Spacecraft target access optimization task stopping method based on local search and exploration enhancement

Abstract

The invention discloses a method for stopping a spacecraft target access optimization task based on local search and exploration enhancement, and belongs to the technical field of spacecraft control. In order to solve the problem of optimization termination control with robustness and self-adaptability, an optimization termination criterion is designed to terminate iterative optimization of Bayesian optimization when the maximum prediction standard deviation of a Gaussian process regression agent model in a current local area is lower than a preset threshold value; the design optimization termination criterion is embedded into the BO; measuring the cognitive uncertainty of the GPR agent model to the target function at a certain point by using the prediction standard deviation of the GPR agent model; and setting a judgment condition for judging whether to enhance the exploration enhancement capability of the acquisition function and whether to trigger local evaluation. According to the invention, optimization termination control with robustness and self-adaptability is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of spacecraft control, and in particular relates to a method for stopping a spacecraft target access optimization task based on local search and exploration enhancement. Background Art

[0002] In space target access mission planning, a spacecraft must achieve rapid rendezvous and transfer with multiple space targets while maintaining known start and end orbits. The total velocity increment of the spacecraft during the transfer process directly determines fuel consumption, which in turn affects the cost and feasibility of the entire access mission, making it necessary to optimize it. When using a multi-pulse transfer method, the velocity increment between two points cannot be expressed analytically due to the introduction of multiple orbit change nodes, requiring numerical optimization to obtain the optimal solution. If such complex trajectory optimization is embedded in the access sequence planning process, it will seriously affect computational efficiency. Therefore, when optimizing the total velocity increment using Bayesian Optimization (BO), effectively terminating the optimization iteration early will play a key role in the overall computational efficiency of the problem.

[0003] BO is a global optimization method for designing black-box functions that are expensive, non-differentiable, or lack explicit expressions. BO uses a surrogate model (typically a Gaussian process regression (GPR)) to approximate the objective function. Using a collection function, BO selects sample points with the greatest potential for improvement based on the surrogate model, effectively approaching the global optimal solution within a limited number of function evaluations. This method has been widely used in resource-intensive tasks such as hyperparameter tuning, experimental design, reinforcement learning, and robotic control.

[0004] In practical applications, BO often relies on a preset maximum number of iterations or time budget as a termination criterion. However, its optimization results are highly sensitive to the number of iterations: too many iterations lead to unnecessary resource overhead, while insufficient iterations can lead to stuck in a local optimum. In practice, BO is difficult to predefine a reasonable maximum number of iterations or time budget due to factors such as the complexity of the objective function, the selection strategy and guidance capabilities of the acquisition function, and the surrogate model's modeling accuracy and uncertainty representation capabilities. This suggests that BO termination should be dynamically adaptable rather than relying on static settings.

[0005] How to design a reasonable and effective termination criterion is a relatively underestimated but highly practical problem in BO research. Currently, there are the following methods: (1) An intuitive strategy is: if the optimal value of the objective function does not improve significantly in several consecutive iterations, the optimization process is considered to have stabilized and can be terminated early. (2) Other studies have proposed termination criteria based on expected improvement (EI) and (3) probability of improvement (PI) starting from the acquisition function, that is, when the improvement value is lower than the set threshold, the optimization is terminated. (4) Some researchers have proposed a strategy based on the difference between the upper and lower confidence bounds of the GPR model to measure whether there are still high-potential areas in the space to avoid premature termination. (5) Another method introduces a backtracking mechanism. When multiple consecutive sampling points are concentrated in a local convex area and the local regret value is lower than the preset threshold, it is judged that the area has been fully explored and the optimization is terminated.

