DEVELOPMENT OF AN OPTIMIZATION MODEL

FOR IMAGE COLLECTION PLANNING

Jinbong Jang, Jiwoong Choi and In-Chan Choi

Department of Industrial Management Engineering, Korea University, 1, 5Ka, Anamdong,

Seongbookku, Seoul 136, Republic of Korea

Keywords: Satellite image collection planning, Scheduling, Optimization.

Abstract: Customer service requests for satellite-based image collection rapidly grow in Korea as the number of

available satellites increases. The customer requests must meet their due dates under several complicating

conditions, such as memory capacity limits, weather conditions, role tilts and segment conflict resolutions.

In this paper, we address this problem by presenting a mixed-integer program model and propose an

investigative solution approach that handles millions of segment conflict resolution constraints. The

proposed approach would reduce the model size to improve its solvability by utilizing a new redundancy

checking pre-processing technique.

1 INTRODUCTION

Since the first satellite was launched, satellite

imagery service has been applied to various practical

areas, including meteorology, agriculture, forestry,

geology, regional planning and warfare.

In recent years, customer service requests for

satellite-based image collection rapidly grow as the

number of available satellites increases. Such ever-

growing requests, which cause major complications

in planning, bring several challenges to service

providers who try to satisfy customer demands as

much as possible. One of the challenges in a satellite

image collection process is to build an image

collection schedule so as to minimize the delays in

the service requests while multiple parameters and

constraints, such as memory capacity limits, weather

conditions, role tilts, segment conflict resolutions

and due dates, must be satisfied. Because of the

complexity of the problem, it is essential to build a

fully automated scheduling system, which utilizes

optimization models and algorithms.

This paper is organized as follows. In section 2,

related works are presented. In section 3, a brief

description of the problem and parameters in the

satellite image collection planning is provided. In

sections 4 and 5, a mathematical formulation and a

solution approach for it are presented, respectively.

Concluding remarks along with future studies are

provided in the last section.

2 RELATED WORKS

Over the years, the satellite image collection

planning has been well-studied. Some of the studies

in literatures, which are pertinent to this study, are as

follows. Vasquez and Hao (2001) generalized

satellite image collection planning as a variation of

the knapsack model and proposed a tabu search

algorithm. Bianchessi et al (2007) developed tabu

search algorithm for a multiple satellite and multiple

orbit problem. Gabrel and Vanderpooten (2002)

formulated a model as a selection of multi criteria

longest path in a directed acyclic graph. Wolfe and

Sorensen (2000) presented a description on the earth

observation system for NASA.

3 SATELLITE IMAGE

COLLECTION PLANNING

The satellite image collection planning builds an

optimal schedule to handle the customers’ requests

in an efficient manner. The schedule has to be

and assumptions into account. Because of a large

number of parameters and constraints to consider,

the construction of an optimal schedule for the

satellite image collection planning becomes a

complicated task. In addition, a general reference

171

Jang J., Choi J. and Choi I..

DEVELOPMENT OF AN OPTIMIZATION MODEL FOR IMAGE COLLECTION PLANNING.

DOI: 10.5220/0003759701710174

In Proceedings of the 1st International Conference on Operations Research and Enterprise Systems (ICORES-2012), pages 171-174

ISBN: 978-989-8425-97-3

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

model is not available in literature for accommodat-

ing different situations.

3.1 Problem Description

The satellite image collection planning problem

aims at maximizing daily collections. The collected

images must meet each customer’s requirements on

picture quality. Figure 1 shows how the image

collection planning system under consideration

works.

All customers’ requests are put in the order

database, and the process handles them as an input

data. After image collection planning process is

done by checking all steps, the activated orders are

passed to the collection assessment. The inactive

orders will remain in the order database for a future

use.

Figure 1: Image collection planning process.

All satellite image collection orders have

specifications on order priorities, maximum cloud/

snow cover limits, due dates and roll tilts. All these

order parameters are employed as an input to the

automated scheduling system. The orders are

assigned to the schedule while maintaining the

memory consumption limit and the segment conflict

resolutions. Currently, the process is carried out

manually by human experts.

