# A Heuristic Genetic Algorithm for Regional Targets’ Small Satellite Image Downlink Scheduling Problem

Authors: Yan-Jie Song; Zhong-Shan Zhang; Kai Sun; Feng Yao; Ying-Wu Chen
Journal: International Journal of Aerospace Engineering
 (2019)

---

## Abstract

Small satellite image downlink scheduling problem (SSIDSP) is an important part of satellite mission planning. SSIDSP mainly needs to balance how to better match the limited receiving capacity of the ground station with the limited satellite resources. In this paper, regional targets are considered with SSIDSP. We propose a mathematical model that maximizes profit by considering time value and regional targets. A downlink schedule algorithm (DSA) is proposed to complete the task sequence arrangement and generate scheduling results. A heuristic genetic algorithm (HGA) is used to optimize the generated task sequence to achieve higher profit. Three scale test instances are used to test the effectiveness of HGA and DSA. We compare the effect of HGA, basic genetic algorithm (GA), and construction heuristic algorithm. The experimental results proved that the proposed approach ensures the successful completion of observation tasks and is effective for SSIDSP.


---

## Body

## 1. Introduction

Since the Soviet Union successfully launched the first man-made earth satellite half a century ago, all countries in the world have begun to explore and use space resources. The use of optical payloads or synthetic aperture radar (SAR) imaging satellites is an important part of satellites. With the continuous development of satellite technology and applications, people are demanding faster satellite development cycles while demanding lower satellite costs and reduced risks. Small satellite technology was born. A large number of imaging satellites need to send data to a satellite ground station after taking photos and reconnaissance to obtain data. How to complete the image downlink task better has become a hot issue in satellite mission planning and scheduling. At present, the common methods of task scheduling or human intervention task planning with heuristic rules have become increasingly difficult to meet the growing demand for small satellite image downlink, and the downlink of small satellite image will greatly impact the development of imaging satellites.The small satellite image downlink scheduling problem (SSIDSP) mainly solves the problem of how to better match the limited receiving capacity of the ground station with the limited satellite resources. The limitation on the storage capacity of satellites requires that the picture data obtained should be downlinked as soon as possible; otherwise, the image data will be deleted from the storage. However, the number of ground stations is limited and the downlink tasks could only be performed when the ground stations and satellites establish communication and are visible to each other. The diagram of imaging satellite data downlink tasks is shown in Figure1, which vividly demonstrates the satellite operation flow and time progress, respectively. The overall process of photographing and data downlinking is that the imaging satellite photographs the task during T0 to T1. After the satellite completes the attitude maneuver, it downloads the data during T2 to T3. The data transmission task can only begin when the satellite passes the visibility mask of the ground station. If a satellite cannot downlink the data after it has passed through the visible mask of all the ground stations, the task will not meet users’ requests.Figure 1
The diagram of imaging satellite data downlink tasks.The image acquisition tasks include point target tasks and regional target tasks. The regional target tasks are generally performed by means of regional segmentation during the observational scheduling, and data obtained is of fragment type. Also, the regional targets require higher standard of data downlink. These data should be easily found and processed by ground stations. In addition, since users’ observational requirements are in chronological order, obtaining the data required earlier means that the tasks are completed better. In the following study, we studied the problems considering regional targets and the time value of the data downlink simultaneously.In recent years, scholars at home and abroad have conducted a series of relevant researches on the issue of downlink scheduling of imaging satellite data. The salient features of SSIDSP are of large demands and the limited resources. This problem is a typical oversubscribed scheduling problem, and it has been proved to be an NP-hard scheduling problem [1]. Also, there are many similarities between the SSIDSP and the multiple knapsack problem [2]. These features provide sufficient theoretical support for the study of SSIDSP.The multiple knapsack problems are mainly divided into two types: deterministic problems and random problems. Akbar et al. and Qin et al. have analyzed and modeled the deterministic multiple knapsack problems [3, 4]. On the other hand, Gibson et al. and Tönissen et al. have solved the random multiple knapsack problems [5, 6]. The solving methods of multiple knapsack problems include exact solution algorithms, heuristic algorithms, and metaheuristic intelligent optimization algorithms [7]. In a recent study, Wang et al. proved that the branching and cutting methods are effective for quadratic knapsack problem with multiple knapsack constraints [8]. García-Martínez et al. proposed an algorithm that uses tabu search to enhance the efficiency of greedy strategies and proposed a memory-enhanced destruction mechanism for iterated greedy [9].The problems of satellite mission scheduling mainly include single-satellite problems and multiple-satellite problems [10]. The difficulties in current research are mainly related to the large number of constraints and problems, so it is necessary to model the problems specifically and solve the problems with special algorithms [11]. Karapetyan et al. have dealt with the downlink scheduling portion of the mission planning operations of Canada’s Earth-observing SAR satellite [12]. Donati et al. introduced the autonomous data transmission and scheduling algorithm proposed by the European Space Agency for the Mars Express Mission [13]. Xhafa et al. summarized a family of problems after combing the problems of satellite mission scheduling. Aiming at these problems, they designed heuristic algorithms and GA [14]. Chen et al. used a resource scheduling model that considers task increments to solve the multisatellite data downlink resource scheduling problem through an evolutionary calculation method [15]. Chu et al. constructed a satellite mission scheduling model with time-dependent constraints and proposed a branch-and-bound algorithm to solve this problem accurately [16]. The cloud optimization task optimization method can also be used as a method to quickly solve large-scale problems [17].Imaging satellite mission scheduling and data downlink mission scheduling are two hot topics in the study of satellite mission scheduling. Although the whole task is considered completed after the imaging satellite completes the photographing mission and transmits the mission to the ground station, the reason why we considered the SSIDSP alone is that there are numerous constraints for both two problems stated above. If we considered the overall process of the task, the quality of the scheduling and the efficiency of the algorithm will be negatively affected. At the same time, due to few researches on the integrated problems at present, it is difficult to demonstrate the feasibility and effectiveness of the methods proposed. This article focuses on the process of satellite data downlink and does researches on how to make satellites overcome the bottleneck of data downlink to promote the development of this field.This article analyzed and researched the SSIDSP in imaging satellite mission scheduling. To deal with the SSIDSP, we considered the point target task and the regional target task. In the design of the model, we considered the impact of time value on the profits of the data downlink tasks. The improvement of these two aspects would increase the complexity of the problem than that of the original SSIDSP. To solve this problem, it is necessary to design an effective algorithm to realize the task scheduling and optimization process.The rest of the article is structured as follows. In the second part, we will carry out a detailed analysis of the SSIDSP and then put forward the model, assumptions, and constraints of the SSIDSP. In the third part, the strategies and algorithms to this problem will be stated in details. To solve the problem, we will propose construction heuristic algorithms, downlink schedule algorithms, and heuristic genetic algorithms (HGA). In the fourth part, we will verify the algorithm with examples and demonstrate the feasibility and validity of the algorithms proposed in the third part. Finally, we will come to a conclusion of the study in the fifth part.


## 2. Model

### 2.1. Description of Variable

Firstly, a description is given for all the variables involved in the SSIDSP studied in this paper, as described in Table1.Table 1
Variable description.
Variables
Description
T=PT,RT
Satellite data downlink tasks
PT=pt1,pt2,…,ptn
Point target tasks
RT=rt1,rt2,…,rtn
Regional target tasks
H
Groups of regional targets
stkIA
Start time of image acquisition
etkIA
End time of image acquisition
estkD
Earliest data downlink start time
stkD
Data downlink start time
Durk
Duration of the data downlink
pkD
Profit of taskk
DLkD
Deadline of data downlink
stkAD
Earliest data downlink start time of regional targets
DLkAD
Latest data downlink end time of regional targets
VM=vm1,vm2,…,vmm
The set of ground station’s visibility mask
EvtVM
Earliest visible time of a ground station
LvtVM
Latest visible time of a ground station
evtkVM
Earliest visible time of a ground station
lvtkVM
Latest visible time of a ground station
ck
Completion of data downlink tasks
α
Data compression ratio
itd→d
Interval time between two data downlink tasks
ita→d
Time interval between the imaging end time and the data downlink start time


