A Novel Spaceborne SAR Constellation Scheduling Algorithm for Sea Surface Moving Target Search Tasks

With the expanding scope of human activities in marine environments, the efficient detection and tracking of mobile targets on the ocean's surface have become increasingly crucial. Synthetic aperture radar (SAR) constellation can obtain ground observation data based on user requests and subject to visibility conditions. Now it is an indispensable tool in sea surface moving target search tasks. Satellite constellation resources are scarce and limited, and user demands are diverse. How to rationally dispatch satellite constellation resources to meet user needs to the maximum extent and improve the application efficiency of satellite resources is an urgent scientific problem that needs to be solved. This article mainly expounds two respects of work. First, modeling SAR constellation scheduling problem for sea surface moving target search tasks to establish the objective function. Second, a novel multistrategy discrete constrained differential evolution algorithm denoted as MSDCDE is proposed in the article. The proposed MSDCDE algorithm integrates cross strategy based on discrete variables, constraint handling techniques, population restart strategy, and left-shift local strategy, which can effectively avoid falling into local optimality, thereby achieving global optimality and improving search and rescue performances. Six sets of experiments, totaling 215 runs, have been conducted to validate the effectiveness of the proposed resolution process framework and the MSDCDE algorithm. The proposed method demonstrated an over 48.98% performance improvement compared with some state-of-the-art algorithms and significantly reduced task completion time.

Abstract-With the expanding scope of human activities in marine environments, the efficient detection and tracking of mobile targets on the ocean's surface have become increasingly crucial.Synthetic aperture radar (SAR) constellation can obtain ground observation data based on user requests and subject to visibility conditions.Now it is an indispensable tool in sea surface moving target search tasks.Satellite constellation resources are scarce and limited, and user demands are diverse.How to rationally dispatch satellite constellation resources to meet user needs to the maximum extent and improve the application efficiency of satellite resources is an urgent scientific problem that needs to be solved.This article mainly expounds two respects of work.First, modeling SAR constellation scheduling problem for sea surface moving target search tasks to establish the objective function.Second, a novel multistrategy discrete constrained differential evolution algorithm denoted as MSDCDE is proposed in the article.The proposed MSDCDE algorithm integrates cross strategy based on discrete variables, constraint handling techniques, population restart strategy, and left-shift local strategy, which can effectively avoid falling into local optimality, thereby achieving global optimality and improving search and rescue performances.Six sets of experiments, totaling 215 runs, have been conducted to validate the effectiveness of the proposed resolution process framework and the MSDCDE algorithm.The proposed method demonstrated an over 48.98% performance improvement compared with some state-of-the-art algorithms and significantly reduced task completion time.
Index Terms-Sea surface moving target search, synthetic aperture radar (SAR), SAR constellation, task scheduling.

A. Background and Motivation
W ITH the expanding scope of human activities in marine environments, the efficient detection and tracking of mobile targets on the ocean's surface have become increasingly crucial.The technological solutions designed to fulfill this vital mission find broad applications in various civilian sectors.These applications encompass activities, such as retrieving vessels, surveilling offshore oil spills, and monitoring planktonic organisms [1], [2], [3], [4].
The utilization of advanced technologies becomes pivotal in search and rescue missions concerning missing sea vessels.Swift and accurate location determination of vessels affected by accidents or unforeseen events is a vital component of successful rescue operations.
Synthetic aperture radar (SAR) sensors serve as valuable instruments in the realm of maritime environmental supervision, primarily owing to their capacity to conduct unfettered observations around-the-clock in divergent weather conditions [5], [6], [7], [8], [9].Nevertheless, certain hurdles persist, namely, the extended revisit cycle and suboptimal surveillance efficacy that typify the use of a single satellite.Consequently, an orchestrated network of satellite constellations or formations has emerged as an indispensable solution, offering 3-D marine environmental monitoring [10].Adopting the core principle of satellite constellation networking, wherein several satellites are positionally coordinated with a fixed phase relationship, augments the observation temporal resolution.An alternate strategy leverages satellite formation, whereby a number of satellites are systematically deployed into an orbit around the Earth, enabling them to concurrently accomplish tasks within the same time frame.
Spaceborne SAR constellation has become an indispensable tool in disaster emergency response and other fields, as it can acquire ground observation data based on user requests, provided that visibility conditions are met [11], [12], [13].However, satellite resources are scarce and limited, while user demands are diverse and extensive.Addressing the urgent scientific problem of rational scheduling of satellite constellation resources to maximize user satisfaction and enhance the application efficiency of satellite constellation resources is crucial [14], [15], [16].

