Discrete Dynamics in Nature and Society

Volume 2018, Article ID 1531452, 11 pages

https://doi.org/10.1155/2018/1531452

## A Hybrid Genetic Algorithm for Satellite Image Downlink Scheduling Problem

College of Information System and Management, National University of Defense Technology, Changsha, Hunan 410073, China

Correspondence should be addressed to Feng Yao; nc.ude.tdun@gnefoay

Received 5 January 2018; Accepted 16 April 2018; Published 17 May 2018

Academic Editor: Lu Zhen

Copyright © 2018 Bingyu Song et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The satellite image downlink scheduling problem (SIDSP) is included in satellite mission planning as an important part. A customer demand is finished only if the corresponding images are eventually downloaded. Due to the growing customer demands and the limited ground resources, SIDSP is an oversubscribed scheduling problem. In this paper, we investigate SIDSP with the case study of China’s commercial remote sensing satellite constellation (SuperView-1) and exploit the serial scheduling scheme for solving it. The idea is first determining a permutation of the downlink requests and then producing a schedule from the given ordered requests. A schedule generation algorithm (SGA) is proposed to assign the downlink time window for each scheduled request according to a given request permutation. A hybrid genetic algorithm (HGA) combined with neighborhood search is proposed to optimize the downlink request permutation with the purpose of maximizing the utility function. Experimental results on six groups of instances with different density demonstrate the effectiveness of the proposed approach.

#### 1. Introduction

Most of the literature on satellite mission planning is divided into two categories: optical satellites [1–4] and Synthetic Aperture Radar (SAR) satellites [5–12]. The satellite image acquisition and image downlink are two main scheduling problems in satellite mission planning. The image acquisition scheduling is a process of selecting observation tasks (shot strips) generated from customer demands. All selected observation tasks consist of a set of requests as the input of SIDSP. The image downlink scheduling is a process of selecting a subset of downlink requests among the candidate set. Only if the image is successfully transmitted can the utility of the corresponding demand be counted. Considering all kinds of constraints, the subset of requests that can eventually be transmitted, their corresponding ground stations and downlink time windows are the output of SIDSP with the purpose of maximizing the utility function. SIDSP is a complex constrained optimization problem.

The growing customer demands and the limited ground resources make SIDSP become an oversubscribed scheduling problem. Not all the requests can be scheduled and there are cases that satellite has sufficient conditions for an imaging but cannot arrange a downlink for it, which causes the imaging to be removed from the image acquisition plan and the corresponding customer demand has to be shelved. Image downlink may become a bottleneck in the efficiency of the whole satellite system.

Satellite image downlink system is mainly composed of on-board transmission system and ground receiving system. The on-board transmission system includes transmitter and antennas. The ground receiving system includes receiver and antennas. Satellite image downlink mission is to transmit the original or compressed data to the ground station by satellite-ground data link under the certain code rate and bit error rate. Satellites can work in two modes: (1) the antennas can work separately and they can independently downlink different images to one or different ground stations simultaneously; (2) only one antenna can work to downlink at a time. Downlink also can be classified into two ways: (1) the observed images are transmitted to the ground station in real time when the observation target and the ground station are simultaneously visible to the satellite; (2) first store observed images in the on-board memory and then transmit data to the ground station when the satellite is passing.

SIDSP and its variations have been studied by many authors, mainly divided into single-satellite problems [10–12] and multisatellite problems [1, 3, 5–9]. Single-satellite problem deals with the resource contention for satellite internal requests, while multisatellite problem should also take the resource contention for requests from different satellites into consideration. If every satellite can transmit data independently without affecting each other, the multisatellite problem can be transformed into a single-satellite problem. The constraints of SIDSP are not fixed, varying with the specific case. Different from the previous literature, we consider the constraints of satellite memory capacity in our case, which is detailed in Section 2.

The solving methods are mainly divided into three categories: (1) exact solution algorithms (e.g., mixed integer programming [13], dynamic programming [14], and branch and bound algorithm [15]); (2) heuristic algorithms (e.g., a priority-based heuristic [3], an ejection-chain heuristic [11], and a Lagrangian heuristic [16]); (3) metaheuristic algorithms (e.g., simulated annealing [12], tabu search [12, 17], and genetic algorithm [18]). The performance of these solving methods is measured through the instances with varied size and complexity.