[0006] Existing technologies have the following deficiencies and limitations in practical applications: (1) The termination strategy is highly sensitive to the number of iterations. When the preset number of iterations is too high, it may cause unnecessary resource consumption; when the number of iterations is insufficient, it may fall into a local optimum, affecting the optimization effect. (2) The threshold setting lacks universality and adaptability. The early stopping strategy based on the change of the single-point optimal value or the sampling function value relies on empirical settings for threshold selection, lacks the ability to adapt to the complexity of the objective function, and is prone to misjudging the convergence state. (3) The error of the proxy model has a significant impact on the termination criterion. When the Gaussian process proxy model has insufficient fitting accuracy or oscillation fluctuations, it may cause premature termination or delayed termination, affecting the optimization performance. (4) The local convexity criterion is not applicable in high-dimensional space. Existing methods assist termination by judging the concentration of local sampling distribution and regret value, but it is difficult to effectively determine whether the local area has been fully explored in high-dimensional space, and lacks the ability to jump out of the local optimum. The overall optimization performance needs to be improved. Therefore, the applicability and stability of the existing Bayesian optimization termination strategy in complex spatial target access tasks are still limited. There is an urgent need to propose an optimization termination control method that is both robust and adaptive to improve the overall computational efficiency and convergence performance. Summary of the Invention

[0007] The problem to be solved by the present invention is to realize optimization termination control with both robustness and adaptability, and propose a stopping method for spacecraft target access optimization task based on local search and exploration enhancement.

[0008] To achieve the above object, the present invention is implemented through the following technical solutions: A stopping method for spacecraft target access optimization task based on local search and exploration enhancement is designed. The optimization termination criterion is designed to be when the maximum prediction standard deviation of the GPR proxy model in the current local area is lower than the preset threshold. When , terminate the iterative optimization of BO; embed the design optimization termination criterion into BO.

[0009] Furthermore, the prediction standard deviation of the GPR proxy model is used To measure the GPR agent model's performance on the objective function Epistemic uncertainty at a certain point; setting judgment conditions to determine whether to enhance the exploration enhancement capability of the acquisition function and whether to trigger local evaluation; Condition 1: First, the current optimal solution is required In continuous No improvement in the first iteration, the second requirement is that the GPR agent model is the current optimal solution The forecast standard deviation of satisfies the following constraints: ; in, is the preset threshold, is the number of consecutive iterations of the current optimal solution; If condition 1 is met, the exploration capability of the acquisition function is enhanced; if not, the termination judgment of this iteration is terminated; Condition 2: Based on the premise that the exploration capability of the acquisition function is enhanced by satisfying condition 1, it is determined whether to perform local evaluation; Condition 2 is to perform local evaluation when the maximum uncertainty in the local area meets the following constraints, which is expressed as: ; Among them, max is the maximum value function, is the decision vector, for The domain of Represents the domain middle The maximum value of , here we use the particle swarm optimization algorithm for approximate calculation; If condition 2 is met, a local evaluation of the optimal solution neighborhood is performed; if not, condition 3 is performed. Condition 3: When condition 2 is not met, it is considered that the prediction of the GPR proxy model in the local area has a considerable confidence level. At this time, if the mean satisfies the following constraints, the subsequent BO iteration is terminated. The expression is: ; in, represents the maximum predicted mean in the local evaluation area, Represents the maximum predicted mean in the entire domain, with a preset deviation .

[0010] Furthermore, a specific implementation method of embedding the design optimization termination criterion into BO includes the following steps: S1. Given the objective function , domain , the initial number of samples , the maximum number of evaluations , termination parameters; S2. Internal Collection An initial sample and use Perform evaluation and obtain the initial training data set ; S3. Based on Train the GPR agent model; S4. Optimizing the acquisition function based on the GPR proxy model , get candidate solutions ; S5. Evaluation The objective function value of ,renew , then returns to step S2 for the next round of iterative optimization, and repeats the above process until the termination criterion is met.

