1.题目和关键词
Title:
A pure proactive scheduling algorithm for multiple earth observation satellites under uncertainties of clouds
云不确定下的多对地观测卫星的纯主动调度算法
Keywords:
earth observation satellites 对地观测卫星
uncertainties of clouds 云不确定
proactive scheduling 主动调度
chance constraint programming 机会约束规划
sample approximation 样本近似
branch and cut 分支-切割
2.摘要
Most earth observation satellites (EOSs) are equipped with optical sensors, which cannot see through the clouds. Hence, observations are significantly affected and blocked by clouds. In this work, with the inspiration of the notion of a forbidden sequence, we propose a novel assignment formulation for EOS scheduling. Considering the uncertainties of clouds, we formulate the cloud coverage for observations as stochastic events, and extend the assignment formulation to a chance constraint programming (CCP) model. To solve the problem, we suggest a sample approximation (SA) method, which transforms the CCP model into an integer linear programming (ILP) model. Subsequently, a branch and cut (B&C) algorithm based on lazy constraint generation is developed to solve the ILP model. Finally, we conduct a lot of simulation experiments to verify the effectiveness and efficiency of our proposed formulation and algorithm.
大多数的对地观测卫星都装有光学传感器，然而它们无法透过云层。因此，观测受到了云层极大的影响和阻碍。在这项工作中，受到禁用序列概念的启发，我们提出了一个新的EOS调度分配公式。考虑到云的不确定性，我们将云覆盖作为观测的随机事件，并且将分配公式扩展到机会约束规划 (CCP)模型中。为了解决这个问题，我们提出了样本近似方法，将CCP模型转化为整数线性规划(ILP)模型。随后，提出基于懒惰约束生成的分支-切割(B&C) 算法来求解ILP模型。最后，我们在大量仿真实验的基础上证实了我们提出的公式和算法的有效性和效率。
3.创新性
In this study, we firstly propose a novel assignment formulation of EOS scheduling, in which the energy constraints are formulated as forbidden sequences. Considering the uncertainties of clouds, we formulate the cloud coverage for each time window of observation as a stochastic event, and extend the assignment formulation to a chance constraint programming (CCP) model. The sample approximation (SA) method is applied to transform the CCP problem into an integer linear programming (ILP) problem, say the SA problem. With respect to the characteristics of the SA problem, a branch and cut (B&C) algorithm based on lazy constraint generation is designed. Afterwards, a large number of experiments by simulation are conducted to verify the effectiveness and efficiency of the sample approximation and the B&C algorithm.
在这项研究中，我们首次提出了一种新的EOS调度分配公式，其中能量约束被表示为禁用序列。考虑到云的不确定性，我们把每个观测时间窗中的云覆盖作为一个随机事件，并把分配公式推广到机会约束规划模型中。把CCP问题通过样本近似的方法转化为整数线性规划(ILP)问题，称为SA问题。根据SA问题的特征，设计了基于懒惰约束生成的分支-切割(B&C)算法。然后，大量的仿真实验证明了样本近似算法和B&C算法的有效性和效率。
4.结论和展望
In this paper, considering the uncertainties of clouds, we formulated the cloud blocks for observations as stochastic events, and then investigated the scheduling of multiple EOSs. After the comparisons of time-indexed, flow and assignment formulations, we proposed a novel assignment formulation with the inspiration of the notion of a forbidden sequence, which has less variables and less constraints. Subsequently, under the uncertainties of clouds, we extended the assignment formulation to a chance constraint programming model. To solve the CCP model, we transformed the model into an integer linear programming model by sample approximation. Afterwards, with lazy constraint generation, we suggested a branch and cut algorithm to solve the sample approximation problem. Finally, a great number of simulation experiments were conducted to verify the effectiveness and feasibility of the sample approximation method and the B&C algorithm.
在本文中，考虑到云的不确定性，我们把云团当作观测的随机事件，接着对多EOSs的调度进行研究。经过时间索引、流量和分配公式的比较后，我们受到禁用序列概念的启发，提出了一种新的分配公式，它具有更少的变量和约束。随后，在云的不确定性下，我们把分配公式推广到机会约束规划模型中。为了求解CCP模型，我们通过样本近似方法把模型转化为整数线性规划模型。然后，基于懒惰约束生成，我们提出了分支-切割算法来求解样本近似问题。最后，通过大量的仿真实验证明了样本近似方法和B&C算法的有效性和可行性。
In the future, we will consider the scheduling of agile EOSs under uncertainties. Different from the non-agile satellites in this study, the agile satellites do not only have the maneuverability of slewing, but also the maneuverability of pitching, along with the orbit. Hence, the satellite will have a long time window for observation. Consequently, we need not only allocate the tasks to the orbits, but also need to decide the start and finish times. In addition, for a unique window, the impact of clouds for different parts will be different, which will make the problem more complicated.
在未来，我们将考虑到不确定性下的敏捷EOSs调度。和本研究中的非敏捷卫星不同的是，敏捷卫星沿着轨道，不仅具有旋转的机动性，也具有俯仰的机动性。因此，卫星将有一个很长的观测时间窗口。因此，我们不仅需要将任务分配给轨道，还需要确定开始和结束的时间。另外，对于一个特定的窗口，云对不同部分的影响是不同的，这将使问题更加复杂。