Mathematical Problems in Engineering

Volume 2015, Article ID 731734, 31 pages

http://dx.doi.org/10.1155/2015/731734

## Imaging-Duration Embedded Dynamic Scheduling of Earth Observation Satellites for Emergent Events

^{1}State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, Beijing 100875, China^{2}Key Laboratory of Environment Change and Natural Disaster, Ministry of Education, Beijing Normal University, Beijing 100875, China^{3}School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China

Received 22 December 2014; Revised 9 May 2015; Accepted 13 May 2015

Academic Editor: Ivanka Stamova

Copyright © 2015 Xiaonan Niu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We present novel two-stage dynamic scheduling of earth observation satellites to provide emergency response by making full use of the duration of the imaging task execution. In the first stage, the multiobjective genetic algorithm NSGA-II is used to produce an optimal satellite imaging schedule schema, which is robust to dynamic adjustment as possible emergent events occur in the future. In the second stage, when certain emergent events do occur, a dynamic adjusting heuristic algorithm (CTM-DAHA) is applied to arrange new tasks into the robust imaging schedule. Different from the existing dynamic scheduling methods, the imaging duration is embedded in the two stages to make full use of current satellite resources. In the stage of robust satellite scheduling, total task execution time is used as a robust indicator to obtain a satellite schedule with less imaging time. In other words, more imaging time is preserved for future emergent events. In the stage of dynamic adjustment, a compact task merging strategy is applied to combine both of existing tasks and emergency tasks into a composite task with least imaging time. Simulated experiments indicate that the proposed method can produce a more robust and effective satellite imaging schedule.

#### 1. Introduction

Recently, earth observing satellites (EOSs) are widely used in applications for national defense, environmental protection, agriculture, meteorology, urban construction, and other fields. However, satellite resources are still scarce with respect to the increasing human demands for imaging. As a result, the process of satellite mission scheduling, which is used to allocate the observation resources and execution time to a series of imaging tasks by maximizing one or more objectives while satisfying certain given constraints, plays an important role in the management of satellites. The scheduling can be primarily divided into static scheduling and dynamic scheduling. The static scheduling assumes that all imaging tasks have been submitted before scheduling, and once the scheduling scheme is produced, it is immutable until all tasks have been finished. In practice, because of several unexpected factors, such as a thick cloud cover, resource changes, and new tasks arrival, the initial scheduling scheme must be adjusted dynamically; such scheduling is called dynamic scheduling. However, either static scheduling or dynamic scheduling is a complex combination optimization problem that has been proved to be NP-complete [1].

Over the last several decades, development of methods to perform satellite mission scheduling has been intensively investigated, most of which are focused on the static scheme. The algorithms to solve the problem can be mainly divided into exact methods and approximate methods. The approximate methods include the intelligent optimization algorithms and rule-based heuristic algorithms. The exact methods, such as dynamic programming, the branch-and-bound algorithm, and the Russian Doll Search, were used mostly at the early stage of satellite scheduling. Verfaillie et al. viewed earth observation satellite scheduling as a valued constraint satisfaction problem and developed the Russian Doll Search to solve it [2]. Ovacik and Uzsoy decomposed the scheduling problem into many subproblems and solved these subproblems to the optimality by a branch-and-bound algorithm [3]. Bensana et al. applied a number of global search approaches, including the depth first branch-and-bound algorithm, the best first branch-and-bound algorithm, and the Russian Doll Search, to obtain the solution for the Spot5 daily scheduling problem [4]. The exact methods can provide optimal solutions. However, these exact methods can only solve small-scaled problems. The approximate methods, that is, the intelligent optimization algorithms and rule-based heuristic algorithms, are aimed at identifying good solutions that may not be optimal. The intelligent optimization algorithms primarily included the Tabu search algorithm, the genetic algorithm, the evolutionary algorithm, simulated annealing, the Lagrangian relaxation technique, and the hybrid ant colony optimization method. Vasquez and Hao translated the scheduling problem into the well-known knapsack model. They proposed a Tabu search algorithm to solve the model [5]. Bianchessi et al. investigated the scheduling problem for a constellation of agile satellites. A Tabu search algorithm was devised to produce solutions [6]. Baek et al. applied a new genetic algorithm for simulations of an actual satellite mission scheduling problem [7]. Mansour and Dessouky developed a genetic algorithm for solving the scheduling problem using a new genome representation for maximizing multicriteria objectives including the profit and the number of acquired photographs [8]. Globus et al. hypothesized that evolutionary algorithms can effectively schedule coordinated fleets of earth observing satellites and compared the evolutionary algorithm and other methods to test the hypothesis [9]. Wang et al. proposed a multiobjective EOS imaging scheduling method based on the Strength Pareto Evolutionary Algorithm-II [10]. Lin et al. adopted the Lagrangian relaxation and linear search techniques to solve the daily imaging scheduling problem to acquire a near-optimal solution [11]. Wu et al. proposed a hybrid ant colony optimization mixed with local search to obtain satisfactory schedules to address the satellite observation scheduling problem [12]. Zhang et al. presented an algorithm for a multisatellite control resource scheduling problem based on ant colony optimization [13]. These intelligent algorithms, as mentioned above, can be used to obtain near-optimal solutions for large size problems. In addition, rule-based heuristic algorithms have been used to solve the satellite scheduling. Hall and Magazine designed eight heuristic methods for selecting and scheduling projects to maximize the value of a space mission. The computational tests revealed that these methods routinely delivered very close to optimal solutions [1]. Wang et al. presented a nonlinear model of the scheduling problem and developed a priority-based heuristic with conflict-avoided, limited backtracking and download-as-needed features to solve it. They found the heuristic method can produce satisfactory and feasible plans in a notably short time [14]. The rule-based heuristic methods are more flexible approaches to obtain satisfactory solutions that are close to optimal solutions. To summarize, the approximate methods can provide near-optimal solutions to large-scaled problems.