### 2.2. Problem Description

At present, the research on satellite data downlink planning problems generally studies SIDSP, such as those studied by Karapetyan et al. [12] and Beyer [18], only considering the target of the target. The research on SSIDSP has not yet existed. The most significant difference between this type of problem and the previous problem is that the addition of regional targets makes the model and constraints increase a lot of new content compared with the SIDSP, and it also increases the difficulty of solving. The SSIDSP is compatible with today’s imaging satellite mission planning issues, as regional target observations have become an important class of tasks.This paper considers the small satellite image downlink scheduling problem (SSIDSP) under the condition that the imaging task sequence has been determined. Due to the large number of imaging tasks and data downlink tasks, the number of ground stations and the time that satellites pass over ground stations are limited. The time window through which satellites can transmit data over the ground station is known as the visibility mask of the ground station. The data downlink mission of the imaging satellite must be performed within the visibility masks of the ground station. The satellite data downlink mission scheduling diagram is shown in Figure2.Figure 2
Downlink mission scheduling diagram.It is worth mentioning that these imaging tasks have time value. For an imaging task, the sooner the work of downloading the data is completed, the higher the profit it will reach. In addition, since imaging tasks include point target imaging tasks and regional target imaging tasks, regional target imaging task downlink must be completed in a single ground station which means a group of regional targets within a visibility mask. Multiple visibility masks or multiple ground stations will result in the loss of imaging data, which means the failure of imaging down tasks in this area.Now we can use mathematical model to describe this problem. First of all, given a set of satellite data downlink tasks,T=PT,RT, which consists of a set of point target tasks PT=pt1,pt2,…,ptn and a set of regional target tasks RT=rt1,rt2,…,rtn. Among them, the regional targets can be divided into H groups, and the group KK∈H has KH tasks. Each determined point target task and regional target task have a start time of image acquisition stkIA and end time of image acquisition etkIA, the earliest data downlink start time estkD, the data downlink start time stkD, the duration of the data downlink Durk, and the profit pkD gained through completing the data downlink successfully. The profit of task depends on the satellite imaging task, which is related to the importance of the task, the length of the imaging, and the size of the occupied. The longer the imaging time, the more important the task, the more the storage leads to more value of profit. In this question, the profit that each task can get is given as a known amount. The deadline of data downlink is DLkD. For a group of regional targets, it also includes the earliest data downlink start time stkAD and the latest data downlink end time DLkAD. Then the relevant attributes of the ground station are defined. The set of ground station’s visibility mask is VM=vm1,vm2,…,vmm. The earliest visible time of all ground stations is EvtVM. The latest visible time is LvtVM. Each visibility mask of the ground station vmk contains an earliest visible time evtkVM and the latest visible time lvtkVM. In addition, ck also needs to be defined to indicate the completion of data downlink tasks. When the imaging satellite passes through the visibility mask and can complete the data downlink task, ck=1 else ck=0.In order to facilitate the subsequent modeling and solving, we also need to define the related attributes between some tasks. Constrained by the satellite hardware conditions, the data downlink must be started after the imaging is completed. The interval time is defined asita→d. At the same time, there is also a time interval between the two data downlink tasks, which is defined as itd→d.In this article, we analyzed the previous research and proposed a model based on the following assumptions:(1)
Assume that satellite imaging missions have undergone mission scheduling to determine the order in which missions are completed
(2)
Consider only a single satellite data downlink scheduling problem
(3)
There is a time interval between two data downlink tasks. This time interval cannot be ignored
(4)
Data downlink task needs to be performed after the satellite imaging task is completed
(5)
Regardless of the time-consuming problem of data downlink from space to the ground, only consider the sequence of data downlink tasks
(6)
The storage capacity of satellites and the power of satellites meet the requirements for data downlink tasks
(7)
Downlinking can start right from the beginning of the scheduling horizon
(8)
The data downlink task does not consider the two working modes of breakpoint retransmission and downloading in real time
(9)
The satellite data compression ratioα is knownThe constraints of data downlink task scheduling are as follows:(1)
The duration of data downlink tasksDuri is limited by the capacity of satellite data compression. The satellite data compression ratio is α and the data downlink duration is
(1)Duri=αetkIA−stkIA,∀at,rt∈T.
(2)
For a data downlink task, the downlink start time and the downlink end time must be displayed in the visibility mask of a ground station(2)evtjVM≤stiD≤lvtjVM,evtjVM≤stiD+Duri≤lvtjVM,∀pt,rt∈T.
(3)
The data downlink task must be returned after the imaging task is completed. The data downlink start time must be later than the data downlink earliest start time, and the data downlink task must be completed before the time limit expires(3)stiD≥etiIA,stiD≥estiD,stiD+Duri≤DLiD,∀pt,rt∈T.
(4)
There is a fixed intervalitd→d between two data downlink tasks, and the interval between tasks and tasks must be greater than or equal to itd→d
(4)stiD+Duri−stjD≥itd→d,∀pt,rt∈T∧i≠j.
(5)
A data downlink task can be performed at most once, and each task cannot be further divided into several fragments(5)ci≤1,∑k=1mcik≤1,∀pt,rt∈T.
(6)
There is a time intervalita→d between the imaging end time and the data downlink start time. The data downlink task can start the transmission at least after the imaging is completed and the time interval constraint is satisfied
(6)estiD−etiIA≥ita→d,∀pt,rt∈T.
(7)
If the regional observing mission cannot download all pictures at a single ground station, it means failure
(8)
Satellite storage space is limited and it must be deleted once all ground stations have failed to complete the downloadThe design of the objective function in this paper is based on the realization of the total profit of the data downlink task scheduling. The model includes the task’s profitpD and the task’s completion decision variable ci. Considering the time attribute of the downlink profit, the task profit value is adjusted by using the data downlink start time stD and the imaging end time estD. The model is expressed as follows:
(7)MaxFPT+FRT,(8)FPT=∑i=1PTpiDstiD−estiD×ci,(9)FRT=∑j=1HFRTj,(10)FRTK=∑k=1KHpkDstkD−estkD,AlltasksinKarecompletedK∈H,0,Otherwise.So far, we have built a mixed integer programming model for SSIDSP problems and proposed assumptions and constraints. The objective function of this problem is shown in equations (7)–(10), and the constraints are shown in equations (1)–(6). We give a complete description of the problem. The seventh and eighth points of the constraint description will introduce new variables that have little to do with the scheduling process if they are described in mathematical expressions. Therefore, we only present them in the program part, but not in the problem description section. The mathematical expressions are as follows.Objective function:(11)MaxFPT+FRT,FPT=∑i=1PTpiDstiD−estiD×ci,FRT=∑j=1HFRTj,FRTK=∑k=1KHpkDstkD−estkD,AlltasksinKarecompletedK∈H,0,Otherwise.Constraints:(12)Duri=αetkIA−stkIA,∀at,rt∈T,evtjVM≤stiD≤lvtjVM,evtjVM≤stiD+Duri≤lvtjVM,∀pt,rt∈T,stiD≥etiIA,stiD≥estiD,stiD+Duri≤DLiD,∀pt,rt∈T,stiD+Duri−stjD≥itd→d,∀pt,rt∈T∧i≠j,ci≤1,∑k=1mcik≤1,∀pt,rt∈T,estiD−etiIA≥ita→d,∀pt,rt∈T.The three important factors affecting the result of the objective function are as follows: for a data downlink task, whether to perform the data downlink task; the start time of the data downlink task selection; and the visibility mask arrangement of the regional target tasks. Considering the task’s time-valued attributes and the regional target’s downlink plans, we can guarantee the quality of the objective function.


## 2.1. Description of Variable

Firstly, a description is given for all the variables involved in the SSIDSP studied in this paper, as described in Table1.Table 1
Variable description.
Variables
Description
T=PT,RT
Satellite data downlink tasks
PT=pt1,pt2,…,ptn
Point target tasks
RT=rt1,rt2,…,rtn
Regional target tasks
H
Groups of regional targets
stkIA
Start time of image acquisition
etkIA
End time of image acquisition
estkD
Earliest data downlink start time
stkD
Data downlink start time
Durk
Duration of the data downlink
pkD
Profit of taskk
DLkD
Deadline of data downlink
stkAD
Earliest data downlink start time of regional targets
DLkAD
Latest data downlink end time of regional targets
VM=vm1,vm2,…,vmm
The set of ground station’s visibility mask
EvtVM
Earliest visible time of a ground station
LvtVM
Latest visible time of a ground station
evtkVM
Earliest visible time of a ground station
lvtkVM
Latest visible time of a ground station
ck
Completion of data downlink tasks
α
Data compression ratio
itd→d
Interval time between two data downlink tasks
ita→d
Time interval between the imaging end time and the data downlink start time


