DynaQUEST: A New Approach to the Dynamic Multi-satellite

Scheduling Problem

J. Berger

1 a

, N. Lo

, M. Noel

and L. Noutegne

Defence Research Development Canada - Valcartier, 2459 Pie-XI Blvd. North, Qu

ebec, PQ, Canada

SATWII Solutions, Qu

ebec, PQ, Canada

Universit

e Laval 1025, Avenue des Sciences-Humaines Qu

ebec, PQ, Canada

Keywords:

Multi-satellite Scheduling, Dynamic Planning, Mixed-integer Quadratic Programming.

Abstract:

Reported dynamic multi-satellite scheduling approaches for Earth observations show many limitations when

operating in time-varying uncertain environment. They largely run over predetermined time periods and often

ofﬂine, assume negligible execution time, improperly account for the passage of time during planning, remain

myopic or fail to show “anytime” behavior. A novel approach to solving the dynamic multi-satellite scheduling

problem is proposed. The open-loop with feedback DynaQUEST approach includes an event-driven controller

monitoring dynamic situation evolution while supervising a co-evolving episodic scheduling problem solver.

Reactive to real-time and delayed information feedback, the controller timely enables the problem-solver to

stay responsive, interruptible and adaptive, taking advantage of emerging opportunities to timely improve so-

lution quality. The problem-solver continually solves a new static problem shaped by dynamic changes and

constrained by current resource commitments to adaptively expand the emergent solution. Problem model

formulation is based on network ﬂow optimization using mathematical programming. Departing from main-

stream approaches widely promoting an exact objective function coupled with a heuristic problem-solving

method, the proposed approach alternatively combines an approximate objective function and an exact algo-

rithm. The approach embraces an extended time horizon relaxing myopic planning. Computational results

prove the approach to be cost-effective and to outperform alternate baseline heuristics.

1 INTRODUCTION

Dynamic space-based collection tasking to support

time-critical mission is pervasive in many application

domains such as military Intelligence, Surveillance

and Reconnaissance, environment monitoring and

disaster/emergency management. Adaptive and efﬁ-

cient multi-satellite collection scheduling is crucial to

maintaining persistent situational awareness in time-

varying uncertain environment. A satellite image ac-

quisition schedule may be very sensitive to uncer-

tainty, stochastic task demand, emergency task surge,

resource capacity ﬂuctuations, dynamic constraints,

plan execution failures, decision cycle latency, com-

putational and/or communication resources available,

changing weather conditions or unexpected exoge-

nous events. As a result, a dynamic collection task-

ing solution approach to be embedded in a decision

support system must be fast, responsive, opportunis-

tic and demonstrates graceful adaptation.

https://orcid.org/0000-0001-5885-9254

Recent research contributions on the dynamic

multi-satellite collection scheduling problem are nu-

merous. (Pemberton and Greenwald, 2002) ﬁrst in-

troduced the dynamic problem, considering contin-

gency conditions. In (Verfaillie and Schiex, 1994),

the authors exploit a dynamic constraint satisfaction

approach to locally search the solution space modi-

fying decision variables. (Kramer and Smith, 2003)

propose a repair-based technique to handle the over-

subscribed scheduling problem. A rule based heuris-

tic algorithm is used by (Wang et al., 2007) to balance

solution performance and solution adjustment. (Dis-

han et al., 2013) promote an integer programming-

based decision model over a receding horizon com-

bined with a ﬂexible approach to schedule dynamic

tasks, but overlook anytime problem-solving consid-

erations while planning. In another respect, (Wang

et al., 2013), (Wang et al., 2015) propose a multi-

objective dynamic scheduling model for emergency

tasks coupled to a dynamic task merging algorithm in

order to revisit tasks and meet real-time constraints.

194

Berger, J., Lo, N., Noel, M. and Noutegne, L.

DynaQUEST: A New Approach to the Dynamic Multi-satellite Scheduling Problem.

DOI: 10.5220/0008975701940201

In Proceedings of the 9th International Conference on Operations Research and Enterprise Systems (ICORES 2020), pages 194-201

ISBN: 978-989-758-396-4; ISSN: 2184-4372

In (Zhai et al., 2015), (Niu et al., 2015), the authors

combine a hybrid genetic algorithm to build an ini-

tial solution and, heuristic variants to adjust and in-

sert dynamically new tasks resorting to task execution

duration to handle both performance and robustness.