B. Related Works
In current satellite scheduling research, the primary focus is on optical imaging satellites.Potter et al. [17] developed a heuristic algorithm for scheduling the Land-Source7 satellite.Vasquez and Hao [18] approached the satellite scheduling problem through a knapsack model and introduced a tabu search algorithm for its resolution.Wang et al. [19] introduced a multiobjective evolutionary algorithm to tackle satellite scheduling problems.Meanwhile, Bianchessi et al. [20] designed a tabu search algorithm for addressing multisatellite scheduling issues.They further utilized column generation techniques to establish an upper bound for the problem, subsequently evaluating satellite scheduling solutions against this benchmark.
SAR satellites, unlike optical satellite systems, are capable of performing tasks under diverse weather conditions [21], [22].These satellites operate based on distinct working principles and constraints compared with optical satellites.As a result, the mission planning models and algorithms designed for optical satellites are not directly applicable to SAR satellites.In the realm of optimizing scheduling for SAR satellites, most research articles primarily address single-satellite, single-orbit scenarios.
Agn and Bensana [23] formulated a problem of task selection, for a multiple instrument satellite as an instance of multidimensional knapsack, which is known to be NP-hard [24].Hall and Magazine [25] conducted research on the dynamic programming problem of single-satellite missions using heuristic methods.Xhafa et al. [26] conducted the experimental evaluation of a basic genetic algorithm using the benchmark for single satellite.Harrison et al. [27] have demonstrated that the enumeration method can generate the optimal task schedule for the largest dataset consisting of 50 imaging requests in less than 12 min.Wolfe and Sorensen [28] devised multiple algorithms, including lookahead search algorithms and genetic algorithms, and conducted a comparative performance analysis.The experimental results demonstrated that genetic algorithms outperformed others as the scheduling problem scaled up.Gabrel and Vanderpooten [29] proposed a two-stage approach to address satellite mission planning problems: generation of efficient paths and selection of a satisfactory path using a multiple criteria interactive procedure.Lin et al. [30] presented the development of a daily imaging scheduling system for a low-orbit, Earth observation satellite.Liao and Yang [31] formulated the problem into a stochastic integer programming problem and adopted the rolling horizon approach to solve for this problem.Wu et al. [32] proposed a hybrid ant colony optimization method mixed with iteration local search to solve the problem.Wu et al. [33] presented an adaptive simulated annealing-based scheduling algorithm integrated with a dynamic task clustering strategy for satellite observation scheduling problems.
In the sea surface moving target search tasks, the primary objective is to maximize target benefits while minimizing both time and energy consumption, which brings a multi-objective optimization problem.Considering the complexity of these tasks, it has become imperative to use multisatellite collaboration to achieve comprehensive search coverage in the sea's target area.However, this inherently results in a large-scale optimization challenge.Therefore, it has been of paramount importance to achieve a balance between objectives and constraints under intricate constraint conditions.Yet, the existing algorithms cannot handle optimization problems with large-scale, multiple constraints and mixed-integer variables.Thus, there has been an urgent need to develop new methods to address this problem.