The detail information of the parameters and the

memory consumption limit are provided in the next

subsection.

3.2 Parameters

Six parameters are considered as major factors in the

satellite image collection planning.

3.2.1 Memory Consumption Limit

The memory consumption limit is a constraint which

enforces the overall memory usage between two

consecutive download stations not to exceed

satellite’s memory size.

3.2.2 Segment

The segment is defined as a possible geographical

section to collect images. The set of segments is

determined prior to build a scheduled plan. A

geometrically large order which is called Area of

Interest (AOI) consists of many segments (Figure 2).

In order to collect all images of an AOI, the image

collection task may span several months to complete

(Martin, 2002).

Figure 2: The Area Of Interest (AOI) (bold black box)

consists of the segments (yellow box).

3.2.3 Priority

A higher priority request must be carried out prior to

a lower one. The priority condition can be satisfied

by sequentially optimizing problems from the

highest priority to the lowest priority.

3.2.4 Weather Condition

Two kinds of weather conditions, cloud and snow

cover, are considered. It is essential to consider

maximum cloud and snow cover limit at the same

time. Collected images with unacceptable cloud/

snow cover must be recollected (Martin, 2002).

3.2.5 Roll Tilt

High quality images are in general obtained when

the camera is positioned at a low angle. Client’s

orders have acceptable intervals of angles so that

only segments which satisfy the angle condition

must be scheduled.

3.2.6 Due Date

Each request has to be finished before its deadline.

ICORES 2012 - 1st International Conference on Operations Research and Enterprise Systems

172

4 MATHEMATICAL

FORMULATION

In a recent paper, Baek et al (2011) regarded the

satellite mission scheduling problem as a knapsack

problem. In this paper, we present a formulation in

which the assignment and the knapsack constraints

both are considered. Two assumptions are made to

derive our formulation and a solution approach.

- All orders can be carried out in a given

planning horizon. That is, the problem has at least

one feasible solution

- Every inter-image-collection epoch has the

same length

The epoch is defined as a time interval between

two consecutive stations on earth for memory

download.

Figure 3: Graphical representation of model.

The following is the formulation for the satellite

image collection planning problem.

Mimimize

(1)

subject to

td jJ

≥− ∀∈

(2)

, , ,

jiik j

tfx iIkKjJ≥∀∈∀∈∀∈

(3)

∈

=∀∈

∑

(4)

kik

ax MR i I

∈

≤∀∈

∑

(5)

1, ( , ) ,

ik ik

xkkCiI

′

+≤ ∀ ∈ ∀∈

(6)

{0,1}, ,

iI kK∈∀∈∀∈

(7)

tjJ≥∀∈

(8)

Notations:

: epoch index,

: AOI index,

: segment index,

iiI

jjJ

kkK

∈

The objective of the model is to deliver collected

images before the due dates. Constraints (1)-(3)

assure the minimization of the maximum lateness of

the orders. Constraint (4) ensures that the segments

are assigned to one of the epochs. The memory

consumption limit for each epoch is considered in

(5). As the image collection requires a set-up time,

conflicts can occur if the moving time between two

consecutive segments is less than the set-up time.

The conflicts are prevented by constraint (6).

The formulation above can be used to obtain

optimal schedule. However, for practical scheduling

problems, millions of segment conflict resolution

constraints reduce the solvability of the problem. In

section 5, we present an investigative solution

approach to handle enormous number of constraints.

5 SOLUTION APPROACH

The mathematical model (1)-(8) has two types of

constraint structures. First, constraints (4)-(5) can be

transformed to an assignment structure by

introducing slack variables. Second, constraints (5)-

(6) have the knapsack structure. The auction

algorithm and dynamic program are well-known

solution approaches for the assignment problem and

the knapsack problem, respectively. It is possible to

develop a Lagrange-relaxation based algorithm by

utilizing the two kinds of constraint structures and

the corresponding algorithms.

Prior to an algorithm development phase, we

explore applicability of a pre-processing procedure

which reduces the number of constraint to improve

the solvability of the problem. The mathematical

model (1)-(8) contains a large number of knapsack

constraints (5)-(6). Especially, the number of

constraints (6) may exponentially explode depending

on AOI structure.