[0011] Furthermore, the method for enhancing the exploration capability of the acquisition function includes the following steps: Current optimal value continuous If there is no improvement in the first iteration, the acquisition function is enhanced The exploration ability of The exploration ability is enhanced, and each time it is enhanced, the exploration-utilization balance coefficient Updated to: ; in, is the inverse of the standard normal cumulative distribution function, is the basic confidence level, is the maximum enhancement degree of confidence level, which is the maximum confidence level and the basic confidence level difference, is the number of exploration enhancements that have been performed so far, and .

[0012] Furthermore, the method for performing local evaluation of the neighborhood of the optimal solution includes the following steps: For the current optimal solution , with the current optimal solution as the center, construct a hypercube with a side length of as the local evaluation space , and in Use Latin hypercube sampling to obtain sampling points; Using the objective function right Sampling points are evaluated and the training sample set is updated and optimal data pair ,in, ; Side length of the hypercube for: ; in, The domains are The upper and lower bounds of ,and ; Number of sampling points ,in, is the decision variable The dimension of ,and Round up.

[0013] Beneficial effects of the present invention: The present invention describes a termination method for spacecraft target access optimization tasks based on enhanced local search and exploration. This method effectively avoids the risk of falling into local optimality during the optimization process and accelerates local convergence while maintaining global search capabilities. By dynamically enhancing the exploratory nature of the acquisition function when the optimal target value fails to improve over multiple rounds, combined with local evaluation of the neighborhood of the current optimal solution to determine the optimization trend, dynamic control of the optimization process is achieved. When the prediction uncertainty of the proxy model in a local area falls below a set threshold, a termination mechanism is automatically triggered, effectively reducing unnecessary computational overhead and improving overall optimization efficiency and performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a flow chart of the present invention; Figure 2 It is the local optimal and local evaluation graph considered by GP; Figure 3 is the local evaluation graph of GP at the current optimal solution; Figure 4 The figures are comparative diagrams of the termination situations of different algorithms of the present invention, wherein (a) is the termination situation diagram of the algorithm when the termination threshold is low; (b) is the termination situation diagram of the algorithm when the termination threshold is medium; and (c) is the termination situation diagram of the algorithm when the termination threshold is high. DETAILED DESCRIPTION

[0015] In order to make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain the present invention and are not intended to limit the present invention. That is, the specific embodiments described herein are only some embodiments of the present invention, not all embodiments. Generally, the components of the specific embodiments of the present invention described and illustrated in the drawings herein can be arranged and designed in various different configurations, and the present invention can also have other embodiments.

[0016] Therefore, the following detailed description of the specific embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but is merely representative of selected specific embodiments of the present invention. All other specific embodiments obtained by those skilled in the art based on the specific embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0017] In order to further understand the content, features and effects of the present invention, the following specific embodiments are given as examples, and the attached Figure 1 -Attached Figure 4 The detailed instructions are as follows:

[0018] Example 1: A stopping method for spacecraft target access optimization task based on local search and exploration enhancement is designed. The optimization termination criterion is designed to be when the maximum prediction standard deviation of the GPR proxy model in the current local area is lower than the preset threshold. When , terminate the iterative optimization of BO; embed the design optimization termination criterion into BO.

[0019] Furthermore, the predicted standard deviation of the GPR proxy model is used to Measuring the GPR agent model's performance on the objective function Epistemic uncertainty at a certain point; setting judgment conditions to determine whether to enhance the exploration enhancement capability of the acquisition function and whether to trigger local evaluation; Condition 1: First, the current optimal solution is required In continuous No improvement in the first iteration, the second requirement is that the GPR agent model is the current optimal solution The forecast standard deviation of satisfies the following constraints: ; in, is the preset threshold, is the number of consecutive iterations of the current optimal solution; If condition 1 is met, the exploration capability of the acquisition function is enhanced; if not, the termination judgment of this iteration is terminated; Condition 2: Based on the premise that the exploration capability of the acquisition function is enhanced by satisfying condition 1, it is determined whether to perform local evaluation; Condition 2 is to perform local evaluation when the maximum uncertainty in the local area meets the following constraints, which is expressed as: ; Among them, max is the maximum value function, is the decision vector, for The domain of Represents the domain middle The maximum value of , here we use the particle swarm optimization algorithm for approximate calculation; If condition 2 is met, a local evaluation of the optimal solution neighborhood is performed; if not, condition 3 is performed. Condition 3: When condition 2 is not met, it is considered that the prediction of the GPR proxy model in the local area has a considerable confidence level. At this time, if the mean satisfies the following constraints, the subsequent BO iteration is terminated. The expression is: ; in, represents the maximum predicted mean in the local evaluation area, Represents the maximum predicted mean in the entire domain, with a preset deviation .