Assuming on-board reactive planning, and monitor-

ing capability to detect imaging precondition viola-

tions, (Maillard et al., 2015) use local plan adapta-

tion to accommodate more suitable tasks to meet data

imaging contingencies. This is achieved minimizing

changes to the plan shared with the ground segment.

In counterpart, (Wang et al., 2016) relies on sequential

decision-making to solve dynamic scheduling. But

they introduce many additional parameters; ad hoc

imaging rewards which are misaligned with the global

objective pursued; and overlook real-time decision-

making contingencies. Concurrently, (Valicka et al.,

2016) promote a three-level stochastic programming

approach with recourse, but use a state aggregation

strategy to signiﬁcantly reduce or bias problem com-

plexity. Recently, (Chu et al., 2017) propose an any-

time branch and bound algorithm for satellite on-

board scheduling, but the algorithm is designed for a

bi-satellite cluster and remains limited to a small time

horizon problem. Alternatively, (Song et al., 2018)

introduce fast and reﬁned emergency tasks greedy in-

sertion algorithms to dynamically revisit a schedule,

exploiting new task demand priority, task dominance

and density to adjust and improve solution quality. In

(Wang et al., 2018b), an approach integrating obser-

vation and downlink scheduling is proposed. It uses

linear programming optimization and a problem de-

composition problem-solving technique (column gen-

eration), but real-time feasibility and run-time perfor-

mances for medium or large size problems remain un-

clear. Finally, (Cui and Zhang, 2019) solve multi-

satellite dynamic mission scheduling using priority.

The objective is to maximize the observation mis-

sion priority and revenues, and minimize the waiting

time. A hybrid genetic tabu search algorithm is used

to compute the initial satellite scheduling plan, and

a dynamic scheduling heuristic is employed to repair

the solution and insert new tasks. Most of the recent

approaches described above mainly rely on a variety

of related exact, heuristic and meta-heuristic problem-

solving methods and variants ranging from operations

research, to artiﬁcial and computational intelligence

techniques.

Despite a large body of research, reported real-

time dynamic scheduling approaches are often my-

opic, uninterruptible or are performed ofﬂine, oc-

cur on arbitrarily predetermined time periods, assume

negligible run time or improperly account for the pas-

sage of time during planning, coming short to demon-

strate anytime behavior. Proposed work contributions

generally assume that world state remains unchanged

while constructing the solution schedule/plan. This

particularly prevails for two-stage myopic approaches

relying on initial plan/schedule generation and dy-

namic repair. As a result, possible computational op-

portunities and events that may impact solution qual-

ity/feasibility or key real-time requirements such as

responsiveness, timeliness and graceful adaptation are

overlooked.

In this work, a new dynamic multi-satellite

scheduling framework is proposed. The open-loop

with feedback DynaQUEST approach involves an

event-driven controller monitoring dynamic situation

development while controlling an episodic multi-

satellite scheduling problem solver evolving concur-

rently. It can be modeled through an event-driven

outer thread, the controller, interacting with an inner

thread, the episodic multi-satellite scheduling prob-

lem solver, running in parallel. Computational re-

sults reporting comparative performance clearly show

the value of the advocated approach. DynaQUEST

proves to be cost-effective and outperforms alternate

baseline heuristics. It demonstrates measurable col-

lection and run-time gains.

The remainder of the paper is structured as fol-

lows. Section 2 ﬁrst introduces the centralized dy-

namic multi-satellite scheduling problem. A descrip-

tion of the proposed open-loop with feedback ap-

proach is then given in Section 3. The basic solu-

tion design and the detailed dynamic framework inte-

grating a static model are presented. Computational

results reporting comparative performance with alter-

nate baseline methods are presented and discussed in

Section 4. A summary of the ﬁndings is ﬁnally given

in Section 5.

2 MULTI-SATELLITE

SCHEDULING PROBLEM

Given a set of information requests (areas of inter-

est to be observed) properly translated into weighted

tasks, the basic multi-satellite scheduling problem

supporting information collection consists of allocat-

ing collection assets (satellites) to observation tasks

(imaging opportunities) to maximize overall expected

collection value, subject to a variety of constraints

over a predetermined time horizon. Constraints may

relate to mission, task and related dependencies, op-

erational, collector, supporting resource, communica-

tion, on-board resource capacity, temporal, itinerary

(e.g. duty cycle) and cost considerations respec-

tively. Image acquisition is characterized by a prob-

DynaQUEST: A New Approach to the Dynamic Multi-satellite Scheduling Problem

195

ability of successful observation to reﬂect outcome

uncertainty. Image downlinks to and command up-

links from the ground segment are ﬁnally ensured

through communication assets (e.g. ground stations).