However, all of the above research studies only focused on common tasks in a static environment. Once a schedule is made, it cannot be changed, which is not feasible in dynamic environment. For example, when an earthquake occurs, new emergency tasks with high priority are very difficult to insert into the scheduling scheme. Therefore, determining how to schedule new tasks dynamically is critical. The general method of recent research is to produce a temporary schedule and then to adjust the schedule as quickly as possible while maintaining the efficiency and stability of the schedule as well. Verfaillie and Schiex modeled the dynamic satellite scheduling as a dynamic constraint satisfaction problem. They proposed a new method by reusing any previous solution and producing a new one by local changes on the previous one [15]. Wu et al. used a hybrid ant colony optimization method mixed with iteration local search to obtain a schedule. Next, they proposed a repair method to schedule emergency tasks [16]. Qiu et al. decomposed scheduling horizon into a series of static scheduling intervals and used a rolling horizon strategy to optimize the scheduling schemes in each interval [17]. Sun et al. described the dynamic scheduling problem as a dynamic weighted maximal constraint satisfaction problem in which constraints can be changed dynamically [18]. Wang et al. analyzed the dynamic properties of satellite scheduling and proposed two heuristic algorithms to schedule new tasks [19]. Wang et al. described the dynamic scheduling problem with a unified form of inserting new tasks. Concentrating on how to insert new tasks in initial schedule, they proposed a rule-based heuristic algorithm [20]. Wang et al. focused on how to insert new tasks dynamically in a schedule. These researchers presented a new dynamic real-time scheduling algorithm considered a task dynamic merging strategy [21].

Unfortunately, to the best of our knowledge, no work has been done with respect to the duration of task execution. In addition, less work considered a task merging mechanism in dynamic scheduling. Although some traditional merging methods were studied in a few of previous researches [12, 22–25], these methods did not take into account the duration of task execution. As is known, the duration of task execution indicates how long an imaging task must be observed practically. Since the length of the available visible time windows must be larger than the duration of the task, there often exists some unnecessary time to finish the task. With the consideration of the duration of task execution, more spare time in the schedule will exist, which may provide more imaging opportunities for new tasks. In addition, the task merging strategy using the duration of task can improve the number of tasks for the satellite to finish, thereby enabling many more new tasks to be assigned to an initial schedule.

In this paper, we present a novel two-stage method for dynamic scheduling of earth observation satellites to address emergent events by making full use of the duration of imaging task execution. The method is comprised of two stages: robust satellite scheduling and dynamic adjustment. In the first stage, we establish a robust satellite scheduling model that accounts for the total task execution time and use the multiobjective genetic algorithm NSGA-II to create feasible initial schemes. In the second stage, we adjust the robust solution to insert new tasks. The dynamic adjusting rule-based heuristic algorithm (CTM-DAHA) is designed to get a satisfactory schedule which generates high revenue and little disturbance. To improve the imaging efficiency as much as possible, we propose to embed a compact composite task merging method that considers task execution time into the algorithm.

The major contributions of this paper are summarized as follows. For the first time, the total task execution time is regarded as an indicator to evaluate the robustness of the scheduling schemes. A compact task merging method that considers the duration of task execution is embedded into the dynamic scheduling algorithm.

The remainder of the paper is organized as follows. The dynamic scheduling problem as well as the two-stage solution framework is described in Section 2. In Section 3, we present the robust satellite scheduling model and algorithm. In Section 4, we propose a new heuristic algorithm considering a compact task merging mechanism to dynamically adjust the initial schedule. In Section 5, we conduct experimental simulations and compare different algorithms used for scheduling. We conclude the paper with a summary in Section 6.

#### 2. Problem Formulation

In current section, we will firstly introduce the process of satellite observation and task merging method in brief. Then we describe the problem of dynamic scheduling oriented emergent events. Moreover, the framework of two-stage dynamic scheduling method is presented.

##### 2.1. Description of Satellite Observation

The satellite scheduling amounts to a reasonable arrangement of satellites, sensors, time windows, and sensor slewing angle for observation tasks to maximize one or more objectives, for example, the overall observation profit, when subject to related constraints. As shown in Figure 1, the EOS operates in space in a certain orbit. When the EOS flies over the target area, its sensor is opened to take the image. We assume that the sensors of the EOSs considered in our study are able to slew laterally. A target is termed as a task in this paper. As the imaging process will last a few seconds, it will produce a strip that covers the target. The strip of EOS can be formed on the ground by the subsatellite point of satellite as well as the field of view of the sensor, the slewing angle of the sensor, and the observation duration. The observation duration indicates how long an imaging task must be observed practically. It depends on the satellite’s travelling speed, the sensor’s scanning speed, and the ground strip to be scanned. A task must be imaged by the satellite within the available time windows. Taking as an example task , at the moment , task begins to appear in the scope of the EOS, and, with the movement of the EOS, disappears at the moment . Therefore, the EOS can observe task between and ; that is, is a time window of . The time windows (as well as slewing angle) between the satellite and the task can be computed based on orbit parameters. Because the length of the available visible time window must be larger than the duration of the task, there exists unnecessary time within the window to finish the task. With the consideration of the duration of task execution, more spare time in the schedule will exist, which may provide more imaging opportunities for new tasks. Therefore, we view the duration of task execution as an important factor.