## 2.2. Problem Description

At present, the research on satellite data downlink planning problems generally studies SIDSP, such as those studied by Karapetyan et al. [12] and Beyer [18], only considering the target of the target. The research on SSIDSP has not yet existed. The most significant difference between this type of problem and the previous problem is that the addition of regional targets makes the model and constraints increase a lot of new content compared with the SIDSP, and it also increases the difficulty of solving. The SSIDSP is compatible with today’s imaging satellite mission planning issues, as regional target observations have become an important class of tasks.This paper considers the small satellite image downlink scheduling problem (SSIDSP) under the condition that the imaging task sequence has been determined. Due to the large number of imaging tasks and data downlink tasks, the number of ground stations and the time that satellites pass over ground stations are limited. The time window through which satellites can transmit data over the ground station is known as the visibility mask of the ground station. The data downlink mission of the imaging satellite must be performed within the visibility masks of the ground station. The satellite data downlink mission scheduling diagram is shown in Figure2.Figure 2
Downlink mission scheduling diagram.It is worth mentioning that these imaging tasks have time value. For an imaging task, the sooner the work of downloading the data is completed, the higher the profit it will reach. In addition, since imaging tasks include point target imaging tasks and regional target imaging tasks, regional target imaging task downlink must be completed in a single ground station which means a group of regional targets within a visibility mask. Multiple visibility masks or multiple ground stations will result in the loss of imaging data, which means the failure of imaging down tasks in this area.Now we can use mathematical model to describe this problem. First of all, given a set of satellite data downlink tasks,T=PT,RT, which consists of a set of point target tasks PT=pt1,pt2,…,ptn and a set of regional target tasks RT=rt1,rt2,…,rtn. Among them, the regional targets can be divided into H groups, and the group KK∈H has KH tasks. Each determined point target task and regional target task have a start time of image acquisition stkIA and end time of image acquisition etkIA, the earliest data downlink start time estkD, the data downlink start time stkD, the duration of the data downlink Durk, and the profit pkD gained through completing the data downlink successfully. The profit of task depends on the satellite imaging task, which is related to the importance of the task, the length of the imaging, and the size of the occupied. The longer the imaging time, the more important the task, the more the storage leads to more value of profit. In this question, the profit that each task can get is given as a known amount. The deadline of data downlink is DLkD. For a group of regional targets, it also includes the earliest data downlink start time stkAD and the latest data downlink end time DLkAD. Then the relevant attributes of the ground station are defined. The set of ground station’s visibility mask is VM=vm1,vm2,…,vmm. The earliest visible time of all ground stations is EvtVM. The latest visible time is LvtVM. Each visibility mask of the ground station vmk contains an earliest visible time evtkVM and the latest visible time lvtkVM. In addition, ck also needs to be defined to indicate the completion of data downlink tasks. When the imaging satellite passes through the visibility mask and can complete the data downlink task, ck=1 else ck=0.In order to facilitate the subsequent modeling and solving, we also need to define the related attributes between some tasks. Constrained by the satellite hardware conditions, the data downlink must be started after the imaging is completed. The interval time is defined asita→d. At the same time, there is also a time interval between the two data downlink tasks, which is defined as itd→d.In this article, we analyzed the previous research and proposed a model based on the following assumptions:(1)
Assume that satellite imaging missions have undergone mission scheduling to determine the order in which missions are completed
(2)
Consider only a single satellite data downlink scheduling problem
(3)
There is a time interval between two data downlink tasks. This time interval cannot be ignored
(4)
Data downlink task needs to be performed after the satellite imaging task is completed
(5)
Regardless of the time-consuming problem of data downlink from space to the ground, only consider the sequence of data downlink tasks
(6)
The storage capacity of satellites and the power of satellites meet the requirements for data downlink tasks
(7)
Downlinking can start right from the beginning of the scheduling horizon
(8)
The data downlink task does not consider the two working modes of breakpoint retransmission and downloading in real time
(9)
The satellite data compression ratioα is knownThe constraints of data downlink task scheduling are as follows:(1)
The duration of data downlink tasksDuri is limited by the capacity of satellite data compression. The satellite data compression ratio is α and the data downlink duration is
(1)Duri=αetkIA−stkIA,∀at,rt∈T.
(2)
For a data downlink task, the downlink start time and the downlink end time must be displayed in the visibility mask of a ground station(2)evtjVM≤stiD≤lvtjVM,evtjVM≤stiD+Duri≤lvtjVM,∀pt,rt∈T.
(3)
The data downlink task must be returned after the imaging task is completed. The data downlink start time must be later than the data downlink earliest start time, and the data downlink task must be completed before the time limit expires(3)stiD≥etiIA,stiD≥estiD,stiD+Duri≤DLiD,∀pt,rt∈T.
(4)
There is a fixed intervalitd→d between two data downlink tasks, and the interval between tasks and tasks must be greater than or equal to itd→d
(4)stiD+Duri−stjD≥itd→d,∀pt,rt∈T∧i≠j.
(5)
A data downlink task can be performed at most once, and each task cannot be further divided into several fragments(5)ci≤1,∑k=1mcik≤1,∀pt,rt∈T.
(6)
There is a time intervalita→d between the imaging end time and the data downlink start time. The data downlink task can start the transmission at least after the imaging is completed and the time interval constraint is satisfied
(6)estiD−etiIA≥ita→d,∀pt,rt∈T.
(7)
If the regional observing mission cannot download all pictures at a single ground station, it means failure
(8)
Satellite storage space is limited and it must be deleted once all ground stations have failed to complete the downloadThe design of the objective function in this paper is based on the realization of the total profit of the data downlink task scheduling. The model includes the task’s profitpD and the task’s completion decision variable ci. Considering the time attribute of the downlink profit, the task profit value is adjusted by using the data downlink start time stD and the imaging end time estD. The model is expressed as follows:
(7)MaxFPT+FRT,(8)FPT=∑i=1PTpiDstiD−estiD×ci,(9)FRT=∑j=1HFRTj,(10)FRTK=∑k=1KHpkDstkD−estkD,AlltasksinKarecompletedK∈H,0,Otherwise.So far, we have built a mixed integer programming model for SSIDSP problems and proposed assumptions and constraints. The objective function of this problem is shown in equations (7)–(10), and the constraints are shown in equations (1)–(6). We give a complete description of the problem. The seventh and eighth points of the constraint description will introduce new variables that have little to do with the scheduling process if they are described in mathematical expressions. Therefore, we only present them in the program part, but not in the problem description section. The mathematical expressions are as follows.Objective function:(11)MaxFPT+FRT,FPT=∑i=1PTpiDstiD−estiD×ci,FRT=∑j=1HFRTj,FRTK=∑k=1KHpkDstkD−estkD,AlltasksinKarecompletedK∈H,0,Otherwise.Constraints:(12)Duri=αetkIA−stkIA,∀at,rt∈T,evtjVM≤stiD≤lvtjVM,evtjVM≤stiD+Duri≤lvtjVM,∀pt,rt∈T,stiD≥etiIA,stiD≥estiD,stiD+Duri≤DLiD,∀pt,rt∈T,stiD+Duri−stjD≥itd→d,∀pt,rt∈T∧i≠j,ci≤1,∑k=1mcik≤1,∀pt,rt∈T,estiD−etiIA≥ita→d,∀pt,rt∈T.The three important factors affecting the result of the objective function are as follows: for a data downlink task, whether to perform the data downlink task; the start time of the data downlink task selection; and the visibility mask arrangement of the regional target tasks. Considering the task’s time-valued attributes and the regional target’s downlink plans, we can guarantee the quality of the objective function.


## 3. Methods

This paper proposes three methods for solving the problem containing regional targets of data downlink scheduling for imaging satellite. The downlink schedule algorithm (DSA) will be proposed in Section3.1. And the heuristic genetic algorithm (HGA) will be given in Section 3.2.For constrained optimization problems, there are various scheduling solutions to solve them. The simplest solution is to artificially select the tasks in order and insert them into the visibility mask one by one in accordance with the principles of greedy rules. This method is often used without regard to regional goals. When the regional target is considered into downlink missions, the problem becomes more complicated, and the profit of the regional target may affect the final result of the entire model. What is more, although the regional targets can get more profits when they can be downloaded successfully, it will also occupy a lot of ground stations’ visibility masks. It may be that this part of the visibility masks left for the other tasks can increase the overall profit. So, numerous constraints, time value of tasks, and regional targets are all factors that need to be considered in the process of calculating profits. Therefore, the addition of these conditions has increased the complexity of the SSIDSP. For the small satellite image downlink scheduling problem, it can also be considered as an optimization a permutation of the downlink requests. It can be converted into a downlink request permutation problem (DRPP). The objective function can also be presented in a way that maximizes the sequence utility function, which is stated as(13)MaxF=φP.In the next section, we will first introduce a downlink schedule algorithm to arrange the appropriate position for the task sequence. This algorithm will be used as one of the algorithms in the experimental part comparison. In the experimental part, the standard genetic algorithm also compares with our proposed heuristic genetic algorithm (HGA).


### 3.1. Downlink Schedule Algorithm (DSA)

DSA is a method we used to get the final data downlink sequences by requesting sequences of the tasks. It is also an algorithm that we need to call repeatedly to calculate the profits of scheduling solutions. In the DSA we proposed, there are two kinds of heuristic rules. We define them as regional target priority rule and greedy heuristic rule. The downlink schedule algorithm also includes a visibility mask reconstruction method and a task filling method. Visibility mask reconstruction method, task filling method, and two heuristic rules will be introduced firstly, and then, the complete flow of the DSA will be given.


#### 3.1.1. Task Filling Method

After a data downlink task is completed, another data downlink task cannot be started immediately. It must satisfy the time interval between tasks that is longer than a certain time interval before the next data downlink task can begin. In order to facilitate the generation of the scheduling scheme afterwards, the task filling method is used to process each data downlink task. The method of filling is to fill in the minimum time interval to the task directly behind each task, see it as a whole, and get a new set of task sequences. The task filling process is shown in Figure3. Our subsequent sequence scheduling process is for newly generated task sequences.Figure 3
Task filling of sequences.From Figure3, it can be seen that the filled task sequence can be easily planned and arranged. At the same time, this method makes the sequence more compact, allowing a certain amount of time remaining in the same length of time, placing more data tasks into sequences that can be successfully downlinked.