The current dynamic problem setting assumes cen-

tralized image acquisition and downlink scheduling,

achieved by a ground (mission control center, ground

station antennas) segment, and distributed plan exe-

cution realized by the space (spacecraft components)

segment. Satellite on-board processing capability and

scheduling adaptations are assumed to be very lim-

ited. Dynamic scheduling problem characteristics in-

clude: Near real-time task demand, an uncertain envi-

ronment with imperfect sensors, stochastic resource

capacity level and exogenous events (e.g. observa-

tion outcomes, new task), bounded rationality (com-

putational resources) and reactivity of the ground

scheduler. These stringent problem features impose

the ground segment to be fast, adaptive, responsive,

opportunistic (timely actions) to support “anytime”

scheduling and re-tasking.

3 DynaQUEST APPROACH

3.1 General Description

A centralized open-loop with feedback scheduling de-

cision model over a rolling time horizon is proposed

in order to reduce computational complexity and

maintain the ground segment responsive. Open-loop

planning assumes a single episode (static model) dis-

regarding explicit any intermediate information feed-

back. Feedback information such as observation out-

comes resulting from plan execution is alternatively

handled through repeated episodic re-optimization

driven by communication opportunities as shown in

Figure 1.

Figure 1: Open-loop with feedback multi-satellite schedul-

ing optimization.

Episodic re-optimization consists to dynamically

compute a solution by solving a new static schedul-

ing problem model given information feedback such

as new tasks, or recent observation outcomes (image

downlink) from the latest episode. Event-driven re-

optimization is achieved over a receding time hori-

zon subject to committed action plans or ongoing re-

source commitments, revisited target/task value, up-

dated constraints and current world state.

3.2 Solution Design

The open-loop with feedback approach called Dy-

naQUEST, involves an event-driven controller mon-

itoring situation evolution and interacting with a

time-varying uncertain environment, supervising an

episodic multi-satellite scheduling problem solver

running continually as shown in Figure 2. It manages

incoming events taking into account the passage of

time capturing world state evolution while planning.

3.2.1 Controller

The outer thread controller timely reacts to, and

processes incoming information feedback (e.g.,

observation outcomes, new tasks) guiding in-

ner thread problem-solving and making it “any-

time”/interruptible. It properly accounts for the pas-

sage of time during solution planning, as situation un-

folds, deciding on timely algorithm activation and/or

interruption over and during communication opportu-

nities (contact periods) with single or multiple satel-

lites. As a wrapper, it is designed to handle world

state transition while constructing the solution. The

outer thread controller enables the problem-solver to

stay responsive, timely and adaptive, beneﬁting from

emerging opportunities (e.g. incoming new tasks, re-

maining communication time) to further enhance so-

lution quality and timely execution.

3.2.2 Problem-solver

The problem-solver continually solves new static

problems dictated by dynamic changes and con-

strained by current resource commitments to adap-

tively expand or improve the emergent solution at

hand. Problem model formulation is based on net-

work ﬂow optimization using mathematical program-

ming. The proposed problem modeling/-solving ap-

proach is called QUEST in reference to its QUadrat-

ically constrained program Solver Technology solu-

tion implementation, exploiting best state-of-the-art

commercial optimization problem-solving machinery

(Berger et al., 2020). The QUEST model embraces a

larger time horizon relaxing myopic planning, while

providing fast problem-solving. QUEST is a new

static problem solver using a mathematical quadratic

programming approach exploiting problem structure

ICORES 2020 - 9th International Conference on Operations Research and Enterprise Systems

196

reﬂected in collection graph and prior domain knowl-

edge (bounding visits to a task) to compute an efﬁ-

cient solution. Based upon the non-linear objective

function proposed by (Wang et al., 2018a), QUEST

relies on an approximate objective function combined

with the utilization of commercially available exact

problem-solving techniques. The QUEST problem

model concurrently captures coverage approximation

and collection uncertainty captured through imaging

probability of success.