[0020] Furthermore, a specific implementation method of embedding the design optimization termination criterion into BO includes the following steps: S1. Given the objective function , domain , the initial number of samples , the maximum number of evaluations , termination parameters; Furthermore, given the objective function , if the optimization goal is to maximize its evaluation value, the problem can be formally expressed as: ; Among them, the decision vector for dimensional real vector, domain ,function ; S2. Internal Collection An initial sample and use Perform evaluation and obtain the initial training data set ; Furthermore, for the training dataset ,in is independent and identically distributed Gaussian random noise; the posterior distribution of GPR It also obeys the Gaussian distribution, so given a new observation point set When , the predicted mean and predicted variance of the objective function are: ; in, for Meet the training point The covariance of is the covariance between observation points, is the covariance between training points, is the predicted value of the noise variance, .

[0021] S3. Based on Train the GPR agent model; Furthermore, the construction is based on The GPR agent model is used to approximate the objective function .

[0022] S4. Optimize the acquisition function based on the GPR proxy model to obtain candidate solutions ; Optimize acquisition function The acquisition function is used to balance exploration and utilization and quantify the potential benefits of candidate query points. BO determines the next evaluation point by maximizing the acquisition function: ; Common acquisition functions include upper confidence bound (UCB), expected improvement, improvement probability, and entropy search (ES), where UCB is expressed as: ; in, is a hyperparameter that balances exploration and exploitation.

[0023] S5. Evaluation The objective function value of ,renew , then returns to step S2 for the next round of iterative optimization, and repeats the above process until the termination criterion is met.

[0024] Further, update the training dataset , determine the next evaluation point After that, BO evaluates the point and obtains the observation value , and the new data Add to the training dataset ; Furthermore, during the BO iteration process, the current optimal value When there is no improvement in multiple consecutive iterations, two situations may occur: (1) The algorithm is stuck in the objective function The local optimal solution is difficult to jump out; (2) it is close to or has reached the global optimal solution. For the first case, in order to avoid repeated sampling and evaluation of the algorithm at this point, the exploration ability of the acquisition function can be enhanced to help the algorithm jump out of the local area. It is particularly important to point out that the local optimal here not only refers to the local optimality of the objective function itself, but also includes the false local optimality generated by the GPR proxy model due to inaccurate modeling. As shown in Figure 2, there is a significant difference between the global optimal estimate of the GPR model and the local optimal solution and the global optimal solution of the true objective function. This phenomenon usually stems from insufficient evaluation of sample points in the neighborhood, resulting in the proxy model failing to fully learn the local characteristics of the objective function, making the proxy model's fitting accuracy in this area insufficient. To this end, as shown in Figure 3, a local dense sampling strategy is introduced to effectively improve the fitting accuracy of the proxy model by directional enhanced evaluation in the candidate optimal area, thereby accelerating convergence. It should be emphasized that the enhancement of the exploration ability of the acquisition function has an upper limit, and local dense sampling should not be performed indefinitely. Therefore, a theoretically based optimization termination criterion is given; Furthermore, the method for enhancing the exploration capability of the acquisition function includes the following steps: Current optimal value continuous If there is no improvement in the first iteration, the acquisition function is enhanced The exploration ability of The exploration ability is enhanced, and each time it is enhanced, the exploration-utilization balance coefficient Updated to: ; in, is the inverse of the standard normal cumulative distribution function, is the basic confidence level, is the maximum enhancement degree of confidence level, which is the maximum confidence level and the basic confidence level difference, is the number of exploration enhancements that have been performed so far, and .