#### 3.1.2. Visibility Mask Reconstruction Method

Visibility mask reconstruction method can also be referred to as visibility mask clipping. The use of reconstruction methods can achieve the effect of simplifying the constraints and improving the scheduling efficiency. When a data downlink task determines its position in the ground station’s visibility masks, this part of the visibility masks has already been used and cannot be used by other data downlink tasks. Therefore, the subsequent sequence scheduling does not make sense for this part of the visibility masks that has already been occupied. We only need to search for those visibility masks that have not yet been occupied by data downlink tasks. The visibility mask reconstruction method is that after a data downlink task is successfully arranged, the visibility masks are processed, a new visibility mask sequence is regenerated, and the next downlink task scheduled only need to consider the constraints other than the visibility mask occupation.


#### 3.1.3. Regional Target Priority Rule

The data downlink tasks of regional target include higher profits and have higher requirements for the visibility masks of ground stations. The schematic diagram of the regional target task scheduling using the regional target priority rule to prioritize the planning and scheduling of regional target tasks can improve the success rate of completion of tasks. At the same time, prioritizing the tasks of regional target can reduce the search scope of the visibility masks of ground stations and enhance the planning efficiency of other observation tasks.The use of the regional target priority rule will be determined based on the relationship between the regional target profit and the overall target profit. The determination rule will be given in Section3.2.1.


#### 3.1.4. Greedy Heuristic Rule

The greedy heuristic rule requires that the data download task first fill in the earliest available position of the visibility masks, that is, it will arrange the task at the earliest position of the earliest available visibility mask that can be downloaded. Visibility mask resources are far from enough for downlink missions, and more intensive sequence arrangements can yield higher returns. By using greedy heuristic rules, the ground station’s visibility mask can be used more compactly. In addition, this method has been shown to obtain optimal solutions in the conventional sequence scheduling problem. We consider the time value of the task. Earlier tasks can get higher value, so we can still satisfy the use of greedy rules to get the best task sequence.Table1 shows the overall flow of the DSA. After the algorithm is initialized and input, the task is first filled and a new task sequence is generated. After that, when the regional target priority scheduling rules are met, the regional targets are prioritized according to the regional target priority rules; otherwise, plan directly regardless of the target attributes. After executing or skipping the regional target arrangement, the visibility mask is reconstructed and the schedule of the point target downlink tasks is started. Regardless of whether it is a point target or regional target task scheduling, the greedy heuristic rule is used to arrange task sequences. Reconstruct visibility masks after each task scheduling. The algorithm is ended after the last task in the sequence is scheduled.


### 3.2. Heuristic Genetic Algorithm (HGA)

The heuristic genetic algorithm (HGA) is an algorithm for optimizing the data downlink task sequence. The overall structure of the HGA is a combination of heuristic rules and genetic algorithm (GA), proposed for the background of specific problem, to enhance the effect of scheduling and planning. In HGA, we use selection, crossover, and mutated operations to generate offspring. As an improvement, we have abandoned the worst generation of the previous generation to prohibit it from entering the next generation. The overall process of the algorithm is shown in Algorithm1. These include the following points.Algorithm 1: Downlink schedule algorithm (DSA).
1Input T=PT,RT, VM=vm1,vm2,…,vmm
2Output Scheme
3If η>threshold do
4RegionaltargetspriorityruleRT
5End If
6For each task in T do
7RT,PT←TaskfillingRT,PT
8Solution←GreedyheuristicruleRT,PT,VM
9VM←VisibilitymaskreconstructionVM
10End For
11Return Scheme


#### 3.2.1. Importance of Regional Targets

Calculating the importance degree of regional targets is an important part of the HGA. The heuristic rule determines whether to implement the regional target priority rule by calculating the importance. The calculation of the regional target importance is determined by calculating the proportion of the time required for the overall downlink of the regional targets to occupy the earliest start time and the latest end time. The formula is shown as(14)η=DLkAD−stkADLvtVM−EvtVM.Calculate the importance degree and compare it with the threshold to decide whether to prioritize the regional targets or plan directly regardless of the target attributes.


#### 3.2.2. Coding

We use the serial number of the task sequence to encode each individual in the HGA. For each individual, its genetic makeup represents a unique sequence of task requests, and the scheduling and calculation of profits should follow this sequence. During the encoding process, the number of downlink task requests in the sequence must occur at most once and cannot be repeated. Since our optimization process and task scheduling process are separate, there is no need to encode decision variables.


#### 3.2.3. Fitness Function

The fitness function is calculated using the objective function proposed in Section2. Each calculation of the fitness function should be generated by the DSA.


#### 3.2.4. Selection

The selection operation is performed according to the method of roulette wheel selection. When the number of individuals in the population isN, the probability that the individual k with fitness Fitk is selected is shown by
(15)pk=Fitk∑i=1NFiti.In small satellite image downlink scheduling problem, since the income gap of each scheduling scheme is small and the numerical value is large, the process of increasing the selection pressure is performed.


#### 3.2.5. Offspring Generation

A new generation of population is mainly accomplished through genetic manipulation, retention of dominant individuals, and elimination of inferior solutions. Genetic manipulation includes crossover operation and mutation operation. The crossover operation uses the partially mapped crossover (PMX) that contains two points. After the crossover is completed, the code repair process is performed to ensure the validity of the individual code. Because of the uniqueness of the individual coding required for the mutation operation, the effect of individual mutation operation is achieved by the two-position code exchange method.Retention of dominant individuals ensures that the population can always be oriented towards a steady and growing degree of fitness. We chose to retain individuals with the highest degree of fitness to enter the genetic operations of the next generation of populations.Our heuristic genetic algorithm accepts inferior solutions but abandons the worst individual and regenerates a random task sequence. At the same time, we do not accept the solution after crossover operation and mutation operation worse than the original task sequence. For such a solution, we also abandon it.


#### 3.2.6. Stop Criterion

The stop criterion of the algorithm is determined by the set number of iterations. HGA continues to iterate until it satisfies the stop criterion, outputs the optimal task request sequence and the task arrangement status, and the final profit that can be obtained. In order to overcome the local optimal problem, we introduce a triggering mechanism. This triggering mechanism is a process of regenerating evolution after the objective function value has not been improved for several consecutive generations until the maximum number of executions set by the triggering mechanism is reached.


#### 3.2.7. Analysis of Algorithm

The complexity of this algorithm is similar to Scharnow study’s use of genetic algorithms to solve integer coding ordering problems. For such problems, the expected optimization time of the algorithm is Ω (n2) for each fitness landscape based on the sorting problem [19]. Because HGA is an improvement of the genetic algorithm, it has good convergence. In addition, the triggering mechanism also ensures the global searchability of genetic algorithm.Genetic algorithms have a good application in sequence scheduling problems. The integer encoding ensures that each task is unique and will not be repeated. Compared with the 0-1 encoding method, the integer encoding method is more suitable for large-scale task scenarios. In the form of integer coding, it is feasible to directly exchange the position of the task number, and the exchange of gene fragments in the individual can greatly increase the diversity of the population. The use of the DSA ensures that the generation plan can be used for execution because the DSA uses task scheduling based on constraint checking to ensure that the current time window of each scheduled time window task is available.


## 3.1. Downlink Schedule Algorithm (DSA)

DSA is a method we used to get the final data downlink sequences by requesting sequences of the tasks. It is also an algorithm that we need to call repeatedly to calculate the profits of scheduling solutions. In the DSA we proposed, there are two kinds of heuristic rules. We define them as regional target priority rule and greedy heuristic rule. The downlink schedule algorithm also includes a visibility mask reconstruction method and a task filling method. Visibility mask reconstruction method, task filling method, and two heuristic rules will be introduced firstly, and then, the complete flow of the DSA will be given.


### 3.1.1. Task Filling Method

After a data downlink task is completed, another data downlink task cannot be started immediately. It must satisfy the time interval between tasks that is longer than a certain time interval before the next data downlink task can begin. In order to facilitate the generation of the scheduling scheme afterwards, the task filling method is used to process each data downlink task. The method of filling is to fill in the minimum time interval to the task directly behind each task, see it as a whole, and get a new set of task sequences. The task filling process is shown in Figure3. Our subsequent sequence scheduling process is for newly generated task sequences.Figure 3
Task filling of sequences.From Figure3, it can be seen that the filled task sequence can be easily planned and arranged. At the same time, this method makes the sequence more compact, allowing a certain amount of time remaining in the same length of time, placing more data tasks into sequences that can be successfully downlinked.


### 3.1.2. Visibility Mask Reconstruction Method

Visibility mask reconstruction method can also be referred to as visibility mask clipping. The use of reconstruction methods can achieve the effect of simplifying the constraints and improving the scheduling efficiency. When a data downlink task determines its position in the ground station’s visibility masks, this part of the visibility masks has already been used and cannot be used by other data downlink tasks. Therefore, the subsequent sequence scheduling does not make sense for this part of the visibility masks that has already been occupied. We only need to search for those visibility masks that have not yet been occupied by data downlink tasks. The visibility mask reconstruction method is that after a data downlink task is successfully arranged, the visibility masks are processed, a new visibility mask sequence is regenerated, and the next downlink task scheduled only need to consider the constraints other than the visibility mask occupation.