C. Contributions
This article aims to address the problem of efficient and effective mission planning for spaceborne SAR constellations tasked with sea surface moving target search.
The main contributions are summarized as follows.
1) This article provides a description of satellite working principles and mechanisms, the observation process, and the task organization implementation process.It summarizes the characteristics and challenges of multisatellite scheduling problems, establishes a mathematical model for sea surface moving target search tasks, and proposes a processing framework.2) An innovative multistrategy discrete constrained differential evolution algorithm denoted as MSDCDE is proposed.
The MSDCDE is developed to address the challenges in the sea surface moving target search task.The primary objective of the MSDCDE algorithm is to meet the critical demand of users for expeditious observation of predefined geographical regions while adhering to constraints and operational limitations.3) Six sets of experiments, totaling 215 runs, were conducted to validate the effectiveness of the proposed resolution process framework and the MSDCDE algorithm.Our method demonstrated an over 48.98% performance improvement compared with existing state-of-the-art algorithms and significantly reduced task completion time.This algorithm can be applied not only in sea surface moving target search tasks but also in various areas, such as environmental disaster mitigation.The rest of this article is organized as follows.In Section II, we concentrate on elucidating the problem model, the essential principles of the SAR, and the optimization objectives.In Section III, we present the proposed scheme in detail.In Section IV, the corresponding simulation results are presented.In Section V, the simulation results are interpreted and analyzed.Finally, Section VI concludes this article.

II. PROBLEM FORMULATION
To analyze the essence and key characteristics of SAR constellation scheduling for sea surface mobile target search tasks, we begin by using the example of rescuing missing vessels.We will first elucidate the principles and mechanisms governing satellite operations, the observation process, and the organization and implementation of tasks.Following this, we will delve into various facets of multisatellite scheduling concerns, encompassing aspects related to observation coverage tasks, satellite resources, and optimization objectives.By scrutinizing the interplay among these elements, we will synthesize the distinctive features and challenges inherent in multisatellite scheduling problems.Ultimately, we will construct a mathematical model to address this issue.

A. Modeling SAR Constellation Scheduling Problem for Sea Surface Mobile Target Search Tasks
Satellite observation scheduling is the process of determining the observation activities for each satellite during each orbit pass.It aims to maximize the benefits of observations while meeting various task requirements and constraints.This scheduling is a critical element in enhancing the efficiency of satellite utilization.In maritime ship target search and rescue tasks, the aim is to maximize target benefit with the least time and energy expenditure, representing a quintessential multi-objective optimization problem.Addressing these complex tasks necessitates the coordination of multiple satellites for in-orbit optimization and thorough search coverage of all target ships throughout the target area, epitomizing a large-scale optimization problem.Concurrently, balancing objectives and constraints under intricate conditions is imperative, ensuring an effective task sequence while complying with these constraints, essentially a constrained optimization problem.
Illustrating with the example of searching for missing ships, consider a scenario in which n satellites are deployed in orbit, as depicted in Fig. 1.These satellites are tasked with locating target ships potentially situated within a defined sea area, hereafter referred to as SEA-Y.This objective is achieved by searching SEA-Y, implementing grid-based segmentation for scanning, and subsequently identifying all target ships within SEA-Y.The satellites operate in two modes: searching and detection, illustrated by yellow beams in Fig. 1, and identification and confirmation, indicated by blue beams in the same figure.These modes provide diverse imaging resolutions and widths, catering to various search and rescue requirements under differing conditions.The searching and detection mode, as the name implies, covers larger areas quickly due to its wide imaging swath, albeit at a lower resolution.In contrast, the identification and confirmation mode utilizes a narrower swath for higher resolution and precise target identification.By accounting for the satellite's positional status and energy conditions, comprehensive coverage of SEA-Y is accomplished expediently, facilitating an extensive search and identification process.
The designated area (SEA-Y) is divided into grids, each representing the fundamental unit of observation.The aim is to achieve comprehensive observation of all grids in the most time-efficient manner.During the optimization process, various task sequences are developed.The mission sequence precisely indicates which satellite observes which grid at each specific moment.
The above discussion can be summarized by the following equation: In ( 1), T signifies the cumulative time required for satellites to complete the observation of all grids (both detection and confirmation) from the outset.Herein, j indicates the grid number, N denotes the total number of grids, and T j w reflects the duration of the satellite's observation on grid j.The term T S corresponds to the aggregate idle time experienced by satellites upon completing the observation of all grids.Given that each grid's observation time is predefined and constant, the optimization objective is to reconfigure the task sequence to minimize the overall idle time.
In (2), M denotes the total number of satellites, and i signifies the identifier of a specific satellite.Grids observed by each satellite are extracted, categorized by distinct satellite identifiers.L i denotes the length of this sequence, and l represents the index variable within this sequence of satellite i. t i,l signifies the starting time of the grid l for satellite i, and t i,l+1 represents the starting time for the l + 1 grid.T j i,l w indicates the required operational duration of satellite i on the grid l.
During task sequence generation, the observation order for each grid by the satellites is determined.Fig. 2 illustrates this with an example of 12 satellites, where alphabetic labels on the grid, such as A, B, etc., denote the observing satellite, and numeric labels, such as 1, 2, indicate the sequence of observation.In Fig. 2, the first row on the right displays the count of satellites, while the second row isolates grids observed by satellite A, arranging them in an ascending order based on their initial observation times by satellite A, with TA1 representing the earliest observation.Similarly, the final row presents the grid sequence covered by the 12th satellite, sequenced by their commencement times (TL1, TL2,. .., TL).
The mission sequence specifically denotes which satellite observes which grid at any given moment.This set encompasses those described in (3), where N denotes the number of grids and M denotes the number of satellites, amounting to a prodigious volume of data.Furthermore, this optimization issue is devoid of an analytical solution, and conventional exact solution methodologies fail to yield precise outcomes.Consequently, researchers are compelled to depend on iterative trial-and-error approaches to ascertain the optimal solution.For problems of this nature, which are classified as NP-hard [24], [34], [35], evolutionary algorithms hold a natural advantage as they progressively unearth the optimal solution through continuous iterative experimentation

