A two-phase scheduling method with the consideration of task clustering for earth observing satellites
Introduction
Earth observing satellites (EOSs), orbiting the Earth, are able to collect images of specified areas of the Earth surface at the request of users [1]. They are playing key roles in environment surveillance, intelligence reconnaissance and others, prompting many countries to increase investments to develop EOSs and associated techniques. For instance, China plans to launch four small optical satellites and four small SAR satellites to form a natural disaster-monitoring constellation [2]. To make full use of scarce satellite resources, effective observation scheduling is of great significance [2]. Since users’ observation requests usually exceed the capabilities of existing satellite resources, the satellite observation scheduling problem (SOSP) is categorized as an over-subscribed problem. In fact, SOSP can be seen as a kind of multi-dimensional knapsack problem [3], which is NP-hard.
In this study, we will introduce a new strategy called task clustering when addressing SOSP, aiming to improve the scheduling efficiency. As shown in Fig. 1, a satellite sensor generates a dummy observation strip of a certain width and length when passing over targets. The width and length of the strip are determined by the altitude of the satellite, the field of view of the sensor, the slewing angle of the sensor and the observation duration of the sensor. Generally, the altitude of the satellite and the field of view of the sensor are fixed. However, we can rationally tune the slewing (pointing) angle and the observation duration of the sensor to enable an observation strip to cover multiple targets. We view the request of observing a target as an observation task. Then multiple observation tasks can be merged into a composite task and then completed by an observation activity. A composite task is called a cluster-task in this study. For example, in Fig. 1, task , and can be combined into a cluster-task and finished by one observation activity. The process that integrates multiple observation tasks into a cluster-task is called task clustering.
In our opinion, considering task clustering in the course of solving SOSP at least has following three advantages.
- (1)
Task clustering can enable a satellite to finish more tasks at the cost of fewer sensor opening times. In each orbit, times for a satellite turning on its sensor are limited due to electrical constraints and the limitation of onboard energy. A satellite has to first open its sensor before it starts an observation. That is to say, the number of observations in each orbit is limited accordingly. Noticeably, task clustering enables the satellite to finish more tasks with fewer observations (i.e. fewer sensor opening times). For example, as shown in Fig. 1, traditionally, the sensor needs to open for eight times (i.e. eight observations) to execute the eight observation tasks. In contrast, tasks clustering enable the satellite to finish the eight tasks with four sensor opening times.
- (2)
Task clustering can enable some previously mutual exclusive tasks to be finished simultaneously. When a satellite goes to finish two tasks consecutively, enough setup time is required for the satellite to turn on its sensor and slew its sensor to an appropriate angle to point at a special target. If there is not enough duration between the time-windows of two consecutive tasks, they will be mutual exclusive. However, if these mutual exclusive tasks can be integrated into a cluster-task, they can be completed together. For example, in Fig. 1, we assume that tasks and are mutual exclusive. Then traditionally either or will be scheduled. While after considering task clustering, or can be clustered and finished together. Similar situation can be found in tasks , and .
- (3)
Task clustering can enable a satellite to accomplish more tasks while reduce sensor slewing times, resulting in less energy consumption. As shown in Fig. 1, we assume that tasks and can be finished consecutively with slewing angle and , respectively. Traditionally, the satellite have to slew its sensor for two times to accomplish and , with total slewing angle being . In contrast, after considering task clustering, the satellite only needs to slew its sensor for only one time with angel .
It is therefore meaningful to develop a scheduling method integrated with task clustering to address SOSP. Unfortunately, to our knowledge, no study has taken into account task clustering up to now. This work aims to fill this gap.
Another motivation of this work is to apply Ant Colony Optimization (ACO) to the solution of SOSP. At present, except ACO, many heuristic algorithms have been employed to solve SOSP, such as Local Search, Simulated Annealing, Tabu Search and Genetic Algorithm. In fact, ACO has been demonstrated to be very effective in solving complex combinatorial optimization problems. As shown in Fig. 1, scheduling satellite observations amounts to arranging an observation sequence for each orbit of satellites. This process is naturally analogous to the route search process of ants, which motivated us to investigate a specialized ACO to tackle SOSP.
Since SOSP is NP-Hard and the problem of task clustering is complicated as well, it might be intractable to integrate task clustering into the task scheduling process dynamically. To reduce complexities, we propose a two-phase based strategy that first implements task clustering then conducts task scheduling.
The major contributions of this study are summarized as follows:
- (1)
We put forward a two-phase scheduling strategy with task clustering to solve SOSP.
- (2)
We analyze the constraints involved in task clustering, and propose effective methods to calculate the slewing angle and the time-window of each cluster-task.
- (3)
We construct a graph model to formulate task clustering and present a minimum clique partition method to generate cluster-tasks.
- (4)
We give an integer programming model and an acyclic directed graph model to formulate SOSP, considering overall tasks and cluster-tasks. In addition, based on the models, we propose a hybrid ant colony optimization mixed with local search (ACO–LS) to obtain satisfactory schedules.
The rest of this paper is organized as follows: Section 2 reviews related work in literatures. Section 3 constructs a graph model for task clustering and employs an improved clique partition method to obtain cluster-tasks. Section 4 builds an integer programming model and an acyclic directed graph model for SOSP, and proposes the ACO–LS algorithm generate high quality schedules. Section 5 gives simulation experiments and performance analysis. Section 6 concludes this paper with a summary and direction of future work.
Section snippets
Related works
Many early studies concentrated on SOSP with single satellite. For instance, Potter and Gasch [4] applied an improved greed algorithm to mission planning and scene acquisition scheduling for the Landsat 7 satellite. Wolfe and Sorensen [5] compared the capability of a dispatch algorithm, a look-ahead algorithm, and a genetic algorithm. They drew the conclusion that the genetic algorithm was most efficient with problem size increasing. Vasquez and Hao [6] translated the scheduling problem into
Task clustering model and algorithm
In this section, we investigate the constraints of task clustering, including slewing angle related constraint and time-window related constraint. Then a task clustering graph model is constructed, such that a clique represents a cluster-task. An improved minimum clique partition algorithm is presented to generate cluster-tasks.
Scheduling model and algorithm
In this section, we will introduce an integer-programming model and an acyclic directed graph model to describe SOSP, and develop a hybrid ant colony optimization mixed with local search (ACO–LS) to produce effective schedules.
We consider overall tasks and obtained cluster-tasks as candidate scheduling tasks. Indeed, the additional cluster-tasks will increase the problem size. It is noticeable that tasks can generate at most cluster-tasks. In regard to a problem with tasks, the number
Simulation setup
To evaluate performance of the proposed algorithm, we needed to conduct extensive simulations. As introduced in Section 2, previous researches usually focused on specific satellites or constellations, causing that constraints and models considered by distinct academic groups were different to some extent. Thus, there is no benchmark instance consistent with the model presented in this study.
We defined two groups of reference scenarios to test the efficiency of our scheduling method. The first
Conclusions and future work
Considering task clustering into the scheduling can improve the efficiency of satellite observation systems. Since both task clustering and scheduling process are complicated, we presented a two-phase strategy to address SOSP, i.e., partition the problem solution process into a task clustering phase and a task scheduling phase. In the task clustering phase, a graph model and an improved minimum clique partition algorithm are employed to generate cluster-tasks. In the task scheduling phase, we
Acknowledgements
This work was supported by the National Basic Research Program of China under Grant no. 97361361 and the National Nature Science Foundation of China under Grant no. 61104180. We are also thankful to the anonymous referees.
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