3.3 DynaQUEST Cycle

New upcoming events such as communication down-

links (environment state, observation outcomes, on-

board satellite resource state: energy level, mem-

ory usage, orbital cumulative observation time), new

tasks and command uplinks mediated by the con-

troller. During respective intermittent contact periods

and based on best current computed solution so far,

the controller ﬁrst handles new information. It then

updates collection value alluding to the latest serviced

targets, interrupts the QUEST solver and revisits the

problem model to re-initiate open-loop optimization

by directing the problem solver toward a new decision

cycle. Kept informed of the latest best computed solu-

tion update, the controller then timely uplinks relevant

revisited satellite collection plans before triggering a

new re-optimization cycle again.

The following description of a simple Dy-

naQUEST cycle and its associated timeline is illus-

trated in Figure 3 over a single contact period. Here,

Figure 2: DynaQUEST framework.

Figure 3: DynaQUEST cycle over a contact/communication period.

DynaQUEST: A New Approach to the Dynamic Multi-satellite Scheduling Problem

197

we assume that a satellite can image and downlink

concurrently.

On a new satellite contact beginning at time

comm min

, the ground segment, based on latest best so-

lution, sends a command uplink, informing the satel-

lite of its new updated local plan from now on, while

stored images and resource state update are down-

linked. Based on latest downlinked information and

assuming sufﬁcient communication time, the ground

segment quickly reﬁnes during a brief period δT,

amounting to a few seconds, its best current solution

to possibly re-synchronize with the satellite if the lo-

cal plan has changed. Plan revision is repeated as re-

quired based on new incoming information emerging

from any sources over the entire communication time

window [t

comm min

, t

comm max

] deﬁning the contact pe-

riod. Such information may include latest observa-

tion outcomes from other satellites, new tasks, revised

constraints, time-varying environmental/weather con-

ditions or any unexpected exogenous events impact-

ing other satellite plan commitments. Reiterated com-

munication may not even take place during that time

interval if short-term satellite plan remains unchanged

until the next communication contact. Mediated by

the controller, an updated local plan is ﬁnally up-

linked to the satellite if required, by a predetermined

deadline t

deadline

before the end of the contact pe-

riod t

comm max

. Satellite-ground synchronization is en-

sured by the controller. Should communication time

be insufﬁcient to complete the downlinks, the satellite

would proceed according to its latest new plan subject

to local resource constraint whereas the ground seg-

ment would pursue its planning activity with partial

information and its current distorted beliefs. Satellite

downlink completion and plan adjustment would then

be delayed to the next communication cycle. Com-

munication is assumed to occur if sufﬁcient time is

minimally available to uplink a new precomputed lo-

cal plan from the ground. Respective activity timeline

for ground and satellite segments is displayed at the

bottom of Figure 3.

3.3.1 Ground Segment Re-planning

A new re-optimization cycle is triggered by the event-

driven controller as described above in Section 3.3 re-

activating the problem-solver. The re-planning prob-

lem is conditional to the computed solution partially

implemented in the previous episode and deﬁned over

the remaining mission time horizon. The new prob-

lem model is provided with new/pending tasks, task

value adjustments based on past collections, commit-

ted imaging actions and current satellite intents, re-

ﬁned environmental conditions, and, revised resource

capacity constraints respectively. The latter include

bounding on-board satellite memory storage until the

next communication period. Problem-solving using

the open-loop QUEST solver is then initiated.

3.3.2 Space Segment

At the satellite platform level, image acquisition is as-

sumed to take place over a given time interval while

image/resource state status (energy budget, available

memory storage, duty cycle, failure) downlink are

predictably scheduled at the beginning of a new con-

tact period to beneﬁt the problem solver (planner)

from fresh information update. Assuming limited on-

board processing and planning capability, a satellite

is nonetheless presumed able to validate task service-

ability preconditions before imaging. In that case, un-

feasible tasks due to temporal delays, poor weather,

on-board resource shortages or exogenous events are

simply ignored and planned image acquisitions sim-

ply dropped from the local plan. Relaxing such as-

sessment ability would simply lead to spoiled images

under adverse circumstances.

4 COMPUTATIONAL RESULTS

A computational experiment has been conducted to

assess the value of the proposed approach. Com-

parative performance results with baseline problem-

solving heuristics are reported and discussed.