Because the knapsack structure is dominant the

model, the pre-processing procedure given by Choi

and Choi (2011) can be employed. Their procedure

identifies redundancy in multi-dimensional knapsack

: memory capacity

: a set of segments for ,

: a set of segments that can be allocated to epoch

:completion time of epoch

: due date of

KAOIjJKK

fiI

dAOIjJ

∈⊂

∈

: amount of memory required for segment

: completion time of image collection for

: a set of a pair of conflict segments, ( , ),

, ,

akK

tAOIjJ

Ckk

kKk Kkk

∈

′

′′

∈∈ <

DEVELOPMENT OF AN OPTIMIZATION MODEL FOR IMAGE COLLECTION PLANNING

173

constraints. This approach utilizes the concept of

constraint intercepts in Paulraj et al (2006) and

extends it by using surrogate constraints. They

construct feasibility problems in which constraint

redundancy can be detected. Then, they suggest a

O(n

) heuristic algorithm for solving the feasibility

problems. To identify redundancy in constraints (6),

we consider the following feasibility problem:

The (i, k, k

) constraint of (6) is redundant if and

only if feasibility problem (9) has any feasible

solution

(, , ')

0, 0, 0

λλ λ

≤≥ >

ikk T

Fe (9)

where

(, , ')

{0,1, }=−

ikk

[

]

λλ

= L

[

]

:1 1= L

: =

BigM value

Figure 4: Matrix pattern of coefficient matrix of (6) and F.

The coefficient matrix F consists of components

with 0, 1 and -M values and the matrix pattern

follows the 0-1 component pattern of A

(A:=

coefficient matrix of (6)). These structures can be

utilized in developing an algorithm for solving the

feasibility problem. Moreover, the above described

redundancy checking procedure can be applied to

constraint (5) in a similar fashion.

6 CONCLUSIONS

In this paper, we presented a mathematical model for

the satellite image collection planning. The

presented model deals with long term planning and

reflects real-world constraints in practice. We also

proposed an investigative solution approach that

utilizes a new redundancy checking pre-processing

technique. It remains to be seen through a further

study on computational experiments whether the

proposed approach results in a high-quality schedule

for the satellite image collection.

ACKNOWLEDGEMENTS

This work was supported by 2010 technology

royalties program (Technical Development of

Optimized Image Collection Planning for Multi-

Satellite) of The Ministry of Education, Science and

Technology.

REFERENCES

Baek, S. W. et al., 2011. Development of a scheduling

algorithm and GUI for autonomous satellite missions.

Acta Astronautica 68.

Bianchessi, N., Cordeau, J. F., Desrosiers, J., Laporte, G.,

Raymond, V., 2007. A heuristic for the multi-satellite,

multi-orbit and multi-user management of Earth

observation satellites. EJOR, Vol.177, No. 2.

Choi, J. W., Choi, I. C., 2011. Identifying redundancy of

multi-dimensional knapsack constraints using

surrogate constraints. Working Paper, Korea

University.

Gabrel., V., Vanderpooten, D., 2002. Enumeration and

interactive selection of efficient paths in a multiple

criteria graph for scheduling an earth observing

satellite. EJOR, Vol. 139, No. 3.

Martin, W., 2002. Satellite image collection optimization.

Optical Engineering. Vol. 41, No.9.

Paulraj, S., Chellappan, C., Natesan, T. R., 2006. A

heuristic approach for identification of redundant

constraints in linear programming models,

International Journal of Computer Mathematics. 83.

Vasquez, M., Hao. J., 2001. A "Logic-Constrained"

Knapsack Formulation and a Tabu Algorithm for the

Daily Photograph Scheduling of an Earth Observation

Satellite. Computational Optimization and

Applications, Vol. 20, No. 2.

Wolfe., W. J., Sorensen, S. E., 2000. Three Scheduling

Algorithms Applied to the Earth Observing Systems

Domain. Management Science, Vol. 46, No.1.

ICORES 2012 - 1st International Conference on Operations Research and Enterprise Systems

174