A spacecraft task allocation method for random burst tasks

Abstract

The application discloses a spacecraft task allocation method for random burst tasks and relates to the technical field of spacecraft task allocation.The method comprises the following steps: defining random variables and their probability distribution, constructing a two-stage random programming model, simplifying the second-stage solving process, calculating the expected cost, and solving a preliminary resource allocation scheme, and finally generating a dynamically adjusted task allocation strategy.Through the utilization of the probability information of random variables, the combination of the linear programming dual theory and the numerical integration method, the resource utilization efficiency and the task completion rate are significantly improved, the calculation complexity is reduced, and the application is suitable for medium-scale task allocation problems.The application can flexibly cope with the randomness of task demand and provides an efficient and reliable solution for spacecraft task allocation.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft mission allocation technology, and more specifically, relates to a spacecraft mission allocation method for random and sudden missions. Background Technology

[0002] During spacecraft missions, unforeseen and unexpected tasks (such as temporary target observation, emergency data transmission, and fault repair support) can disrupt the balance of pre-planned missions, becoming a key factor affecting resource utilization efficiency and mission success rate. These unexpected tasks typically feature uncertain priorities, random execution time windows, and large fluctuations in data volume, placing extremely high demands on the dynamic adaptability and real-time performance of task allocation methods.

[0003] Traditional deterministic task allocation methods formulate allocation schemes based on fixed task parameters, which cannot identify and respond to random and sudden tasks. This can easily lead to the failure of sudden tasks due to insufficient resource reservation, or the excessive idleness of regular task resources due to reserved resources. While robust optimization methods based on unknown probability distributions can handle some uncertainty, they often adopt conservative resource allocation strategies to cope with extreme and sudden scenarios, which significantly reduces the utilization rate of regular task resources and cannot optimize resource allocation according to the probabilistic characteristics of sudden tasks. Although traditional stochastic programming methods can theoretically utilize probabilistic information, their high dependence on sample size and complex calculation process make it difficult to meet the real-time adjustment needs when sudden tasks occur, making engineering implementation extremely difficult.

[0004] Current technical solutions have significant limitations in balancing the response to unpredictable and sudden missions, the support of routine missions, and resource efficiency: deterministic methods lack adaptability to unpredictable missions, robust optimization methods sacrifice efficiency due to conservative strategies, and traditional stochastic programming methods cannot respond in real time due to computational complexity. Therefore, there is an urgent need for a spacecraft mission allocation method that can fully utilize the probability distribution information of unpredictable missions, efficiently respond to unpredictable and sudden missions while ensuring the execution of routine missions, and has low computational complexity. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of spacecraft mission allocation methods for random and sudden missions in terms of handling randomness, balancing resource efficiency, and controlling computational complexity, and to provide a spacecraft mission allocation scheme that can accurately adapt to the characteristics of random and sudden missions.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A spacecraft mission allocation method for stochastic, sudden missions includes the following steps:

[0008] S1, define the random variables and their known probability distributions in spacecraft mission allocation;

[0009] S2, construct a two-stage stochastic programming model; the first stage is the initial task allocation decision, and the second stage is the task adjustment based on the actual values ​​of the random variables;

[0010] S3 transforms the two-stage stochastic programming model into two optimization problems: the first-stage optimization problem and the second-stage optimization problem.

[0011] S4. The solution process of the second-stage optimization problem is simplified by using the duality theory of linear programming, and the expected cost of the second-stage optimization problem is calculated.

[0012] S5. Combining the expected cost of the second-stage optimization problem, we solve the first-stage optimization problem to obtain the optimal spacecraft mission allocation scheme.

[0013] Furthermore, in this invention, the random variable includes:

[0014] The random vector representing the characteristics of sudden tasks indicates the relevant random factors in task allocation;

[0015] The first-stage decision variables represent the initial resource allocation of the spacecraft for each mission, while reserving basic resources to deal with unforeseen missions.