4.1 Experimental Setting and Scenarios

Performance comparison is based on expected collec-

tion value (CV) successfully obtained over the en-

tire mission time horizon. The measure of perfor-

mance combines cumulative gathered collection value

as well as expected collection value associated with

acquisition tasks planned to be ongoing or incomplete

by the end of the time horizon. A negative observa-

tion outcome conveys no collection contribution for

the related task. The average CV random variable can

be estimated through Monte Carlo simulation over a

set of dynamic scenarios characterized by a degree

of dynamism, stochastic task demand and observa-

tion outcomes. The experiment has been conducted

for a 3-satellite constellation daily mission involving

a total of 45 orbits (3 satellites x 15 orbits/satellite),

subject to 35 re-planning episodes/ground commu-

nication time windows with a maximum of 3 con-

tact periods per satellite orbit, responding to a dy-

namic task demand. Dynamic demand is captured

through two stochastic scenarios/datasets presenting

a medium (60%) and a high (93%) dynamism level,

ICORES 2020 - 9th International Conference on Operations Research and Enterprise Systems

198

respectively. The dynamism level reﬂects the propor-

tion of initially unknown tasks on average composing

total demand. Correspondingly, the scenarios include

on average 420 (1000) tasks generated dynamically

against 250 (75) tasks assumed to be known initially.

Tasks are randomly created using a uniform distribu-

tion over [409, 429] and [800, 1200] for respective

datasets. Simulation parameters such as space-time

episodic task demand, imaging time windows, task

value ranging over [0.1, 0.9], probability of success-

ful observation running into [0.25, 1] and, commu-

nication time window duration spanning across [0, 4]

minutes are all randomly selected using a uniform dis-

tribution. Other satellite resource capacity parameters

introduced in the QUEST decision model are indi-

cated in (Berger et al., 2020). A sample of 30 sim-

ulation runs has been considered to estimate average

collection value for each dataset.

4.2 Problem-solving Algorithms

Comparative performance investigation has been per-

formed by substituting the QUEST problem-solver of

the two-thread DynaQUEST framework by respective

baseline heuristic methods for the two dynamic sce-

narios. These include MY PICC (Berger et al., 2018),

a simple myopic technique, and GATHER (Berger

et al., 2018), a competitive best state-of-the-art heuris-

tic. All scheduling algorithms were implemented in

Java on an Intel - Core i7-7700 3.6GHz Quad-Core

Processor 64 GB RAM memory.

4.2.1 MY PICC

The MY PICC Planning-based Image acquisition

heuristic (MY PICC) (Berger et al., 2018) is a my-

opic heuristic naively mimicking a human-like strat-

egy. The myopic heuristic consists in moving along

orbital collection graphs in parallel, and to construc-

tively schedule the next image acquisition, awarding

the collection presenting the highest payoff rate (per

time units) within the vicinity of the latest observa-

tion of a current path solution. The payoff rate refers

to the ratio of expected collection gain over combined

delays imposed by satellite travel, feasible transition

and imaging durations respectively. Earliest start time

occurrence breaks ties.

4.2.2 GATHER

The Genetic Algorithm-based collecTion scHedulER

(GATHER) (Berger et al., 2018) evolves a mixed

population of feasible/unfeasible solution individuals

based on natural selection to maximize expected col-

lection value. The advocated hybrid genetic algorithm

explicitly takes advantage of collection graphs reﬂect-

ing problem structure in representing feasible imag-

ing opportunity transitions, to better manage tempo-

ral constraint handling during crossover and mutation

operations. A low-cost task scheduling heuristic em-

bedded in genetic operators, further provides directed

search and speed-up, generating feasible high-quality

solutions.

4.2.3 QUEST

QUEST implementation is mainly relying on La-

grangian relaxation (decision variable integrality re-

laxation) and a variety of efﬁcient built-in problem-

solving search methods to ﬁnd an integer solution.

4.3 Results

Computational results are reported in Figures 4-5

for respective scenarios. DynaQUEST is compared

with two dynamic baseline heuristics named Dy-

naMY PICC and DynaGATHER, in terms of per-

formance gap with respect to expected collection

value, and computational run-time performances. The

smaller the expected collection value (CV) gap, the

better the solution quality.

Performance gap is computed as (CV

− CV ) /

where CV

is the estimated expected collec-

tion value for DynaQUEST.

Average collection value estimators for respective

methods are also summarized in Table 1 over both

medium (60%) and high (93%) dynamism level sce-

narios, assuming a 30 simulation sample and a 95%

conﬁdence interval. Average cumulative planning

run-time and related standard deviation are also re-

ported.

Figure 4: Medium dynamism level scenario relative perfor-

mance gap to DynaQUEST against problem instances.