### 3.1.3. Regional Target Priority Rule

The data downlink tasks of regional target include higher profits and have higher requirements for the visibility masks of ground stations. The schematic diagram of the regional target task scheduling using the regional target priority rule to prioritize the planning and scheduling of regional target tasks can improve the success rate of completion of tasks. At the same time, prioritizing the tasks of regional target can reduce the search scope of the visibility masks of ground stations and enhance the planning efficiency of other observation tasks.The use of the regional target priority rule will be determined based on the relationship between the regional target profit and the overall target profit. The determination rule will be given in Section3.2.1.


### 3.1.4. Greedy Heuristic Rule

The greedy heuristic rule requires that the data download task first fill in the earliest available position of the visibility masks, that is, it will arrange the task at the earliest position of the earliest available visibility mask that can be downloaded. Visibility mask resources are far from enough for downlink missions, and more intensive sequence arrangements can yield higher returns. By using greedy heuristic rules, the ground station’s visibility mask can be used more compactly. In addition, this method has been shown to obtain optimal solutions in the conventional sequence scheduling problem. We consider the time value of the task. Earlier tasks can get higher value, so we can still satisfy the use of greedy rules to get the best task sequence.Table1 shows the overall flow of the DSA. After the algorithm is initialized and input, the task is first filled and a new task sequence is generated. After that, when the regional target priority scheduling rules are met, the regional targets are prioritized according to the regional target priority rules; otherwise, plan directly regardless of the target attributes. After executing or skipping the regional target arrangement, the visibility mask is reconstructed and the schedule of the point target downlink tasks is started. Regardless of whether it is a point target or regional target task scheduling, the greedy heuristic rule is used to arrange task sequences. Reconstruct visibility masks after each task scheduling. The algorithm is ended after the last task in the sequence is scheduled.


## 3.1.1. Task Filling Method

After a data downlink task is completed, another data downlink task cannot be started immediately. It must satisfy the time interval between tasks that is longer than a certain time interval before the next data downlink task can begin. In order to facilitate the generation of the scheduling scheme afterwards, the task filling method is used to process each data downlink task. The method of filling is to fill in the minimum time interval to the task directly behind each task, see it as a whole, and get a new set of task sequences. The task filling process is shown in Figure3. Our subsequent sequence scheduling process is for newly generated task sequences.Figure 3
Task filling of sequences.From Figure3, it can be seen that the filled task sequence can be easily planned and arranged. At the same time, this method makes the sequence more compact, allowing a certain amount of time remaining in the same length of time, placing more data tasks into sequences that can be successfully downlinked.


## 3.1.2. Visibility Mask Reconstruction Method

Visibility mask reconstruction method can also be referred to as visibility mask clipping. The use of reconstruction methods can achieve the effect of simplifying the constraints and improving the scheduling efficiency. When a data downlink task determines its position in the ground station’s visibility masks, this part of the visibility masks has already been used and cannot be used by other data downlink tasks. Therefore, the subsequent sequence scheduling does not make sense for this part of the visibility masks that has already been occupied. We only need to search for those visibility masks that have not yet been occupied by data downlink tasks. The visibility mask reconstruction method is that after a data downlink task is successfully arranged, the visibility masks are processed, a new visibility mask sequence is regenerated, and the next downlink task scheduled only need to consider the constraints other than the visibility mask occupation.


## 3.1.3. Regional Target Priority Rule

The data downlink tasks of regional target include higher profits and have higher requirements for the visibility masks of ground stations. The schematic diagram of the regional target task scheduling using the regional target priority rule to prioritize the planning and scheduling of regional target tasks can improve the success rate of completion of tasks. At the same time, prioritizing the tasks of regional target can reduce the search scope of the visibility masks of ground stations and enhance the planning efficiency of other observation tasks.The use of the regional target priority rule will be determined based on the relationship between the regional target profit and the overall target profit. The determination rule will be given in Section3.2.1.


## 3.1.4. Greedy Heuristic Rule

The greedy heuristic rule requires that the data download task first fill in the earliest available position of the visibility masks, that is, it will arrange the task at the earliest position of the earliest available visibility mask that can be downloaded. Visibility mask resources are far from enough for downlink missions, and more intensive sequence arrangements can yield higher returns. By using greedy heuristic rules, the ground station’s visibility mask can be used more compactly. In addition, this method has been shown to obtain optimal solutions in the conventional sequence scheduling problem. We consider the time value of the task. Earlier tasks can get higher value, so we can still satisfy the use of greedy rules to get the best task sequence.Table1 shows the overall flow of the DSA. After the algorithm is initialized and input, the task is first filled and a new task sequence is generated. After that, when the regional target priority scheduling rules are met, the regional targets are prioritized according to the regional target priority rules; otherwise, plan directly regardless of the target attributes. After executing or skipping the regional target arrangement, the visibility mask is reconstructed and the schedule of the point target downlink tasks is started. Regardless of whether it is a point target or regional target task scheduling, the greedy heuristic rule is used to arrange task sequences. Reconstruct visibility masks after each task scheduling. The algorithm is ended after the last task in the sequence is scheduled.


## 3.2. Heuristic Genetic Algorithm (HGA)

The heuristic genetic algorithm (HGA) is an algorithm for optimizing the data downlink task sequence. The overall structure of the HGA is a combination of heuristic rules and genetic algorithm (GA), proposed for the background of specific problem, to enhance the effect of scheduling and planning. In HGA, we use selection, crossover, and mutated operations to generate offspring. As an improvement, we have abandoned the worst generation of the previous generation to prohibit it from entering the next generation. The overall process of the algorithm is shown in Algorithm1. These include the following points.Algorithm 1: Downlink schedule algorithm (DSA).
1Input T=PT,RT, VM=vm1,vm2,…,vmm
2Output Scheme
3If η>threshold do
4RegionaltargetspriorityruleRT
5End If
6For each task in T do
7RT,PT←TaskfillingRT,PT
8Solution←GreedyheuristicruleRT,PT,VM
9VM←VisibilitymaskreconstructionVM
10End For
11Return Scheme


### 3.2.1. Importance of Regional Targets

Calculating the importance degree of regional targets is an important part of the HGA. The heuristic rule determines whether to implement the regional target priority rule by calculating the importance. The calculation of the regional target importance is determined by calculating the proportion of the time required for the overall downlink of the regional targets to occupy the earliest start time and the latest end time. The formula is shown as(14)η=DLkAD−stkADLvtVM−EvtVM.Calculate the importance degree and compare it with the threshold to decide whether to prioritize the regional targets or plan directly regardless of the target attributes.


### 3.2.2. Coding

We use the serial number of the task sequence to encode each individual in the HGA. For each individual, its genetic makeup represents a unique sequence of task requests, and the scheduling and calculation of profits should follow this sequence. During the encoding process, the number of downlink task requests in the sequence must occur at most once and cannot be repeated. Since our optimization process and task scheduling process are separate, there is no need to encode decision variables.


### 3.2.3. Fitness Function

The fitness function is calculated using the objective function proposed in Section2. Each calculation of the fitness function should be generated by the DSA.


### 3.2.4. Selection

The selection operation is performed according to the method of roulette wheel selection. When the number of individuals in the population isN, the probability that the individual k with fitness Fitk is selected is shown by
(15)pk=Fitk∑i=1NFiti.In small satellite image downlink scheduling problem, since the income gap of each scheduling scheme is small and the numerical value is large, the process of increasing the selection pressure is performed.


### 3.2.5. Offspring Generation

A new generation of population is mainly accomplished through genetic manipulation, retention of dominant individuals, and elimination of inferior solutions. Genetic manipulation includes crossover operation and mutation operation. The crossover operation uses the partially mapped crossover (PMX) that contains two points. After the crossover is completed, the code repair process is performed to ensure the validity of the individual code. Because of the uniqueness of the individual coding required for the mutation operation, the effect of individual mutation operation is achieved by the two-position code exchange method.Retention of dominant individuals ensures that the population can always be oriented towards a steady and growing degree of fitness. We chose to retain individuals with the highest degree of fitness to enter the genetic operations of the next generation of populations.Our heuristic genetic algorithm accepts inferior solutions but abandons the worst individual and regenerates a random task sequence. At the same time, we do not accept the solution after crossover operation and mutation operation worse than the original task sequence. For such a solution, we also abandon it.


### 3.2.6. Stop Criterion

The stop criterion of the algorithm is determined by the set number of iterations. HGA continues to iterate until it satisfies the stop criterion, outputs the optimal task request sequence and the task arrangement status, and the final profit that can be obtained. In order to overcome the local optimal problem, we introduce a triggering mechanism. This triggering mechanism is a process of regenerating evolution after the objective function value has not been improved for several consecutive generations until the maximum number of executions set by the triggering mechanism is reached.


