Focused on the dynamic scheduling problem for earth-observing satellites (EOS), an integer programming model is constructed after analyzing the main constraints. The rolling horizon (RH) strategy is proposed according to the independent arriving time and deadline of the imaging tasks. This strategy is designed with a mixed triggering mode composed of periodical triggering and event triggering, and the scheduling horizon is decomposed into a series of static scheduling intervals. By optimizing the scheduling schemes in each interval, the dynamic scheduling of EOS is realized. We also propose three dynamic scheduling algorithms by the combination of the RH strategy and various heuristic algorithms. Finally, the scheduling results of different algorithms are compared and the presented methods in this paper are demonstrated to be efficient by extensive experiments.

The mission of an earth-observing satellite (EOS) is to scout targets with a certain range of ground to produce high-resolution photographs [

Nowadays, EOS is attracting more and more interests worldwide be accompanied with the dramatic increase of the demand for imaging service. One major research trend is that the single satellite used in early reconnaissance is replaced by cooperation of large satellites, yielding the socalled multi-satellite application. Unfortunately, as the number of satellites grows large, the traditional manual coordination will no longer be feasible because multisatellite scheduling (MSS) is an NP-hard combinatorial optimization problem [

There exist numerous studies on scheduling algorithm for multi-satellite to realize automated resource planning. Wang et al. [

However, those above researches have been primarily focused on static scheduling problem of EOSs. It is usually assumed that the imaging tasks have been submitted before scheduling and their information is acquired. In practice, the requests from customers are continuously delivered, which lead to the imaging tasks arriving one by one. The most significant feature of dynamic scheduling is time urgency; that is, the task must be completed within a specified time limit, or it will lose its execution value caused by failure. The satellite imaging reconnaissance mission generally has a deadline, which can reflect its execution urgency. Execution of the task must be completed within the specified deadline; otherwise, the expected benefits will not be obtained. The traditional static scheduling methods tend to overlook the timeliness feature of imaging task, which makes them inapplicable to the dynamic scheduling problem of imaging satellite.

At present, there are a few works on the dynamic scheduling problem of EOSs. Baolin et al. [

It is difficult for these proposed algorithms to generate a task planning within a short time. A dynamic planning process consists of repeated scheduling events, and the traditional intelligence algorithm (IA) has high timing complexity, which cannot rapidly generate the planning scheme. Therefore, the high-efficiency heuristic algorithm should be used to address the dynamic scheduling problem of EOSs.

The impacts of scheduling time on the available tasks were not considered. Since tasks are dynamic arrivals, the planning system collects dissimilar task sets at different scheduling times. Thus, the task set should be determined based on current scheduling time before the scheduling.

The constraints during dynamic scheduling have not been adequately considered. Many constraints (i.e., the storage capacity, maximum swing angle, and continuous observation time) which have been simplified in static scheduling should be considered in dynamic scheduling.

In this paper, we tackle the above challenges imposed on the dynamic scheduling problem of EOSs by handling the impacts of deadline constraint and scheduling time on planning scheme. The integer programming model is constructed based on various constraints in actual reconnaissance activities, and the rolling horizon (RH) strategy and heuristic algorithms are employed to solve this model.

The remainder of this paper is organized as follows. Section

The EOS operates in the space in a certain orbit as shown in Figure

The observation field of EOS.

The purpose in addressing the dynamic scheduling problem of EOSs is to appoint observation resources and execution time for the dynamical submitted tasks with various constraints, so as to maximize the task benefits of reconnaissance activity and minimize the resource consumption as far as possible.

The imaging tasks in dynamic scheduling problem are submitted to the planning system in independent times compared to the static scheduling problem which can obtain all the tasks in advance. The dynamic scheduling system only acquires the information of arrived tasks but can not gain the situation of following tasks. Hence it needs to trigger multiple scheduling in order to cope with the new tasks which are successively submitted to the scheduling system. Therefore, the dynamic scheduling algorithms designed in this paper should have the overall coordination capacity; that is, the algorithm should be able to timely adjust the execution scheme of planned tasks for executing the emergency tasks submitted later, so as to maximize task benefits. For future reference, we summarize main notations used in this paper as the following:

Task =

Sat =

In addition,

The decision of scheduling times is affected by many factors, for example, the quantity and density of task, the upload period of satellite instructions, and the communication capacity of control center. The decision variable of the dynamic scheduling problem provided in this paper is as follows:

Assume

In this paper, the dynamic scheduling algorithm based on the RH strategy [

The basic method of RH strategy is to divide the tasks into multiple task sets with certain overlaps based on the arrival sequence, and the division can be continuously updated along with the scheduling time. Each scheduling will decide and only assign its task set, which is called as rolling horizon. The new tasks are continuously added to the rolling horizon, and the finished tasks are gradually deleted with the advancement of the scheduling time, so as to realize the update of rolling horizon. The advantage of RH strategy is that it can decompose the complicated dynamic scheduling problem into multiple simple static scheduling sub-problems, and the optimization solution of previous problem is replaced with the optimized solutions of sub-problems, so that the complexity of the original problem will be reduced.