Overall computational results show DynaQUEST

to outperform other baseline methods, indicating a

DynaQUEST: A New Approach to the Dynamic Multi-satellite Scheduling Problem

199

Table 1: Average performance.

Medium dynamism level - 60% High dynamism level - 93%

Average

collection

value

estimator

Average

cumulative

planning

run-time (s)

over mission

time horizon

Average

collection

value

estimator

Average

cumulative

planning

run-time (s)

over mission

time horizon

DynaQUEST 286.17± 1.84 59.4±20.67 313.47±8.23 12.40±1.7

DynaGATHER 233.56±1.22 51.54±1.42 248.96±8.14 60.81±6.49

DynaMY PICC 186.29±1.41 5.77±0.17 186.97±7.35 5.16±0.70

Figure 5: High dynamism level scenario relative perfor-

mance gap to DynaOUEST against problem instances.

relative performance gap of nearly 20% and 35% in

comparison to DynaGATHER and DynaMY PICC,

respectively. Differential estimated average collec-

tion value for the medium and high dynamism level

scenarios convincingly proves the same outstanding

domination as well as shown in Table 1.These re-

sults also implicitly suggest relative DynaQUEST su-

periority for even smaller dynamism level or task de-

mand surge, as the approach further promotes longer

term planning. In another respect, one can note from

Figures 4-5 a small positive correlation between dy-

namism and relative CV performance gap. Perfor-

mance gap is slightly larger for higher dynamism.

This is due to a performance degradation expected for

myopic methods when uncertainty on task demand in-

creases.

Cumulative planning run-time performance re-

ported in Table 1 expectedly indicates QUEST to be

5 times faster than DynaGATHER and only twice

slower than the myopic DynaMY PICC when the ini-

tial number of tasks is small. Conversely, relative

planning run-time slightly degrades when initial task

demand is large. Open-loop optimization using ex-

act method (QUEST) and conditional to previous ac-

tion commitments is very fast, given episodic small

task demand. It appears that episodic re-planning

run-time for DynaQUEST is on the order of few sec-

onds ( 2s), typically an order of magnitude under the

minute timescale, making it very fast by any near real-

time Earth observations standards and virtually “any-

time” in steady-state condition. Additional run-time

gains could be further expected should a faster com-

puter be used.

5 CONCLUSION

A novel open-loop with feedback approach to solv-

ing the centralized dynamic multi-satellite schedul-

ing problem has been proposed. The two-thread

DynaQUEST framework couples a responsive event-

driven controller monitoring situation evolution to the

new efﬁcient non-myopic open-loop problem-solver

QUEST responsible for episodic re-planning. In re-

sponse to incoming events, the problem-solver adapts

and expands the solution schedule by solving a new

constrained static problem instance subject to on-

going resource commitments. Combining an ap-

proximate objective function and an exact algorithm,

QUEST departs from traditional myopic planning,

while providing fast problem-solving. These features

confer to the approach suitable real-time properties

such as timeliness, responsiveness, speed and grace-

ful adaptation and anytime behavior. A computational

experiment has demonstrated DynaQUEST to outper-

form alternate baseline heuristics.

Future work aims at exploring non-myopic on-

board plan adaptations assuming sufﬁcient processing

capability. The challenge consists in efﬁciently com-

bining an evolving open-loop with feedback ground

segment solution and, a closed-loop re-planning space

segment more responsive to local event contingencies

to better handle uncertainty. This would pave the

way toward progressively examining multi-satellite

distributed scheduling. Another direction is to look

at potential implications of full network connectivity

that can be provided by communication satellite net-

works, on dynamic planning solution quality.

ICORES 2020 - 9th International Conference on Operations Research and Enterprise Systems

200

REFERENCES

Berger, J., Giasson, E., Florea, M., Harb, M., Teske, A.,

Petriu, E., Abielmona, R., Falcon, R., and Lo, N.

(2018). A graph-based genetic algorithm to solve the

virtual constellation multi-satellite collection schedul-

ing problem. In 2018 IEEE Congress on Evolutionary

Computation (CEC), pages 1–10. IEEE.

Berger, J., Lo, N., and Barkaoui, M. (2020). Quest–a

new quadratic decision model for the multi-satellite

scheduling problem. Computers & Operations Re-

search, 115:104822.