III. MULTISTRATEGY DISCRETE CONSTRAINED DIFFERENTIAL EVOLUTION ALGORITHM
The genetic algorithm initiates with a population, representing a set of potential solutions, each comprising individuals encoded by genes.Each individual in this context is a chromosome, characterized by specific entities.Chromosomes, as primary carriers of genetic material, consist of multiple genes.Their internal expression, or genotype, a unique gene combination, dictates an individual's external traits.Consequently, initial steps involve mapping from phenotype to genotype, essentially the coding process.Because of the complexity of modeling genetic codes, simplifications, such as binary coding, are often employed.Subsequent to generating the initial population, evolutionary principles, such as survival of the fittest, lead to progressively refined solutions over generations.In each generation, selection hinges on individual fitness within the problem domain, facilitating combinatorial crossover and mutation through natural genetic operators, thus creating a population representing a novel solution set.This process engenders population evolution akin to natural selection, with each subsequent generation displaying greater adaptability.The optimal individual from the final generation can be decoded, providing an approximate optimal solution.In this article, we present a novel multistrategy discrete constrained differential evolution algorithm denoted as MSDCDE.The basic framework of MSDCDE is as shown in Fig. 3.
First, this article designs three improved discrete crossover methods to generate new excellent offspring individuals and uses the feasibility criteria in C2ODE for individual selection.Subsequently, a task-based left-shift local operation is designed for local search of individual tasks to enhance algorithm performance.Moreover, an effective voting mechanism is introduced to perform selection between offspring and parent generations, and constraint handling techniques based on the voting mechanism can effectively enhance algorithm generalization.In addition, to overcome local optima, this article proposes a population restart technique based on diversity checks.Finally, based on task characteristics, a left-shift local operation is designed to perform a left-shift operation for the last task of each satellite, effectively reducing the time required to complete the tasks.