In general, tasks will go through four states based on current scheduling time: a new task, waiting task, running task, and finished task. One task may be scheduled in different time, thus the state of task is dynamic; that is, a task might be in two states in different scheduling.

In the example shown in Figure

Task states based on current scheduling time.

The rolling horizon is used to store the tasks that need be scheduled currently. There are two key elements about rolling-horizon: the quantity and state of tasks in rolling-horizon. From the perspective of task quantity, the more the tasks fall into the rolling horizon, the stronger the capacity of scheduling system to obtain comprehensive task information is, which is important to acquire the better solution. But the timing complexity of scheduling algorithm will also be aggravated. From the perspective of task state, the rolling-horizon consists of the running tasks, waiting tasks, and new tasks generally. Among them, the processing method for the running task is an important criterion to distinguish the preemptive and nonpreemptive scheduling. The later scheduling mode is out of the interest of this paper; that is, the rolling-horizon only includes the waiting tasks and new tasks. It should be noticed that during actual scheduling, the rescheduling of waiting task will not consume any additional resources because waiting task has not been executed yet.

The arrangement of scheduling time is the key factor which affects the application efficiency of RH strategy, and it is mainly determined by the trigger mode of scheduling. The general trigger modes include the following types.

(i)

(ii)

(iii)

The mixed-trigger mode is adopted in this paper, and the scheduling time for period factors and event factors is embodied in the elements belonging to

In Algorithm

(1)

(2) RH

(3)

(4)

(5) Add

(6)

(7) Add

(8)

(9)

(10) Sort all task in set RH, and schedule each task by

(11) Add

(12) Update the scheduling decisions;

(13)

The above algorithm needs to assign satellite resources and execution time for each task, so

(1)

(2) Validwindow

(3)

(4)

(5)

(6) Delete

(7)

(8)

(9)

(10) Remove

(11)

(12)

(13) Calculate

(14)

(15) Assign

(16)

(17)

This paper has proposed the heuristic algorithms AIS, DIS, and WIS based on the arrival time priority, the deadline priority, and the waiting time priority inspired by the earlier arrived time first (EAT) algorithm [

Let

After the standardization, we record the basic parameters of

The deadline priority degree of

The waiting time priority degree of

The main steps of the heuristic algorithm adopted in this paper are described as follows.

The three priority degrees of each task in rolling-horizon are calculated.

The tasks in the rolling-horizon are sorted by their different priority-degrees, and the ranking results can be obtained corresponding to the AIS, DIS, and WIS algorithms, respectively.

The assignment strategy based on windows conflict index (WCI) is used to assign satellites and execution time for each task based on ranking results, and the scheduling scheme is generated after all tasks have been assigned.

In the aforementioned steps, WCI denotes the total impact on the unassigned tasks when a task is allocated to an available opportunity window. If

Let

In Algorithm

We incorporate RH strategy with AIS, DIS, and WIS to yield three new algorithms named RH-AIS, RH-DIS, and RH-WIS, respectively. Meanwhile, AIS, DIS, and WIS can also be used to solve the dynamic scheduling problem separately; that is, only new tasks are scheduled in each scheduling by those heuristic algorithms. The six algorithms mentioned before are compared in the following experiment to evaluate the efficiency of the RH strategy.

The proposed algorithms are implemented by Matlab2007 on a laptop with Pentium IV 3.06 GHz CPU, 2 GB memory, and Windows XP operating system. The experimental scenarios are generated randomly for there has been no benchmark in the field of satellite scheduling yield. The operating points of simulated experiment are given as follows [

The reconnaissance activity period is from March 21, 2010, to March 22, 2010, and the scheduling period is two hours; that is,

The imaging tasks are generated in the area with a longitude 0°~150° and latitude −30°~60° randomly. The task quantity varied from 100 to 400. The arrival time gap between two adjacent tasks is subject to the negative exponential distribution, with a density of 0.1. Set the execution value of task from 1 to 10, the required continuous time 3~5 minute, and the occupied storage 2~4 G, and the deadline is a random variable generated between the arrival time of the task and the ending time of the observation activity, which abides by the uniform distribution.