Chu, X., Chen, Y., and Tan, Y. (2017). An anytime branch

and bound algorithm for agile earth observation satel-

lite onboard scheduling. Advances in Space Research,

60(9):2077–2090.

Cui, J. and Zhang, X. (2019). Application of a multi-

satellite dynamic mission scheduling model based on

mission priority in emergency response. Sensors,

19(6):1430.

Dishan, Q., Chuan, H., Jin, L., and Manhao, M. (2013). A

dynamic scheduling method of earth-observing satel-

lites by employing rolling horizon strategy. The Sci-

entiﬁc World Journal, 2013.

Kramer, L. and Smith, S. F. (2003). Maximizing ﬂexibil-

ity: a retraction heuristic for oversubscribed schedul-

ing problems. In Proceedings of the 18th Interna-

tional Joint Conference on Artiﬁcial Intelligence (IJ-

CAI ’03), 1218–1223.

Maillard, A., Verfaillie, G., Pralet, C., Jaubert, J., Sebbag,

I., Fontanari, F., and Lhermitte, J. (2015). Adaptable

data download schedules for agile earth-observing

satellites. Journal of Aerospace Information Systems,

13(8):280–300.

Niu, X., Tang, H., Wu, L., Deng, R., and Zhai, X. (2015).

Imaging-duration embedded dynamic scheduling of

earth observation satellites for emergent events. Math-

ematical Problems in Engineering, 2015.

Pemberton, J. and Greenwald, L. G. (2002). On the need

for dynamic scheduling of imaging satellites. In Re-

mote Sensing and Spatial Information Sciences, 34,

165–171. International Archives of Photogrammetry.

Song, Y., Huang, D., Zhou, Z., and Chen, Y. (2018). An

emergency task autonomous planning method of agile

imaging satellite. EURASIP Journal on Image and

Video Processing, 2018(1):29.

Valicka, C. G., Rowe, S., Zou, S., Mitchell, S. A., Ire-

lan, W. R., Pollard, E. L., Garcia, D., Hackebeil,

G. A., Staid, A., Rintoul, M. D., et al. (2016). Dy-

namic multi-sensor multi-mission optimal planning

tool. Technical report, Sandia National Lab.(SNL-

NM), Albuquerque, NM (United States).

Verfaillie, G. and Schiex, T. (1994). Solution reuses in dy-

namic constraint satisfaction problems. In Proceed-

ings of the 12th National Conference on Artiﬁcial In-

telligence, 307–312. Seattle, Wash, USA.

Wang, C., Tang, J., Cheng, X., Liu, Y., and Wang, C. (2016).

Distributed cooperative task planning algorithm for

multiple satellites in delayed communication environ-

ment. Journal of Systems Engineering and Electron-

ics, 27(3):619–633.

Wang, J., Demeulemeester, E., Hu, X., Qiu, D., and Liu,

J. (2018a). Exact and heuristic scheduling algorithms

for multiple earth observation satellites under uncer-

tainties of clouds. IEEE Systems Journal.

Wang, J., Zhu, X., Qiu, D., and Yang, L. T. (2013). Dynamic

scheduling for emergency tasks on distributed imag-

ing satellites with task merging. IEEE Transactions on

Parallel and Distributed Systems, 25(9):2275–2285.

Wang, J., Zhu, X., Yang, L. T., Zhu, J., and Ma, M. (2015).

Towards dynamic real-time scheduling for multiple

earth observation satellites. Journal of Computer and

System Sciences, 81(1):110–124.

Wang, J.-m., Li, J.-f., and Tan, Y.-j. (2007). Study on heuris-

tic algorithm for dynamic scheduling problem of earth

observing satellites. In Eighth ACIS International

Conference on Software Engineering, Artiﬁcial Intel-

ligence, Networking, and Parallel/Distributed Com-

puting (SNPD 2007), volume 1, pages 9–14. IEEE.

Wang, Y., Sheng, M., Zhuang, W., Zhang, S., Zhang, N.,

Liu, R., and Li, J. (2018b). Multi-resource coordinate

scheduling for earth observation in space information

networks. IEEE Journal on Selected Areas in Com-

munications, 36(2):268–279.

Zhai, X., Niu, X., Tang, H., Wu, L., and Shen, Y. (2015).

Robust satellite scheduling approach for dynamic

emergency tasks. Mathematical Problems in Engi-

neering, 2015.

DynaQUEST: A New Approach to the Dynamic Multi-satellite Scheduling Problem

201