[0016] The second-stage decision variable represents the amount of adjustment to resources for regular tasks and the amount of resources allocated to sudden tasks when random emergencies actually occur.

[0017] The first-stage cost function represents the cost of allocating initial resources for routine missions and reserving basic resources for contingency missions for the spacecraft.

[0018] A random coefficient matrix with a known probability distribution represents the correlation coefficients of the first-stage decision variables in the second-stage constraints under the actual characteristics of a random, sudden task.

[0019] A fixed coefficient matrix with known constants represents the correlation coefficients of the second-stage decision variables in the second-stage constraints;

[0020] The random right-hand term vector with a known probability distribution represents the target threshold of the resource allocation balance constraint in the second stage under the actual characteristics of random sudden tasks.

[0021] Furthermore, given that the decision variables and random vector values ​​are determined in the first stage, the optimization problem in the second stage is: to minimize the cost of the second stage, satisfy the resource allocation balance constraint and the non-negativity constraint of the adjustment amount, and solve for the optimal adjustment amount.

[0022] Furthermore, the optimization problem in the first stage is to determine the optimal initial resource allocation and minimize the sum of the cost in the first stage and the expected cost in the second stage.

[0023] Furthermore, in step S4, the dual problem of the second-stage optimization problem is determined according to the strong duality theorem, and the optimal cost of the second stage is obtained given the decision variables and random vectors of the first stage.

[0024] Furthermore, in step S4, if the random vector of the sudden task characteristics is a continuous random vector, then the formula for calculating the expected cost of the second-stage optimization problem is:

[0025]

[0026] in, x Indicates the decision variables in the first stage. This is a random vector representing the characteristics of sudden tasks. f ( z )for The probability density function; representing the random vector of sudden task characteristics. The expected value of the optimal cost in the second stage under probability distribution P0; Ω is the random vector of sudden task characteristics. The support set; Q ( x, ) indicates a given x and The optimal cost in the second stage; Q ( x,z ) indicates a given x Compared with the actual value z The optimal cost in the second stage; z represents the random vector of sudden task characteristics. The actual value of;

[0027] If the random vector representing the characteristics of the sudden task is a discrete random vector, then the formula for calculating the expected cost of the second-stage optimization problem is:

[0028]

[0029] in, P ( =z) is a random vector representing the characteristics of sudden tasks. The probability mass function.

[0030] If the random vector representing the characteristics of the sudden task is a discrete random vector, then the formula for calculating the expected cost of the second-stage optimization problem is:

[0031]

[0032] in, P ( =z) is a random vector representing the characteristics of sudden tasks. The probability mass function.

[0033] Furthermore, in step S5, a convex optimization method is used to solve the first-stage optimization problem.

[0034] Furthermore, in step S5, the optimal spacecraft mission allocation scheme is: for any random vector of sudden mission characteristics... Actual value z The spacecraft for the first i The final resource allocation for each task is, where, Indicates the spacecraft's position on the first i Optimal initial resource allocation for each task for y ( z ) in and the i Adjustments related to each task y ( z ) represents the adjustment value under a given state; if As a discrete random vector, it can be directly applied to each possible... z The value is used to calculate the corresponding final resource allocation; if If it is a continuous random vector, then depending on the actual application scenario, for z The range of values ​​is divided, and a corresponding resource allocation adjustment strategy is given for each range.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] (1) This invention constructs a two-stage stochastic programming model. In the first stage, basic resources are reserved for sudden tasks. In the second stage, the resources are dynamically adjusted according to the actual characteristics of the sudden tasks. This not only avoids the defect that deterministic methods cannot cope with sudden tasks, but also overcomes the problem of overly conservative robust optimization methods. It significantly improves the completion rate of sudden tasks (reduces the failure of sudden tasks due to insufficient resources) and the guarantee rate of regular tasks (reduces the idle resources of regular tasks due to excessive reservation of resources).