### 3.2.7. Analysis of Algorithm

The complexity of this algorithm is similar to Scharnow study’s use of genetic algorithms to solve integer coding ordering problems. For such problems, the expected optimization time of the algorithm is Ω (n2) for each fitness landscape based on the sorting problem [19]. Because HGA is an improvement of the genetic algorithm, it has good convergence. In addition, the triggering mechanism also ensures the global searchability of genetic algorithm.Genetic algorithms have a good application in sequence scheduling problems. The integer encoding ensures that each task is unique and will not be repeated. Compared with the 0-1 encoding method, the integer encoding method is more suitable for large-scale task scenarios. In the form of integer coding, it is feasible to directly exchange the position of the task number, and the exchange of gene fragments in the individual can greatly increase the diversity of the population. The use of the DSA ensures that the generation plan can be used for execution because the DSA uses task scheduling based on constraint checking to ensure that the current time window of each scheduled time window task is available.


## 3.2.1. Importance of Regional Targets

Calculating the importance degree of regional targets is an important part of the HGA. The heuristic rule determines whether to implement the regional target priority rule by calculating the importance. The calculation of the regional target importance is determined by calculating the proportion of the time required for the overall downlink of the regional targets to occupy the earliest start time and the latest end time. The formula is shown as(14)η=DLkAD−stkADLvtVM−EvtVM.Calculate the importance degree and compare it with the threshold to decide whether to prioritize the regional targets or plan directly regardless of the target attributes.


## 3.2.2. Coding

We use the serial number of the task sequence to encode each individual in the HGA. For each individual, its genetic makeup represents a unique sequence of task requests, and the scheduling and calculation of profits should follow this sequence. During the encoding process, the number of downlink task requests in the sequence must occur at most once and cannot be repeated. Since our optimization process and task scheduling process are separate, there is no need to encode decision variables.


## 3.2.3. Fitness Function

The fitness function is calculated using the objective function proposed in Section2. Each calculation of the fitness function should be generated by the DSA.


## 3.2.4. Selection

The selection operation is performed according to the method of roulette wheel selection. When the number of individuals in the population isN, the probability that the individual k with fitness Fitk is selected is shown by
(15)pk=Fitk∑i=1NFiti.In small satellite image downlink scheduling problem, since the income gap of each scheduling scheme is small and the numerical value is large, the process of increasing the selection pressure is performed.


## 3.2.5. Offspring Generation

A new generation of population is mainly accomplished through genetic manipulation, retention of dominant individuals, and elimination of inferior solutions. Genetic manipulation includes crossover operation and mutation operation. The crossover operation uses the partially mapped crossover (PMX) that contains two points. After the crossover is completed, the code repair process is performed to ensure the validity of the individual code. Because of the uniqueness of the individual coding required for the mutation operation, the effect of individual mutation operation is achieved by the two-position code exchange method.Retention of dominant individuals ensures that the population can always be oriented towards a steady and growing degree of fitness. We chose to retain individuals with the highest degree of fitness to enter the genetic operations of the next generation of populations.Our heuristic genetic algorithm accepts inferior solutions but abandons the worst individual and regenerates a random task sequence. At the same time, we do not accept the solution after crossover operation and mutation operation worse than the original task sequence. For such a solution, we also abandon it.


## 3.2.6. Stop Criterion

The stop criterion of the algorithm is determined by the set number of iterations. HGA continues to iterate until it satisfies the stop criterion, outputs the optimal task request sequence and the task arrangement status, and the final profit that can be obtained. In order to overcome the local optimal problem, we introduce a triggering mechanism. This triggering mechanism is a process of regenerating evolution after the objective function value has not been improved for several consecutive generations until the maximum number of executions set by the triggering mechanism is reached.


## 3.2.7. Analysis of Algorithm

The complexity of this algorithm is similar to Scharnow study’s use of genetic algorithms to solve integer coding ordering problems. For such problems, the expected optimization time of the algorithm is Ω (n2) for each fitness landscape based on the sorting problem [19]. Because HGA is an improvement of the genetic algorithm, it has good convergence. In addition, the triggering mechanism also ensures the global searchability of genetic algorithm.Genetic algorithms have a good application in sequence scheduling problems. The integer encoding ensures that each task is unique and will not be repeated. Compared with the 0-1 encoding method, the integer encoding method is more suitable for large-scale task scenarios. In the form of integer coding, it is feasible to directly exchange the position of the task number, and the exchange of gene fragments in the individual can greatly increase the diversity of the population. The use of the DSA ensures that the generation plan can be used for execution because the DSA uses task scheduling based on constraint checking to ensure that the current time window of each scheduled time window task is available.


## 4. Experimental Analysis

In this section, we verify the downlink schedule algorithm (DSA) and heuristic genetic algorithm (HGA) proposed in Section3 through experiments.


### 4.1. Experimental Environment

The proposed algorithms are implemented by Matlab 2016b on a laptop with Core I5-3337U 1.8 GHz CPU, 4 GB memory, and Windows 8.1 operating system.


### 4.2. Test Instance

Because of the lack of benchmarking examples for small satellite image downlink scheduling problem, we designed three types of test cases from the practical application needs. They are small-scale missions, medium-scale missions, and large-scale missions. Three kinds of specific scenarios are set for each scale. These scenarios include two types of tasks: downlink task of the regional target and point target. Our task size is chosen to be 50, 100, 150, 200, 250, and 300. For satellite ground station time windows, we gave 22 ground station visibility masks. Our experiments will use these test instances and ground station visibility masks.


### 4.3. Evaluation Indicator

We have proposed two indicators that are considered from different perspectives. One is the task revenue index considered from the perspective of planning problem quality, and the other is the number of tasks successfully completed in the task request sequence from the quantitative perspective and the task completion percentage index. Combining these two indicators can provide a more comprehensive assessment of the algorithm we proposed in Section3.