[0025] Furthermore, the method for performing local evaluation of the neighborhood of the optimal solution includes the following steps: For the current optimal solution , taking the current optimal solution as the center, construct a The hypercube is used as the local evaluation space , and in Use Latin hypercube sampling to obtain sampling points; Using the objective function right Sampling points are evaluated and the training sample set is updated and optimal data pair ,in, ; Side length of the hypercube for: ; in, The domains are The upper and lower bounds of ; Number of sampling points ,in, is the decision variable The dimension of ,and Round up.

[0026] The present embodiment is described with examples as follows: 1. First, take the benchmark test set as an example to illustrate the effectiveness of the present invention.

[0027] The classic test functions Ackley, Levy, Schwefel, and Rastrigin, which are widely used in the field of optimization, are selected and tested in the dimensions Set the maximum number of evaluations. , where the initial evaluation amount is . And three hyperparameter optimization problems widely used in the field of machine learning to verify the performance of BO were used for testing, namely support vector machine (SVM) with =2, =5 Multi-layer perceptron (MLP) and =8 The other settings are the same as the test function.

[0028] The following two indicators are used to evaluate the effectiveness of the termination method: (1) Relative computational cost: ; in, Indicates the number of times the BO is evaluated when the termination method terminates. The smaller the value, the less evaluation budget the termination method spends.

[0029] (2) Relative performance loss: ; in, and Indicates BO completion The best and worst solutions in the evaluation process, Represents the optimal solution when the termination method is used. The smaller the value, the less optimization performance is lost by the termination method.

[0030] use Indicates the low, medium and high termination thresholds set by each method. Table 1 shows the cost consumption and performance loss of different termination methods when BO is terminated, respectively. As can be seen from the table, method 1 has the lowest cost, followed by the method of this embodiment, but the performance loss of the method of this embodiment is about 5% lower than that of method 1. Although the median index is small, its cost consumption is the most unstable and the performance loss is the largest. In addition, the performance loss of the method in this embodiment is The time is shorter than all other methods, and due to the effects of exploration enhancement and local evaluation, better optimization results will appear than the original BO.

[0031] Table 1 Different methods Significance Assessment

[0032] Table Notes: The significance level is set at 0.05. The symbol indicates that the method of this embodiment is significantly better than other methods. If the results are in agreement, it means that other methods are significantly better than the method in this embodiment.

[0033] 2. Then, the method of this embodiment is applied to space target access mission planning: In this task, is the number of pulses applied, and the decision variables include the time when each pulse is applied and the applied pulse vector , where the last two pulses can be determined based on and It is obtained by solving a two-point boundary value problem. Its optimization objective is the total velocity increment: ; To accurately model this type of orbital transfer process, a spacecraft rendezvous and transfer simulation model that can apply multiple velocity pulses is used to evaluate the total velocity increment and trajectory feasibility under different transfer strategies. The relevant parameters are shown in Table 2: Table 2 Spacecraft rendezvous and transfer model parameters

[0034] Set the number of pulses applied to As shown in Figure 4, Method 1 terminates first, followed by Method 4. Although the method of this embodiment terminates later, it achieves the best optimization performance at termination. The remaining methods exhaust all evaluation times and exhibit inferior optimization performance compared to the method of this embodiment, consistent with the analysis in the first section. This further demonstrates the advantages of the method of this embodiment in maintaining optimization performance and effectively reducing optimization costs.

[0035] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.

[0036] Although the present application has been described above with reference to specific embodiments, various modifications may be made thereto and components may be substituted with equivalents without departing from the scope of the present application. In particular, as long as there are no structural conflicts, the various features of the embodiments disclosed herein may be combined with each other in any manner, and the omission of an exhaustive description of these combinations in this specification is solely for the sake of space and resource conservation. Therefore, the present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions within the scope of the claims.