[0037] (2) This invention transforms the second-stage optimization problem into a dual problem through the dual theory of linear programming. It combines numerical integration (such as Monte Carlo integration, Gaussian integration) or discrete probability weighted summation to quickly calculate the expected cost, avoiding the high sample dependence and complex calculation of traditional stochastic programming methods. The first stage adopts convex optimization method to ensure polynomial time convergence, and the overall computational complexity is reduced from exponential to polynomial level. It can be adapted to medium-scale scenarios containing dozens to hundreds of regular and sudden tasks, and meets the real-time requirements of spacecraft mission allocation.

[0038] (3) This invention achieves the optimal global resource cost for routine tasks and emergency tasks by minimizing the sum of the cost of the first stage and the expected cost of the second stage; through the association mechanism of "preliminary allocation + dynamic adjustment", it formulates differentiated adjustment strategies for different types of random emergency tasks (discrete / continuous characteristics) to ensure that in any emergency scenario, resource allocation can meet the needs of emergency tasks and minimize the losses and adjustment costs of routine tasks (such as energy consumption and time loss of resource reallocation). Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0040] The present invention will be further described below with reference to the accompanying drawings and embodiments. The embodiments of the present invention include, but are not limited to, the following embodiments.

[0041] like Figure 1 As shown, this invention discloses a spacecraft mission allocation method for stochastic, contingent missions. The method addresses the single spacecraft mission allocation problem by first identifying the random variables (such as mission data volume and mission execution time) and their known probability distributions in the spacecraft mission allocation. A two-stage stochastic programming model is then constructed (the first stage is the initial mission allocation decision, and the second stage is the mission adjustment based on the actual values ​​of the random variables). By transforming and solving the model, the optimal spacecraft mission allocation scheme is obtained. This requires determining the variables and parameters in the spacecraft mission allocation:

[0042] 1) Let the decision variables for the first stage be... ,in This is the first phase of the feasible region. x This indicates the initial resource allocation for each mission of the spacecraft (such as the proportion of allocated storage resources and computing resources), while also including reserved resources for contingency missions (such as reserving 10% of storage resources for contingency missions). n For the number of tasks, This represents the initial amount of resources allocated to the first mission by the spacecraft.

[0043] 2) Let the decision variables for the second stage be... ,in A random vector representing the characteristics of sudden tasks (e.g., ...). For the probability of unexpected tasks occurring, For sudden task data volume, Prioritize emergency tasks. Represents a random vector based on the characteristics of sudden tasks. The actual adjustment amount of resource allocation for each task based on the selected value. k For the second stage decision variable dimension, Indicates the first j The values ​​of the second-stage decision variables.

[0044] 3) First-stage cost function This represents the cost of initial resource allocation for a spacecraft (such as resource configuration costs, preparation costs, etc.). c ( x Let ) be a known convex function, for example ,in a i , b i , c i Let be known constants, and represent the secondary cost coefficient, primary cost coefficient, and fixed cost of the initial resource allocation for the i-th task, respectively.

[0045] 4) Random coefficient matrix ,in l This represents the number of constraints in the second phase. The random vector representing the characteristics of sudden tasks is: At that time, the first p The coefficient of the first-stage decision variable in each second-stage constraint, and The probability distribution is known.

[0046] 5) Fixed coefficient matrix , is a known constant matrix. Indicates the first p In the second phase constraint, the first q The coefficients of the second-stage decision variables.

[0047] 6) Random right-hand term vector The random vector representing the characteristics of sudden tasks is: At that time, the first p The right-hand side of each second-stage constraint, and The probability distribution is known.

[0048] 7) The random vector of sudden task characteristics is: probability distribution Known support set ( m (where the dimension is a random vector), and its probability density function f ( z Given (if it is a discrete distribution, then the probability mass function) (Known).