### 4.4. Comparison Algorithm

Construction heuristic algorithm is a simple and efficient algorithm for solving the downlink problem of satellite data. According to the research of satellite mission planning, this algorithm sets several priority rules for task scheduling and completes the matching of the requested task sequence with the visibility masks of the ground station. This problem has many similarities with the multiple knapsack problem (MKP) and can be considered as one of the MKPs. Therefore, the commonly used heuristic rules for solving the MKP can also be applied to the small satellite image downlink scheduling problem. This kind of scheduling scheme generation algorithm is acceptable because we pay attention to the feasibility and simplicity of the scheduling scheme in the actual application process, and the quality of the solution is only considered afterwards. The sorting criteria for SSIDSP we consider are as follows:Criterion 1: the profit of higher image acquisition tasks pkD is preferred; Criterion 2: earlier end time of image acquisition tasks etkIA is preferred; Criterion 3: higher unit profit for image acquisition tasks pkD/Durk is preferred; and Criterion 4: shorter data downlink task duration Durk is preferred. In addition, we also selected the most basic genetic algorithm as a comparison algorithm [18]. In this kind of scheduling problem, the genetic algorithm has a good advantage. The exact algorithm is difficult to solve large-scale problems. Other metaheuristic problems lack research on this kind of problem. Therefore, we have not chosen to compare the exact algorithm and other metaheuristic algorithms.Our experimental results are shown in Table2. Table 2 compares HGA with GA and construction heuristic algorithm. The result of the profit is shown in the table, which is shown as Profit, and the number of successful small satellite image downlink requests, which is shown as SR.Table 2
Comparison of HGA, GA, and construction heuristic algorithm.
Instance
HGA
GA
Construction heuristic algorithm
Criterion 1
Criterion 2
Criterion 3
Criterion 4
Profit
SR
Profit
SR
Profit
SR
Profit
SR
Profit
SR
Profit
SR
50-1
2452.9
48
2417.6
46
1830.2
46
1637.3
47
1906.5
47
2210.4
48
50-2
1769.8
48
1720.6
48
810.4
49
1203.2
49
952.4
49
1087.9
49
50-3
2266.6
49
2045.4
47
1231.5
48
1172.6
49
1358.1
49
1358.8
49
100-1
4736.2
95
4543.5
93
2734.7
94
3395.1
96
2630.4
95
3950.1
95
100-2
3728.9
95
3668.5
95
2290.8
94
2243.5
96
2561.1
94
3511.5
94
100-3
4145.3
93
3989.2
93
2461.1
90
2550.5
91
2707.0
95
3909.5
95
150-1
5279.4
141
5177.3
140
3275.8
137
2388.6
141
3261.6
140
4674.8
141
150-2
5803.8
139
5776.6
139
3063.7
137
3218.8
140
3536.8
140
5744.1
140
150-3
4857.5
142
4789.4
136
2940.8
138
2821.4
141
2996.2
140
3764.4
140
200-1
6744.3
183
5808.5
176
3680.3
179
2959.1
185
3392.0
182
5276.0
183
200-2
6553.3
184
6509.3
183
3971.7
182
4314.3
185
4214.7
184
3951.8
183
200-3
6701.9
185
6293.9
185
3318.0
184
3538.7
188
3458.9
183
3843.8
184
250-1
7577.8
235
7209.9
234
3711.0
229
2762.9
230
4541.1
231
4927.8
232
250-2
7496.2
233
7465.2
229
4012.7
229
4304.4
232
4310.4
231
5005.3
232
250-3
7755.4
234
7491.9
230
4390.2
227
3949.7
227
4254.6
225
5135.9
229
300-1
8984.6
277
8783.5
271
3751.2
269
4971.8
270
4374.7
268
4844.3
265
300-2
8126.9
276
7692.5
275
4509.4
266
3190.1
272
4743.7
268
6210.4
269
300-3
7770.3
278
7758.1
278
4509.4
271
3190.1
272
4743.7
273
6210.4
274It can be seen from Algorithm2 that compared with the construction heuristic algorithm, GA and HGA are superior to the construction heuristic algorithm in terms of both the task completion revenue and the number of successfully completed tasks. Then compare the HGA with the GA, we can easily see that the HGA is better than the GA, which has a great relationship with the heuristic rules in the algorithm. The increase in the size of the task makes the effect of heuristic rules effectively reflected.Algorithm 2: Heuristic genetic algorithm (HGA).
1Input T=PT,RT, VM=vm1,vm2,…,vmm
2Output Best Scheme
3Random Initialize Population P
4Bestsolution←DSAP
5Do until reach Stop Criterion
6P←UpdateworstindividualP
7p∗←RetainbestindividualP
8p1,p2←SeclectionP
9p1,p2←Crossoverp1,p2
10If DSAP′>DSAP do
11UpdateP←P′
12End If
13p3,p4←SeclectionP
14p3,p4←MutationP
15If DSAP′>DSAP do
16UpdateP←P′
17End If
18Bestsolution′←DSAP
19If Bestsolution′>Bestsolution do
20Bestsolution←Bestsolution′
21Else
22P←Updatep∗
23End If
24If No improvement > η and counter< τ do
25     Redo HGA
26     counter = counter+1
27End If
28End Do
29Return Best SchemeIn order to display the profits of planning requests more intuitively, we present the results in Figure4. It can be seen from the figure that the profits of GA and HGA are better than all construction heuristic algorithm and that the algorithm’s income gap increases as the task size increases. In solving large-scale downlink scheduling problem, GA and HGA have better performance. In construction heuristic algorithm, the heuristic rule 4, i.e., the shorter data downlink duration Durk priority rule has a better performance. This is related to scheduling tasks with shorter durations and leaving more residuals for other tasks.Figure 4
Profit comparison.After that, we calculate the average results of different algorithms for each task number and compare the overall performance of the algorithms. We compared the average number of completions of the downlink requests and the average percentage of request completion. The results are shown in Table3.Table 3
Comparison of average results of HGA and GA and construction heuristic algorithm.
Instance
HGA
GA
Construction heuristic algorithm
Criterion 1
Criterion 2
Criterion 3
Criterion 4
Avg. value
Avg. percentage
Avg. value
Avg. percentage
Avg. value
Avg. percentage
Avg. value
Avg. percentage
Avg. value
Avg. percentage
Avg. value
Avg. percentage
50
2163.100
0.967
2061
0.940
1290.698
0.953
1337.700
0.967
1405.654
0.967
1552.367
0.973
100
4203.467
0.943
4067.067
0.937
2495.533
0.927
2729.700
0.943
2632.833
0.947
3790.367
0.947
150
5313.567
0.938
5247.767
0.922
3093.433
0.916
2809.600
0.938
3265
0.933
4727.767
0.936
200
6667
0.920
6203.900
0.907
3656.667
0.908
3604
0.930
3689
0.915
4357.200
0.917
250
7610
0.936
7389
0.924
4037.967
0.913
3672.333
0.919
4369
0.916
5023
0.924
300
8294
0.923
8078.033
0.916
4256.667
0.896
3784.000
0.904
4620.700
0.899
5755.033
0.898It can be seen from Table3 that compared with GA and the construction heuristic algorithm, the proposed HGA can guarantee more downlink requests under large-scale task scenarios. When the scale rises to 300, there is still 92.3% of the average task completion rate, which can meet the needs of data downlink tasks well. To further analyze the number of tasks completed by the HGA and DSA, we show the average profit of different algorithms in Figure 5 and the average task completion ratio in Figure 6.Figure 5
Average profit of different algorithms.Figure 6
Average task completion.The results of the different algorithms are shown in Figure5. In the case of different scenarios and different task sizes, the performance of the HGA is obviously better compared with the other four heuristic algorithms. In the heuristic algorithm, the performance of Criterion 4 is the best. As can be seen from the figure, the increase in average profit has been reduced with the same increasing speed. But the rate of decline is within the controllable range, which is what DSA does.As can be seen from Figure6, the percentage of task requests that can be completed by the HGA declines due to task conflicts that grow rapidly as the number of tasks increases. Although the completion rate of the task as a whole showed a declining trend in the process of scale increase, it still maintains a task completion rate of more than 90%. Compared with the construction heuristic algorithms’ Criterions 1-4, as the task scale increases, HGA’s advantage in the completion rate of the task is gradually obvious. In the case of small-scale, Criterion 4 is also one of the algorithms that can be used as an alternative.Through experimental analysis, the following conclusions can be made:(1)
The GA and the HGA are superior to the construction heuristic algorithm and have greatly improved the planning results. After the increase of the task scale, the advantages of the planning results of the HGA and GA are more obvious, and the gap between the algorithms and construction heuristic algorithm is increasing. Comparing HGA with GA, the task revenue and task completion rate have been further improved, which have played a role in improving the revenue and the completed number of task requests
(2)
In construction heuristic algorithm, Criterion 4, that is, the shorter duration of the data downlink, has a better effect than the other three heuristic rules. The shorter duration allows more tasks to reflect its time value
(3)
The profit of the HGA is stable with the increase of the task scale. However, from the perspective of completing percentage, the task completion rate shows a downward trend as a whole, which is related to the increase of the task density after the increase of the task scale. The increase in mission density has exacerbated the competition of ground station visibility mask resources and also increased the conflict between tasks
(4)
The HGA and DSA can guarantee more than 90% completion rate of the task in our test instance, which can well meet the needs of the data downlink mission. In the case of a small task scale, Criterion 4 in construction heuristic algorithm can also be one of the algorithms that can be selected


## 4.1. Experimental Environment

The proposed algorithms are implemented by Matlab 2016b on a laptop with Core I5-3337U 1.8 GHz CPU, 4 GB memory, and Windows 8.1 operating system.


## 4.2. Test Instance

Because of the lack of benchmarking examples for small satellite image downlink scheduling problem, we designed three types of test cases from the practical application needs. They are small-scale missions, medium-scale missions, and large-scale missions. Three kinds of specific scenarios are set for each scale. These scenarios include two types of tasks: downlink task of the regional target and point target. Our task size is chosen to be 50, 100, 150, 200, 250, and 300. For satellite ground station time windows, we gave 22 ground station visibility masks. Our experiments will use these test instances and ground station visibility masks.


## 4.3. Evaluation Indicator

We have proposed two indicators that are considered from different perspectives. One is the task revenue index considered from the perspective of planning problem quality, and the other is the number of tasks successfully completed in the task request sequence from the quantitative perspective and the task completion percentage index. Combining these two indicators can provide a more comprehensive assessment of the algorithm we proposed in Section3.