Claims

1. A stopping method for a spacecraft target access optimization task based on local search and exploration enhancement, characterized in that: The optimization termination criterion is designed to be when the maximum prediction standard deviation of the GPR proxy model in the current local area is lower than the preset threshold. When , terminate the iterative optimization of BO; embed the design optimization termination criterion into BO.

2. The method for stopping a spacecraft target access optimization task based on local search and exploration enhancement according to claim 1, characterized in that: Forecast standard deviation using the GPR proxy model Measuring the GPR agent model's performance on the objective function Epistemic uncertainty at a certain point; setting judgment conditions to determine whether to enhance the exploration enhancement capability of the acquisition function and whether to trigger local evaluation; Condition 1: First, the current optimal solution is required In continuous No improvement in the first iteration, the second requirement is that the GPR agent model is the current optimal solution The forecast standard deviation of satisfies the following constraints: in, is the preset threshold, is the number of consecutive iterations of the current optimal solution; If condition 1 is met, the exploration capability of the acquisition function is enhanced; if not, the termination judgment of this iteration is terminated; Condition 2: Based on the premise that the exploration capability of the acquisition function is enhanced by satisfying condition 1, it is determined whether to perform local evaluation; Condition 2 is to perform local evaluation when the maximum uncertainty in the local area meets the following constraints, which is expressed as: Among them, max is the maximum value function, is the decision vector, for The domain of Represents the domain middle The maximum value of , here we use the particle swarm optimization algorithm for approximate calculation; If condition 2 is met, a local evaluation of the optimal solution neighborhood is performed; if not, condition 3 is performed. Condition 3: When If the constraint is not satisfied, it means that the prediction of the GPR proxy model in the local area has a considerable confidence level. At this time, if the mean satisfies the following constraint, the subsequent BO iteration is terminated. The expression is: in, represents the maximum predicted mean in the local evaluation area, Represents the maximum predicted mean in the entire domain, with a preset deviation .

3. The method for stopping a spacecraft target access optimization task based on local search and exploration enhancement according to claim 2, characterized in that: The specific implementation method of embedding the design optimization termination criterion into BO includes the following steps: S1. Given the objective function , domain , the initial number of samples , the maximum number of evaluations , termination parameters; S2. Internal Collection An initial sample and use Perform evaluation and obtain the initial training data set ; S3. Based on Train the GPR agent model; S4. Optimizing the acquisition function based on the GPR proxy model , get candidate solutions ; S5. Evaluation The objective function value of ,renew , then returns to step S2 for the next round of iterative optimization, and repeats the above process until the termination criterion is met.

4. The method for stopping a spacecraft target access optimization task based on local search and exploration enhancement according to claim 3, characterized in that: The method for enhancing the exploration capability of the acquisition function includes the following steps: Current optimal value continuous If there is no improvement in the first iteration, the acquisition function is enhanced The exploration ability of The exploration ability is enhanced, and each time it is enhanced, the exploration-utilization balance coefficient Updated to: in, is the inverse of the standard normal cumulative distribution function, is the basic confidence level, is the maximum enhancement degree of confidence level, which is the maximum confidence level and the basic confidence level difference, is the number of exploration enhancements that have been performed so far, and .

5. The method for stopping a spacecraft target access optimization task based on local search and exploration enhancement according to claim 4, characterized in that: The method for local evaluation of the neighborhood of the optimal solution includes the following steps: For the current optimal solution , taking the current optimal solution as the center, construct a The hypercube is used as the local evaluation space , and in Use Latin hypercube sampling to obtain sampling points; Using the objective function right Sampling points are evaluated and the training sample set is updated and optimal data pair ,in, ; Side length of the hypercube for: in, 、 The domains are The upper and lower bounds of ,and ; Number of sampling points ,in, is the decision variable The dimension of ,and Round up.

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