[0049] Next, we construct a two-stage stochastic programming model. First, we explain the second-stage problem, where the decision-making process in the first stage involves random vectors representing unexpected task characteristics. Given a fixed value, the second stage problem is to find the optimal adjustment amount. To minimize the cost of the second phase, i.e.:

[0050] (1)

[0051] In the formula, Indicates a given x and The optimal cost in the second stage; Total cost of Phase Two; constraints This indicates ensuring that resource needs for unforeseen missions are met, meaning that both initial and adjusted resource allocations must meet the actual mission requirements; constraints. This indicates that the adjustment amount is non-negative.

[0052] Next, for the first-stage optimization problem, we first need to determine the optimal initial resource allocation to minimize the sum of the first-stage cost and the expected cost of the second stage, that is:

[0053] (2)

[0054] In the formula, Represents the random vector of characteristics in sudden tasks probability distribution Below, the expected value of the optimal cost in the second stage; for continuous random vectors , , f ( z )for The probability density function; for discrete random vectors , , for The probability mass function.

[0055] The second stage problem is then solved. Since the second stage problem is a linear programming problem (when...), , D , When the condition is determined, according to the duality theory of linear programming, its dual problem is:

[0056] (3)

[0057] In the formula, As dual variables, Indicates the first p The dual price of a second-stage constraint; To find the optimal value for the dual problem, according to the strong duality theorem, when the primal problem is feasible and bounded, ... By solving the dual problem described above, we can obtain... aboutx and The expression is used to prepare for subsequent calculations of the expected cost.

[0058] Subsequently, the expected cost of the second phase is calculated. For the case of continuous random vectors, the above results... Substituting the expression into the expectation formula, we get:

[0059] (4)

[0060] like For about z An integrable function can have its integral calculated using numerical integration methods (such as Monte Carlo integration, Gaussian integration, etc.). Taking Monte Carlo integration as an example, the specific steps are as follows:

[0061] From random vectors probability distribution Extraction N Sample ;

[0062] For each sample Solving the second stage problem yields... ;

[0063] Calculate an approximate value of the expectation:

[0064] For discrete random vectors, if The possible values ​​are The corresponding probability is ,but:

[0065] (5)

[0066] The second-stage problem is solved directly for each possible value, and the expected cost is obtained by summing the probabilities.

[0067] Next, we solve the first-stage optimization problem by substituting the expected cost (5) calculated above into the first-stage optimization model, and obtain:

[0068] (6)

[0069] because c ( x ) is a convex function, and under reasonable assumptions Since the function is also convex, this optimization problem is a convex optimization problem, and can be solved using convex optimization methods (such as gradient descent, Newton's method, interior point method, etc.). Taking gradient descent as an example, the specific steps are as follows:

[0070] 1) Initialize iteration points Set the iteration precision With step size ;

[0071] 2) Calculate the objective function in The gradient at, where ;

[0072] 3) Update iteration points: and ensure ;

[0073] 4) If Then stop iterating. This is the optimal initial resource allocation scheme; otherwise, return to step 2) to continue iterating.

[0074] Finally, the final spacecraft mission allocation scheme is determined. Based on the optimal preliminary resource allocation obtained from the above steps, and combined with the second-stage decision rules, the final spacecraft mission allocation scheme is obtained: for any random vector of sudden mission characteristics... Actual value z The final resource allocation for the first mission by the spacecraft is (in for Middle and the first i The specific adjustments related to each task need to be determined based on... (Definition determined); if For a discrete random vector, the final resource allocation can be calculated directly for each possible value; if As a continuous random vector, the range of values ​​can be divided according to the actual application scenario, and a corresponding resource allocation adjustment strategy can be given for each interval.

[0075] The above embodiments are merely one of the preferred embodiments of the present invention and should not be used to limit the scope of protection of the present invention. Any modifications or refinements made to the main design concept and spirit of the present invention that are not of substantial significance, but solve the same technical problem as the present invention, should be included within the scope of protection of the present invention.