In this paper, we investigate SIDSP with the case study of China’s commercial remote sensing satellite constellation, SuperView-1. SuperView-1 consists of four optical satellites with the resolution of 0.5 meters. Two of them were launched in December 28, 2016, and the other two were launched in the later stage of the project. The four satellites will network with a 90-degree angle between each other, realizing the global revisit within one day. As a commercial satellite constellation, SuperView-1 will provide global customers with remote sensing data services for national land resources mapping, environmental monitoring, financial insurance, and value-added service in the Internet industry. There are a large number of images that need to be transmitted every day. In addition, China’s ground stations are built on the mainland and not scattered around the world. In the project of SuperView-1, three domestic ground stations and one Arctic ground station are used to downlink images. It takes a fee to use the Arctic ground station for downlink in each orbit. These specific situations increase the difficulty of scheduling.

The process currently in use for SuperView-1 downlink scheduling includes two phases: (1) construction of the schedules with a priority-based heuristic and (2) human intervention, which do not perform very well. To improve the efficiency of the downlink scheduling is significant for the whole satellite system. Adapting to the characteristic of SIDSP, we exploit the serial scheduling scheme involving two key parts: (1) determining a permutation of the downlink requests and (2) producing a schedule from the given ordered requests. A schedule generation algorithm (SGA) is proposed to assign the downlink time window for each scheduled request. In SGA, we use the greedy heuristic rule, scheduling each request to the earliest available time and designing two heuristic rules to improve the utility considering the cost of the Arctic ground station. We propose a hybrid genetic algorithm (HGA) combined with neighborhood search to optimize the downlink request permutation with the purpose of maximizing the utility function. To validate the effectiveness of the proposed approach, we carry out experiments on several groups of instances with different density and compare HGA with the commonly used construction heuristic algorithms. The experimental results show that HGA and the heuristic rules we design in SGA significantly improve downlink throughput and schedule quality.

The remainder of the paper is organized as follows. Section 2 gives the description of SIDSP in SuperView-1. The solution approach for SIDSP and several key algorithms are introduced in Section 3. Section 4 presents the experimental results of the proposed approach on several groups of instances with different density and the comparison between HGA and the construction heuristic algorithms. Concluding remarks are drawn in Section 5.

#### 2. Problem Description

In this section, SIDSP in SuperView-1 is detailed as the studied case. Each SIDSP has its own restrictions and properties that can be exploited. We hope to discover the commonalities of SIDSP and show the special properties through investigating the case to make preparations for the design of solution approach.

Due to the special structure of the constellation where four satellites operate with a 90-degree angle between each other, every satellite can transmit data independently. For this reason, SIDSP in SuperView-1 can be transformed into a single-satellite problem. Let be a set of downlink requests. Each request is associated with the start time of image acquisition , the end time of image acquisition , the start time of downlink , the end time of downlink , the profit , the size , and the deadline . A downlink activity can be carried out only when the satellite is passing over a ground station. This time interval is called visibility mask of the station. Let be a set of visibility masks. Each visibility mask is associated with the start time , the end time , and the cost (only each visibility mask of the Arctic ground station needs a cost; other visibility masks’ cost is 0). Moreover, the memory capacity of each satellite is . Let be the current satellite storage when the image acquisition of request is finished. Let be binary matrix such that if the downlink of request is assigned to visibility mask and otherwise. Let be a set of scheduled downlink requests.

We make the following assumptions:(a)The image acquisition schedule is given and not to be changed; that is, and are already generated.(b)The gaps between two consecutive downlinks are ignored.(c)The compression ratio of each image is (in SuperView-1, ); that is, the image acquisition duration is times as long as the downlink duration, which can be stated as(d)The satellites work in the mode that only one antenna can work to downlink at a time; that is, any two downlink time windows do not overlap, which can be stated as(e)The downlink way that the observed images are transmitted to the ground station in real time is not considered.(f)The storage of each request can be released immediately, once the corresponding downlink finishes.