A. Cross Strategy Based on Discrete Variables
Variables, such as sea area grid numbers and satellite numbers, are all integer variables, making this an optimization problem with discrete variables.To tackle this discrete optimization problem, we have employed three discrete crossover strategies: single-point crossover, uniform crossover, and order crossover.
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where c i represents the ith element of the gene sequence of parent individual Cz, and d i represents the ith element of the gene sequence of parent individual Dz.Task sequence updating is achieved through the above single-point crossover.
2) Uniform Crossover Strategy: Uniform crossover is an extension of single-point crossover used to combine the genes of two parent individuals to generate offspring.It selects genes from both parent individuals at each position based on a certain probability, thereby increasing the diversity of the population.Multiple crossover points can be used to cross the parent individuals, generating two offspring individuals.Similarly, assuming there are parent individuals Af and Bf , their gene sequences are represented, as shown in (4).
For offspring individuals Cz and Dz, genes are probabilistically selected from the same positions in parent individuals Af and Bf , and if an element of the gene sequence of parent individual Af is selected at position i, then the ith element of the gene sequence of offspring individuals Cz and Dz is a i , otherwise it is b i , as shown in the following: where rand denotes a random number generated in the range [0,1].Uniform crossover can increase the diversity between individuals, aiding the algorithm in escaping local optima.
3) Order Crossover Strategy: Order crossover is a genetic operator that entails the selection of two random positions within parent individuals.The gene segment between these two positions is preserved and then filled in with genes from another parent individual.In this context, let us assume that we have parent individuals Af and Bf , and their gene sequences are represented as follows: where p and w represent two random crossover points.Subsequently, q random crossover points are selected, distributed at different positions within the gene sequence.Let us assume that these q crossover points are arranged in an ascending order, with the first crossover point at position Order crossover can preserve the order information of parent individuals and increase the diversity of the population by obtaining gene segments from another parent individual, which helps the algorithm find better solutions in permutation problems.

B. Constraint Handling Techniques 1) Constraint Handling Techniques
Based on Feasible Solution Superiority: After obtaining three new individuals through the discrete crossover strategies mentioned earlier, the next step involves selecting the best among these offspring individuals.To achieve this, constraint handling techniques that prioritize feasible solutions are employed.These techniques facilitate the quick identification of the optimal solution, guided by the following criteria.
1) Feasible solutions take precedence over infeasible ones.
2) In cases where both solutions are infeasible, preference is given to the one with a smaller degree of constraint violation.3) If both solutions are feasible, the choice leans toward the one with a smaller fitness value.By applying these criteria based on the superiority of feasible solutions, the most promising offspring individual is chosen from the pool of three.
2) VOTE-Voting Mechanism for Individual Selection: This VOTE method integrates three constraint-handling techniques: adaptive penalty function, superiority of feasible solutions, and constraints.Each constraint-handling technique serves as a voter, and all voters cast their votes for each set of solutions.According to the following equation, the solution with the highest weighted votes is considered better.Furthermore, an adaptive strategy has been developed to adjust the weight of voters based on their historical voting performance Ensemble(x) = arg max where Ensemble(x) represents an adaptive strategy, x is the solution under evaluation, argmax is a function that finds the maximum value, x is the current individual's parent, x (l) represents the solution provided by the lth voter, K is the total number of voters, w l is the weight of the lth voter, determined by their importance in the overall context, and IsBetter(x , x (l) ) is an indicator function.It takes the value of 1 when the lth voter determines that x is a better solution than x (l) , otherwise, it is 0, thus obtaining the optimal solution.The voters include methods based on adaptive penalty functions, methods based on the superiority of feasible solutions, and β-constraint methods.The method based on adaptive penalty functions scales the constraint violations adaptively and constructs new fitness values based on the scaling, using these new fitness values to assess the quality of individuals.
The β-constraint method is defined as follows, where β is called the penalty weight.The value of β typically falls between [0, 1] and is used to control the weight of the constraint term in the objective function.When β is close to 0, the weight of the constraint term is smaller, and the objective function focuses more on optimizing the primary objective itself.When β is close to 1, the weight of the constraint term is larger, and the objective function places greater emphasis on satisfying the constraints.G(x) represents the degree of constraint violation, and the original objective function and constraints are transformed into a new objective function using the equation below, which is used to evaluate individuals based on the new objective function:

C. Population Restart Strategy
Evolutionary algorithms have the drawback of falling into a local optimum.In view of that, this study designs a population restart mechanism and develops a diversity detection method, which is defined by the following formula.When the population diversity is below a predefined threshold, it is considered that the population has fallen into a local optimum.At this point, a population restart is needed, new individuals are generated, and the best individuals in the population are retained where X represents the current population, and Y represents the population for the next iteration; P dist(X, Y ) u,j represents the Euclidean distance between the uth point in X and the jth point in Y .By using the above formula, the individual similarity within the entire population is calculated, and when the average similarity among population individuals falls below 1e − 6, it is considered that the population has entered a local optimum, and a population restart is triggered at this point.