Claims

1. A spacecraft task assignment method for random burst tasks, characterized in that, The method comprises the following steps: S1, determining random variables in spacecraft task allocation and their known probability distribution; S2, constructing a two-stage stochastic programming model; wherein, the first stage is a preliminary task allocation decision, and the second stage is a task adjustment according to actual values of the random variables; S3, converting the two-stage stochastic programming model into two optimization problems, i.e., a first-stage optimization problem and a second-stage optimization problem; S4, simplifying a solving process of the second-stage optimization problem by using a linear programming duality theory, and calculating an expected cost of the second-stage optimization problem; wherein, according to a strong duality theorem, a dual problem of the second-stage optimization problem is determined, and an optimal cost of the second stage when the first-stage decision variable and a sudden task characteristic random vector are given is obtained; If the sudden task characteristic random vector is a continuous random vector, a calculation formula of the expected cost of the second-stage optimization problem is: where x represents the first-stage decision variable, is the probability density function of the random vector z. represents the expected value of the optimal cost of the second stage under the probability distribution P0 of the random vector z. Ω is the support set of the random vector z. Q(x, z) represents the optimal cost of the second stage given x and the actual value z of z. Q(x, z) represents the optimal cost of the second stage given x and the actual value z of z. z represents the actual value of the random vector z.​​ If the sudden task characteristic random vector is a discrete random vector, a calculation formula of the expected cost of the second-stage optimization problem is: where P(z) is the probability mass function of the burst task feature random vector z).​ S5, combining the expected cost of the second-stage optimization problem, solving the first-stage optimization problem, and obtaining an optimal spacecraft task allocation scheme.

2. The spacecraft task allocation method for random burst task according to claim 1, wherein, The random variables comprise: a sudden task characteristic random vector, representing a related random factor in task allocation; a first-stage decision variable, representing a preliminary resource allocation amount of the spacecraft to each task, and reserving a basic resource for coping with a sudden task; a second-stage decision variable, representing an adjustment amount of resource adjustment for a regular task and supplementary resource allocation for a sudden task when the random sudden task actually occurs; a first-stage cost function, representing a cost of the spacecraft for configuring a preliminary resource for a regular task and reserving a basic resource for a sudden task; a random coefficient matrix with known probability distribution, representing a correlation coefficient of the first-stage decision variable in the second-stage constraint under actual characteristics of the random sudden task; a fixed coefficient matrix of known constant, representing a correlation coefficient of the second-stage decision variable in the second-stage constraint; a random right end item vector with known probability distribution, representing a target threshold of the second-stage resource allocation balance constraint under actual characteristics of the random sudden task.

3. The spacecraft task allocation method for random burst tasks according to claim 2, wherein, In a case where the first-stage decision variable and the random vector are determined, the second-stage optimization problem is to minimize the second-stage cost as an object, to satisfy the resource allocation balance constraint and the non-negative adjustment constraint, and to solve the optimal adjustment amount.

4. The spacecraft task allocation method for random burst tasks according to claim 3, wherein, The first-stage optimization problem is to determine the optimal preliminary resource allocation amount and to minimize a sum of the first-stage cost and the second-stage expected cost.

5. The spacecraft task assignment method for random burst task according to claim 4, wherein, In the step S5, a convex optimization solving method is used to solve the first-stage optimization problem.

6. The spacecraft task assignment method for random burst task according to claim 5, wherein, In the step S5, the optimal spacecraft mission allocation scheme is that for any actual value z of the random vector of the mission characteristics , the final resource allocation of the spacecraft for the ith mission is , where represents the optimal initial resource allocation of the spacecraft for the ith mission, is the adjustment amount of y(z) related to the ith mission, and y(z) represents the adjustment amount value in the determined state; if is a discrete random vector, the final resource allocation amount corresponding to each possible z value can be directly calculated; if it is a continuous random vector, the value range of z is divided according to the actual application scenario, and the corresponding resource allocation adjustment strategy is given for each interval.

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