Our scheduling results must satisfy the following constraints:(a)If the downlink of request is assigned to visibility mask , and must be within visibility mask , which can be stated as(b)The start time of downlink must be after the end time of image acquisition and the end time of downlink cannot be after the deadline , which can be stated as(c)Once a downlink starts, it cannot be preempted; that is, an image cannot be split into several fragments, which can be stated as(d)The satellites cannot observe and downlink at the same time and there must be a gap of at least units between consecutive image acquisition and downlink, which can be stated as(e)The satellite storage cannot exceed the memory capacity at any time, which can be stated as

We consider the storage constraint (Constraint (e)) in SIDSP. The limited on-board memory makes us consider how to improve the utilization efficiency by downlink schedule. Image acquisition is a process of loading while image downlink is a process of unloading. There are cases that the satellite cannot acquire image because of the lack of storage. Image downlink can release storage to make it possible for image acquisition to improve the efficiency of the whole satellite system.

Note that SIDSP deals with the problem of finding an image downlink schedule so that a utility function is maximized. The utility function considers the profit of each scheduled request and the cost of each used visibility mask. In order to record which visibility masks are used, we set a variable such that if the visibility mask is used and otherwise, which can be stated as

Our objective function is maximizing the utility function of solution , which can be stated as

To solve SIDSP, we need to determine two points. One is to determine the corresponding visibility mask assigned for each request (i.e., the binary matrix ); the other one is to determine the downlink time window of each request (i.e., the start time of downlink , the end time of downlink ). The requests which cannot be scheduled eventually are removed from the image acquisition plan.

#### 3. Solution Approach

In this section, the solution approach based on serial scheduling is described to deal with SIDSP. The construction heuristic algorithms for comparison are detailed in Section 3.1; the schedule generation algorithm (SGA) is detailed in Section 3.2; the hybrid genetic algorithm (HGA) is detailed in Section 3.3.

Serial scheduling scheme is an effective approach to deal with constrained optimization problems such as Job Shop scheduling [19, 20]. The solver searches in the space of request permutations while a polynomial time schedule generator converts the request permutations into schedules. The schedule generator is a greedy algorithm scheduling the requests in the given order, choosing the earliest available position for each of them considering the constraints. An important property of the schedule generator is that it always generates active schedules; that is, none of the unscheduled requests can be added to it without delaying some scheduled requests [21]. If we do not consider the cost of visibility mask, there exists a request permutation generating an optimal schedule [22]. Our utility function considers the cost of visibility mask so that sometimes delaying or deleting a downlink can improve the solution, which makes us design two other heuristic rules. There also exists a request permutation generating an optimal schedule in our case, which is explained in Section 3.2. With the serial scheduling scheme in mind, SIDSP can be viewed as a problem of optimizing a permutation of the downlink requests. Our objective function also can be maximizing the utility function of permutation , which is stated as

Note that to evaluate the solution profit of a permutation we need to generate the schedule from that permutation, that is, to apply the schedule generation algorithm. In the following section, let be the th request in and if the downlink of request is assigned to visibility mask and otherwise.

##### 3.1. Construction Heuristic

The construction heuristic algorithms are efficient for quick request permutation generation. By using the construction heuristic algorithms reasonably, we can quickly get a schedule with a high profit. Adapted to the characteristic of SIDSP in SuperView-1, the problem can be seen as a variant of multiple knapsack problem: there are items (analogous to requests) and knapsacks (analogous to visibility masks). Each item has its own profit (analogous to request profit) and weight (analogous to downlink duration). Each knapsack has its own capacity (analogous to visibility mask duration). We should find a schedule of how to assign each item to maximize the total profit without violating knapsack capacity constraints [23]. The following sorting criterions commonly used in solving multiple knapsack problem are considered,

*Criterion 1. *Higher profit occurs first.

*Criterion 2. *Shorter downlink duration exists first.

*Criterion 3. *Higher exists first.

Adapted to our purpose of maximizing the utility, Criterion 1 gives priority to those requests with high profit and may make the total profit of the scheduled requests higher. Adapted to Constraint (a), when it is a tight constraint (i.e., the visibility masks are oversubscribed), Criterion 2 can increase the number of scheduled requests and may have a good performance; Criterion 3 focuses on those requests with high profit per unit time, which can be seen as the balance between Criterions 1 and 2.

##### 3.2. Schedule Generation Algorithm (SGA)

SGA is used to produce a schedule from a given request permutation. As the key part in serial scheduling scheme, SGA is applied each time we evaluate the solution profit of a permutation. The general procedure of SGA is described in Algorithm 1, mainly including three heuristic rules and time window clipping.