This breakthrough breaks the previous experimental limitation that completion rate and latency could not be simultaneously achieved. The Pareto solution set exhibits an extremely rich variety of trade-off patterns, with completion rates ranging from 20.55% to 100%, latency characteristics ranging from zero to extremely high latency, and energy ranges from 7.46 to 299.99. In particular, several high-quality solutions with high completion rates (90%-97%) and low latency (1000-6000 seconds) have emerged, providing decision-makers with unprecedented flexibility in dealing with extremely complex needs.

[0070] The technical features of this invention not described can be implemented by or using existing technology, and will not be repeated here. Of course, the above description is not a limitation of this invention, and this invention is not limited to the examples above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of this invention should also be within the protection scope of this invention.

Claims

1. A method of satellite task scheduling, characterized in that, The method comprises the following steps: acquiring a satellite and a satellite task set, and determining decision variables of satellite task scheduling according to the satellite and the satellite task set; constructing a satellite task scheduling model based on the decision variables of satellite task scheduling; solving the satellite task scheduling model by using a multi-objective genetic algorithm to obtain a satellite task scheduling solution; generating a scheduling instruction based on the satellite task scheduling solution, and scheduling tasks of the satellite according to the scheduling instruction.

2. The method of claim 1, wherein, The decision variables of the satellite task scheduling comprise: wherein, is a task is a satellite is an assignment relationship, is an actual start time for the satellite to perform the task, is an actual end time for the satellite to perform the task, is a completion status of the task under the scheduling scheme, is a satellite set, is a task set.

3. The method of claim 2, wherein, The construction of the satellite task scheduling model comprises: defining an objective function of the satellite task scheduling and constructing constraint conditions for the decision variables of the satellite task scheduling; the objective function of the satellite task scheduling comprises minimizing a negative value of a weighted task completion rate, minimizing a total time expenditure of all satellites executing tasks, minimizing actual start times of all tasks, and minimizing a proportion of uncompleted tasks; the constraint conditions comprise task allocation uniqueness constraints, time window constraints, timing mutual exclusion constraints, visibility constraints, storage capacity constraints, and maximum working time constraints.

4. The method of claim 3, wherein, The solving of the satellite task scheduling model by using the multi-objective optimization algorithm comprises: generating an initial population and constructing an external elite set by using a multi-population initialization strategy according to the satellite task scheduling model; the initial population comprises a main population and a plurality of auxiliary populations; the external elite set is used to store optimal solutions in iterations; defining a dynamic Epsilon constraint relaxation mechanism and initializing an Epsilon value, and iteratively performing parallel evolution, population migration, environmental selection, and external elite set updating on the initial population; repeating the iteration, updating the Epsilon value according to the dynamic Epsilon constraint relaxation mechanism after each iteration, until an iteration termination condition is reached, outputting a solution in the external elite set, and taking the solution in the external elite set as the satellite task scheduling solution.

5. The method of claim 4, wherein, The generation of the initial population comprises uniformly generating the main population with a size of N in a decision space by using Latin hypercube sampling according to a dimension of the decision variables; calculating the number and size of the auxiliary populations based on the constraint conditions, and the calculation is represented as follows: wherein, is the number of auxiliary populations, is the preset maximum number of auxiliary populations, is the total number of constraints, is the th auxiliary population, is the size of the main population, is the size proportionality coefficient; initializing the auxiliary populations according to the number and size of the auxiliary populations.

6. The method of claim 5, wherein, The dynamic Epsilon mechanism comprises: defining a maximum function evaluation number, calculating a control number of the dynamic Epsilon mechanism based on the maximum function evaluation number and a population size; in each iteration, calling an evolution stagnation detection function to calculate a stagnation index value and presetting a stagnation threshold value, comparing the stagnation index value with the stagnation threshold value, if the stagnation index value exceeds the stop threshold value, increasing the Epsilon value by using an adaptive adjustment strategy, if the stagnation index value does not exceed the stop threshold value, judging whether a current iteration number exceeds the control number of the dynamic Epsilon mechanism, if the current iteration number does not exceed the control number of the dynamic Epsilon mechanism, updating the Epsilon value by using a nonlinear decay formula, and if the current iteration number exceeds the control number of the dynamic Epsilon mechanism, setting the Epsilon value to 0; the adaptive adjustment strategy is represented as follows: wherein, is the updated Epsilon value, is the adjustment factor, is the current Epsilon value, is the stall detection indicator; the nonlinear decay formula is represented as follows: wherein, is the updated Epsilon value, is the control algebra, is the curvature parameter.

7. The method of claim 6, wherein, the parallel evolution comprises main population evolution and active auxiliary population evolution; The main population evolves to perform tournament selection and genetic operation on the main population to obtain a main offspring population; The active auxiliary population evolves to include calculating constraint average positive violation degrees and sorting the constraint average positive violation degrees in descending order to obtain a constraint average positive violation degree sorting; the constraint average positive violation degree calculation formula is as follows: wherein, is the degree of violation of the constraint by the individual, is the number of individuals in the population that violate the constraint; According to the constraint average positive violation degrees and the constraint average positive violation degree sorting, the top several auxiliary populations in the sorting are screened as active auxiliary populations; Selection and genetic operation are performed on the active auxiliary populations to obtain an auxiliary offspring population.

8. The method of claim 7, wherein, The population migration includes: Defining a migration iteration interval, and in each iteration, determining whether the current iteration number meets the migration iteration interval; if so, calculating the average Euclidean distance of each main population individual from other individuals and sorting the distances in descending order, screening the top several individuals in the sorting to distribute to the auxiliary populations; at the same time, calculating the constraint violation degrees of the individuals in the auxiliary populations and arranging the degrees in ascending order, screening the top several individuals in the sorting to join the main offspring population.

9. The method of claim 8, wherein, The environment selection and external elite set updating include: Combining the main population, the main offspring population and the auxiliary offspring population to obtain a combined population; Performing fast non-dominated sorting and crowdedness calculation on the combined population to obtain non-dominated levels and individual densities; According to the non-dominated levels and the individual densities, screening a new generation of main population with a size of N from the combined population, and updating the external elite set with the non-dominated solutions in the new generation of main population with a size of N.

10. A satellite mission scheduling system, characterized by, A satellite task scheduling method is provided, including: a data acquisition module, configured to acquire a satellite and a satellite task set, and determine decision variables of satellite task scheduling according to the satellite and the satellite task set; a model construction module, configured to construct a satellite task scheduling model based on the decision variables of satellite task scheduling; a model solving module, configured to solve the satellite task scheduling model by using a multi-objective genetic algorithm to obtain a satellite task scheduling solution; a scheduling execution module, configured to generate a scheduling instruction based on the satellite task scheduling solution, and perform task scheduling on the satellite according to the scheduling instruction.

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