D. Left-Shift Local Strategy
To further enhance the algorithm's performance in handling the proposed optimization problem mentioned above, another major factor constraining task performance is the completion time of the last job task.Therefore, if it is possible to advance the completion time of the last job task as much as possible, a better solution can be achieved.
With the above considerations in mind, this article, based on task characteristics, introduces a left-shift local operation for the last job task of each satellite.For the last job task of each satellite, an insertion is made at the position of the task immediately preceding it.If the resulting new job task sequence satisfies the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.constraint conditions, the process stops; otherwise, it continues with an insertion at the position of the task preceding the one just inserted, and the sequence's compliance with the constraint conditions is checked.If the entire job task sequence is traversed without finding a position that satisfies the constraint conditions after insertion, the left-shift operation is not executed.Through this left-shift local operation, the required time for searching the optimal solution is effectively reduced.

IV. SIMULATION
To validate the effectiveness and robustness of the processing framework and algorithm we proposed, we constructed a simulated scenario for a case study.This section describes the problem setup, simulation process, and the results obtained by the proposed algorithm.

A. Assumptions for the Simulation
In this case study, the scenario start time was set to 12 October, 2013, and was run for two days with an end time of 14 October, 2013.The selected area scene consists of the sea surface within the region defined by four points (4.29  4. The points on the map represent the grids we have divided, with each grid measuring 100 km × 100 km and a spacing of 100 km.The total number of grids is 1080, and the goal is to cover all grids as quickly as possible.The orbit parameters of constellation satellites are given in Table I.In order to conduct simulation experiments, the following basic assumptions have been made. 1) The target sea area is divided into grids of 100 km × 100 km each, and each grid's center point is considered observable, indicating that the grid can be searched.(In other words, the satellite's swath width under detection mode is 100 km × 100 km).2) After each grid is searched by a satellite, the satellite needs to immediately confirm identification.(In other words, the grid searched by Satellite 1 is confirmed by Satellite 1).
3) The time required for each satellite to work on each grid consists of two parts: the first part is the detection mode, which has a fixed duration of 6 s for each grid, and the second part is the confirmation mode, which has a duration of a random integer between 0 and 15 s for each grid.4) False alarm rates and detection error rates are not considered.5) Intersatellite link resources are unconstrained, meeting the requirements for intersatellite collaborative operations.6) Energy consumption due to mode switching is not considered.7) Storage resources and energy are abundant.8) The initial working mode for all satellites is set to detection.

B. Simulation Results
Six sets of experiments, totaling 215 runs, were conducted to validate the effectiveness of the proposed resolution process framework and the MSDCDE algorithm.In addition, we compare our algorithm with some state-of-the-art algorithms.
It should be pointed out that although there is no specific algorithm designed directly to solve this problem, there are some state-of-the-art evolutionary algorithms that can be partially referenced.
For example, ATM [36], C2ODE [37], FROFI [38], and VMCH [39] are four different kinds of evolutionary algorithms for the mixed-variable problems.In particular, the C2ODE and FROFI algorithms are designed for continuous problems, and we have modified them to address discrete problems, renaming them as dC2ODE and dFROFI, respectively.We select these four algorithms as comparison algorithms.
To have a fair comparison, the parameters of the proposed MSDCDE and the comparison algorithms are same in this article.The parameter settings of the experiments are as follows.
1) All algorithms are executed independently for 20 runs.
2) The maximum number of iterations is set to 2000.
4) The probability of crossover P c = 0.8.