The satellite quantity varied from 4 to 6, the memory storage is 240 G, the field angle is 3°, the maximum sway angle is 35°, the maximum tilting angle is 40°, and the maximum number of position transfers within a single orbit is no more than 5.

For the convenience of description, the dynamic scheduling problem of

Simulation results in different scenarios.

Problem scale | RH-CIS | RH-DIS | RH-AIS | CIS | DIS | AIS | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Task |
Guarantee |
Task |
Guarantee |
Task |
Guarantee |
Task |
Guarantee |
Task |
Guarantee |
Task |
Guarantee | |

100 × 4 | 396 | 0.672 | 401 | 0.683 | 397 | 0.674 | 382 | 0.642 | 397 | 0.677 | 396 | 0.673 |

100 × 5 | 412 | 0.705 | 417 | 0.716 | 416 | 0.713 | 401 | 0.681 | 416 | 0.713 | 409 | 0.698 |

100 × 6 | 425 | 0.733 | 430 | 0.745 | 424 | 0.729 | 408 | 0.696 | 426 | 0.726 | 424 | 0.729 |

200 × 4 | 679 | 0.622 | 672 | 0.613 | 633 | 0.574 | 559 | 0.497 | 559 | 0.497 | 554 | 0.492 |

200 × 5 | 746 | 0.691 | 740 | 0.682 | 699 | 0.638 | 611 | 0.553 | 611 | 0.553 | 610 | 0.550 |

200 × 6 | 804 | 0.741 | 813 | 0.754 | 763 | 0.707 | 688 | 0.625 | 688 | 0.625 | 693 | 0.637 |

300 × 4 | 808 | 0.492 | 813 | 0.506 | 725 | 0.442 | 665 | 0.409 | 663 | 0.405 | 658 | 0.392 |

300 × 5 | 890 | 0.551 | 900 | 0.562 | 812 | 0.506 | 745 | 0.458 | 744 | 0.453 | 736 | 0.450 |

300 × 6 | 1027 | 0.649 | 1021 | 0.642 | 933 | 0.580 | 873 | 0.541 | 877 | 0.549 | 860 | 0.531 |

400 × 4 | 897 | 0.423 | 895 | 0.413 | 801 | 0.366 | 729 | 0.339 | 722 | 0.332 | 717 | 0.326 |

400 × 5 | 992 | 0.468 | 990 | 0.461 | 876 | 0.403 | 815 | 0.377 | 802 | 0.370 | 800 | 0.364 |

400 × 6 | 1152 | 0.549 | 1143 | 0.541 | 1025 | 0.487 | 959 | 0.448 | 953 | 0.441 | 946 | 0.435 |

From Table

From Figure

Search time of algorithm in different satellite quantities.

The satellite number is 4

The satellite number is 5

The satellite number is 6

Set the scheduling period from one to twelve hours in order to analyze the impact of scheduling time interval on the overall performance of planning algorithm. The six algorithms are tested in different problem scales and shown in Figure

Performance of algorithms in different problem scales.

Problem scale

Problem scale

Problem scale

Problem scale

Problem scale

Problem scale

Problem scale

Problem scale

Problem scale

Problem scale

Problem scale

Problem scale

From Figure

This paper has studied the dynamic scheduling problem of EOSs. An integer programming model has been constructed by considering the independent arrival time and deadline of the imaging tasks. A dynamic scheduling algorithm based on the RH strategy which can be combined with multiple heuristic algorithms proposed in many researches and its timing complexity has been analyzed.

The scheduling algorithms adapted to RH strategy can effectively adjust to the planning scheme based on the satellite workload to execute the emergency tasks. The effectiveness of this strategy has been verified by comparing the scheduling results of six algorithms in the experiment. It is worth to restate that the RH strategy might cause a high time consumption to yield an optimized scheme if a large amount of tasks are involved in the scheduling system. This problem can be solved by limiting the size of the rolling horizon.

Also for our future work, we plan to research the detection method of scheduling time, which is a significant factor to impact the performance of scheduling algorithm and system. With the method in place, we will extend our algorithm to cooperative scheduling of EOSs; we will consider Qos requirements in our RH-WIS; we are going to combine the dynamic resources management into our scheme.