## 4.4. Comparison Algorithm

Construction heuristic algorithm is a simple and efficient algorithm for solving the downlink problem of satellite data. According to the research of satellite mission planning, this algorithm sets several priority rules for task scheduling and completes the matching of the requested task sequence with the visibility masks of the ground station. This problem has many similarities with the multiple knapsack problem (MKP) and can be considered as one of the MKPs. Therefore, the commonly used heuristic rules for solving the MKP can also be applied to the small satellite image downlink scheduling problem. This kind of scheduling scheme generation algorithm is acceptable because we pay attention to the feasibility and simplicity of the scheduling scheme in the actual application process, and the quality of the solution is only considered afterwards. The sorting criteria for SSIDSP we consider are as follows:Criterion 1: the profit of higher image acquisition tasks pkD is preferred; Criterion 2: earlier end time of image acquisition tasks etkIA is preferred; Criterion 3: higher unit profit for image acquisition tasks pkD/Durk is preferred; and Criterion 4: shorter data downlink task duration Durk is preferred. In addition, we also selected the most basic genetic algorithm as a comparison algorithm [18]. In this kind of scheduling problem, the genetic algorithm has a good advantage. The exact algorithm is difficult to solve large-scale problems. Other metaheuristic problems lack research on this kind of problem. Therefore, we have not chosen to compare the exact algorithm and other metaheuristic algorithms.Our experimental results are shown in Table2. Table 2 compares HGA with GA and construction heuristic algorithm. The result of the profit is shown in the table, which is shown as Profit, and the number of successful small satellite image downlink requests, which is shown as SR.Table 2
Comparison of HGA, GA, and construction heuristic algorithm.
Instance
HGA
GA
Construction heuristic algorithm
Criterion 1
Criterion 2
Criterion 3
Criterion 4
Profit
SR
Profit
SR
Profit
SR
Profit
SR
Profit
SR
Profit
SR
50-1
2452.9
48
2417.6
46
1830.2
46
1637.3
47
1906.5
47
2210.4
48
50-2
1769.8
48
1720.6
48
810.4
49
1203.2
49
952.4
49
1087.9
49
50-3
2266.6
49
2045.4
47
1231.5
48
1172.6
49
1358.1
49
1358.8
49
100-1
4736.2
95
4543.5
93
2734.7
94
3395.1
96
2630.4
95
3950.1
95
100-2
3728.9
95
3668.5
95
2290.8
94
2243.5
96
2561.1
94
3511.5
94
100-3
4145.3
93
3989.2
93
2461.1
90
2550.5
91
2707.0
95
3909.5
95
150-1
5279.4
141
5177.3
140
3275.8
137
2388.6
141
3261.6
140
4674.8
141
150-2
5803.8
139
5776.6
139
3063.7
137
3218.8
140
3536.8
140
5744.1
140
150-3
4857.5
142
4789.4
136
2940.8
138
2821.4
141
2996.2
140
3764.4
140
200-1
6744.3
183
5808.5
176
3680.3
179
2959.1
185
3392.0
182
5276.0
183
200-2
6553.3
184
6509.3
183
3971.7
182
4314.3
185
4214.7
184
3951.8
183
200-3
6701.9
185
6293.9
185
3318.0
184
3538.7
188
3458.9
183
3843.8
184
250-1
7577.8
235
7209.9
234
3711.0
229
2762.9
230
4541.1
231
4927.8
232
250-2
7496.2
233
7465.2
229
4012.7
229
4304.4
232
4310.4
231
5005.3
232
250-3
7755.4
234
7491.9
230
4390.2
227
3949.7
227
4254.6
225
5135.9
229
300-1
8984.6
277
8783.5
271
3751.2
269
4971.8
270
4374.7
268
4844.3
265
300-2
8126.9
276
7692.5
275
4509.4
266
3190.1
272
4743.7
268
6210.4
269
300-3
7770.3
278
7758.1
278
4509.4
271
3190.1
272
4743.7
273
6210.4
274It can be seen from Algorithm2 that compared with the construction heuristic algorithm, GA and HGA are superior to the construction heuristic algorithm in terms of both the task completion revenue and the number of successfully completed tasks. Then compare the HGA with the GA, we can easily see that the HGA is better than the GA, which has a great relationship with the heuristic rules in the algorithm. The increase in the size of the task makes the effect of heuristic rules effectively reflected.Algorithm 2: Heuristic genetic algorithm (HGA).
1Input T=PT,RT, VM=vm1,vm2,…,vmm
2Output Best Scheme
3Random Initialize Population P
4Bestsolution←DSAP
5Do until reach Stop Criterion
6P←UpdateworstindividualP
7p∗←RetainbestindividualP
8p1,p2←SeclectionP
9p1,p2←Crossoverp1,p2
10If DSAP′>DSAP do
11UpdateP←P′
12End If
13p3,p4←SeclectionP
14p3,p4←MutationP
15If DSAP′>DSAP do
16UpdateP←P′
17End If
18Bestsolution′←DSAP
19If Bestsolution′>Bestsolution do
20Bestsolution←Bestsolution′
21Else
22P←Updatep∗
23End If
24If No improvement > η and counter< τ do
25     Redo HGA
26     counter = counter+1
27End If
28End Do
29Return Best SchemeIn order to display the profits of planning requests more intuitively, we present the results in Figure4. It can be seen from the figure that the profits of GA and HGA are better than all construction heuristic algorithm and that the algorithm’s income gap increases as the task size increases. In solving large-scale downlink scheduling problem, GA and HGA have better performance. In construction heuristic algorithm, the heuristic rule 4, i.e., the shorter data downlink duration Durk priority rule has a better performance. This is related to scheduling tasks with shorter durations and leaving more residuals for other tasks.Figure 4
Profit comparison.After that, we calculate the average results of different algorithms for each task number and compare the overall performance of the algorithms. We compared the average number of completions of the downlink requests and the average percentage of request completion. The results are shown in Table3.Table 3
Comparison of average results of HGA and GA and construction heuristic algorithm.
Instance
HGA
GA
Construction heuristic algorithm
Criterion 1
Criterion 2
Criterion 3
Criterion 4
Avg. value
Avg. percentage
Avg. value
Avg. percentage
Avg. value
Avg. percentage
Avg. value
Avg. percentage
Avg. value
Avg. percentage
Avg. value
Avg. percentage
50
2163.100
0.967
2061
0.940
1290.698
0.953
1337.700
0.967
1405.654
0.967
1552.367
0.973
100
4203.467
0.943
4067.067
0.937
2495.533
0.927
2729.700
0.943
2632.833
0.947
3790.367
0.947
150
5313.567
0.938
5247.767
0.922
3093.433
0.916
2809.600
0.938
3265
0.933
4727.767
0.936
200
6667
0.920
6203.900
0.907
3656.667
0.908
3604
0.930
3689
0.915
4357.200
0.917
250
7610
0.936
7389
0.924
4037.967
0.913
3672.333
0.919
4369
0.916
5023
0.924
300
8294
0.923
8078.033
0.916
4256.667
0.896
3784.000
0.904
4620.700
0.899
5755.033
0.898It can be seen from Table3 that compared with GA and the construction heuristic algorithm, the proposed HGA can guarantee more downlink requests under large-scale task scenarios. When the scale rises to 300, there is still 92.3% of the average task completion rate, which can meet the needs of data downlink tasks well. To further analyze the number of tasks completed by the HGA and DSA, we show the average profit of different algorithms in Figure 5 and the average task completion ratio in Figure 6.Figure 5
Average profit of different algorithms.Figure 6
Average task completion.The results of the different algorithms are shown in Figure5. In the case of different scenarios and different task sizes, the performance of the HGA is obviously better compared with the other four heuristic algorithms. In the heuristic algorithm, the performance of Criterion 4 is the best. As can be seen from the figure, the increase in average profit has been reduced with the same increasing speed. But the rate of decline is within the controllable range, which is what DSA does.As can be seen from Figure6, the percentage of task requests that can be completed by the HGA declines due to task conflicts that grow rapidly as the number of tasks increases. Although the completion rate of the task as a whole showed a declining trend in the process of scale increase, it still maintains a task completion rate of more than 90%. Compared with the construction heuristic algorithms’ Criterions 1-4, as the task scale increases, HGA’s advantage in the completion rate of the task is gradually obvious. In the case of small-scale, Criterion 4 is also one of the algorithms that can be used as an alternative.Through experimental analysis, the following conclusions can be made:(1)
The GA and the HGA are superior to the construction heuristic algorithm and have greatly improved the planning results. After the increase of the task scale, the advantages of the planning results of the HGA and GA are more obvious, and the gap between the algorithms and construction heuristic algorithm is increasing. Comparing HGA with GA, the task revenue and task completion rate have been further improved, which have played a role in improving the revenue and the completed number of task requests
(2)
In construction heuristic algorithm, Criterion 4, that is, the shorter duration of the data downlink, has a better effect than the other three heuristic rules. The shorter duration allows more tasks to reflect its time value
(3)
The profit of the HGA is stable with the increase of the task scale. However, from the perspective of completing percentage, the task completion rate shows a downward trend as a whole, which is related to the increase of the task density after the increase of the task scale. The increase in mission density has exacerbated the competition of ground station visibility mask resources and also increased the conflict between tasks
(4)
The HGA and DSA can guarantee more than 90% completion rate of the task in our test instance, which can well meet the needs of the data downlink mission. In the case of a small task scale, Criterion 4 in construction heuristic algorithm can also be one of the algorithms that can be selected


## 5. Conclusion

In this paper, we studied SSIDSP that contains regional targets. We give a description of the textual and mathematical form of the SSIDSP that contains the regional targets. For this problem, the difficulty of the problem has been greatly improved and increased in the planning process due to the simultaneous need of the profit of the task, the ground visibility mask, and other complicated constraints.According to the characteristics of the problem, we proposed a mathematical model that considers the time value of the task. Subsequently, we gave three algorithms for this problem, namely, construction heuristic algorithm, DSA, and HGA. We use four rules in construction heuristic algorithm. The DSA contains two heuristic rules, and it also contains two methods that are effective for problem solving. HGA is an improvement of GA. On the one hand, it considers the index of the importance of regional targets to judge whether to use heuristic rules; on the other hand, it designs a dedicated genetic algorithm flow.To verify the validity of the proposed algorithms, we conducted small-scale, medium-scale, and large-scale experimental tests. Through experiments, it is verified that the HGA and DSA have higher planning profit and more number of task requests that can be completed compared to the GA and the construction heuristic algorithm. At the same time, the result also shows that as the number of tasks increases, the advantages of the HGA are more pronounced. In the construction heuristic algorithm, shorter data downlink task duration priority rule is better than that of other heuristic rule algorithms. In addition, with the increase in the size of the tasks, although the completion ratio of the schedule has decreased, the overall effect is still better, and it can be said that it is an effective solution to the scheduling problem of data downlink tasks that include regional targets.The SSIDSP we studied belongs to the issue of a single satellite. In the future research, we can consider the issue of multisatellite mission planning. In addition, the situation that includes the problem of randomly reaching the task can also be considered. These tasks are emergency tasks, have higher task priorities, and need to be prioritized during data downlink. The addition of this kind of task will make the task constraints complicated, and it also needs to propose an algorithm that adapts to the emergency task to solve this problem.



---

*Source: 1371852-2019-01-27.xml*