5)
The probability of mutation P m = 0.1.
6) The working time required for each grid by each satellite is randomly determined.This randomness remains consistent across various algorithm tests, as illustrated in the figure below.In Fig. 5, each square symbolizes a grid, with the color intensity indicating the required observation time for each grid by the satellite, as delineated by the color bar.Given the total of 1080 grids, for visual clarity, the grids are numbered in a format of 36 rows and 30 columns.        the population restart ratio to 0, 0.2, 0.4, 0.6, and 0.8.The results obtained are shown in the Fig. 11.It can be observed that when the population restart ratio is set to 0, it is prone to getting trapped in local optima and obtaining the global optimal solution becomes challenging.The convergence speed also significantly slows down compared with conditions where the population restart ratio is set to 0.2, 0.4, and so on.This demonstrates the effectiveness of the population restart strategy in our proposed algorithm.

V. DISCUSSION
This research introduces the MSDCDE algorithm, a novel approach to scheduling spaceborne SAR constellations for maritime target search tasks.The effectiveness of the MSDCDE algorithm resides in its capacity to optimize the scheduling process under complex constraints, thereby augmenting the efficiency and success rate of sea surface moving target searches.Compared with existing methods, the MSDCDE algorithm demonstrates a significant improvement in task completion time, as evidenced by extensive simulation results.The field of SAR constellation scheduling for sea surface moving target search tasks is undergoing rapid evolution.This algorithm contributes to the field by offering a more dynamic and adaptive scheduling solution.Although this algorithm demonstrates promising results, it is important to acknowledge certain limitations.In the experiment, assumptions were made, such as dividing the observation sea area into grids, fixing the observation time for each grid, and omitting the consideration of mode-switching times.Addressing these assumptions in subsequent research will be imperative.

VI. CONCLUSION
Efficiently scheduling the resources of spaceborne SAR constellations to accomplish sea surface moving target search tasks is of paramount importance.To achieve this objective, this article introduces a processing framework and the MSDCDE algorithm.In addition, six sets of experiments, totaling 215 runs, were conducted to validate the effectiveness of the proposed algorithm.The experiments demonstrate that the MSDCDE algorithm can efficiently schedule spaceborne SAR constellation resources for sea surface moving target search tasks.Compared with state-ofthe-art algorithms, its performance can be effectively improved by over 48.98%, avoiding local optima and achieving global optimality.
The MSDCDE algorithm we proposed effectively addresses the sea surface moving target search task, but there are still unresolved issues.For instance, we did not account for false alarm rates and detection rates of missing ships during model construction.Furthermore, the granularity of grid sizes presents a challenge.Different grid sizes have distinct performance requirements for the algorithm, and grids that are excessively large or small do not meet practical application demands.These shortcomings will be further studied in future work.

Fig. 5 .
Fig. 5. Working time required for each grid by each satellite.

Fig. 8 .
Fig. 8. Experimental comparison results of different probability of crossover with different algorithms.

Fig. 9 .
Fig. 9. Experimental comparison results of different probability of mutation with different algorithms.

Fig. 10 .
Fig. 10.Experimental comparison results of different iterations with different algorithms.

Fig. 11 .
Fig. 11.Experimental comparison results of different population restart ratio with MSDCDE.
the elements of the gene sequence of offspring individual Cz are the same as parent individual Af between crossover points p and w, while they are the same as parent individual Bf at other positions.The elements of the gene sequence of offspring individual Dz, on the other hand, are the same as parent individual Bf between crossover points p and w, while they are the same as parent individual Af at other positions, as shown in the following: 1 and the last one at position n − 1.Based on these crossover points, parent individuals Af and Bf undergo crossover to produce offspring individuals Cz and Dz Cz = [c 1 , c 2 , ..., c p , ..., c w , ..., c n ] Dz = [d 1 , d 2 , ..., d p , ..., d w , ..., d n ](11)Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.where • N, 145.91 • E; 5.23 • N, 175.00 • E; 37.22 • N, 174.59 • E; 36.28 • N, 146.49• E), as is shown in Fig.