An Ant colony Optimization Algorithm for the Daily ...

An Ant Colony Optimization Algorithm for the Daily Photograph Selection Problem of Earth Observation Satellites Sezgin KILIÇ Department of Industrial Engineering, Turkish Air Force Academy Istanbul, Turkey [email protected]

Outline • Introduction • Daily photograph selection problem (DPSP) of earth observation satellites (EOSs) • Previous Works • Ant Colony Optimization Algorithm for DPSP • Computational Experiments • Conclusion

S.Kilic, IFORS 2014, Barcelona

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Introduction • High-quality photographs of particular areas – Public – Commercial – Military

• Combining imagery with other information is valuable

Lithograph by Honoré Daumier, appearing in Le Boulevard, May 25, 1863.

– Planning – Decision making

• Earliest attempts – Gaspar Felix Tournachon or "Nadar" in 1858 – Landsat, the first satellite for earth observation by US in 1972 http://www.cnes.fr/web/CNES-en/1415-spot.php, 2013 S.Kilic, IFORS 2014, Barcelona

Landsat 1

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Introduction •

•

•

The Earth Observing Satellites (EOSs) orbit the Earth to capture photographs and can collect data of almost any point of the planet. Images become powerful scientific tools to enable better understanding and improved management of the Earth and its environment. Applications – Environmental monitoring – Natural disaster management – Mapping – Agriculture and farming – Forestry – Renewable energy – Road-network management – Security and resilience...


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This Envisat MERIS image, acquired on 11 January 2011, shows the plume of smoke billowing into the atmosphere from Mount Etna, Sicily, Italy. Activity gradually increased the following day, peaking in the evening. http://www.esa.int/spaceinimages/Images/2011/01/Etna_eruption_seen_by_Envisat2 S.Kilic, IFORS 2014, Barcelona

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Daily photograph selection problem (DPSP) of the satellite • The main mission for a EOS is taking images of specific areas of the ground based on the cutomers’ requests. • Each photograph generates a profit but not all of the requests can be satisfied. • Effective mission planning is necessary in order to obtain a suitable return in the large capital investment of such systems. – maximizing a profit function subject to a set of satellite technological constraints over the planning horizon.

• DPSP is an optimization problem related to customers’ orders and constrained by technical capabilities of the satellite. S.Kilic, IFORS 2014, Barcelona

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DPSP of the SPOT5 satellite • SPOT (Satellite Pour l’Observation de la Terre, French for "Earth observation satellite") • high-resolution, optical imaging system operating from space. • Since 1986, the SPOT family of satellites has been viewing our planet and providing remarkably high-quality images. • In spite of increasing competition, SPOT has become the worldwide standard in satellite imagery.

*http://spot5.cnes.fr/gb/index3.htm

SPOT 5 on orbit* (artist's impression)

Launch Date May 3, 2002 Orbital Altitude 822 kilometers Orbital Inclination 98.7°, sun-synchronous 7.4 Km/second (26,640 Speed Km/hour) Orbit Time 101.4 minutes 2-3 days, depending on Revisit Time latitude


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DPSP of the SPOT5 satellite Relative movement of the satellite with respect to the Earth does not permit to continuously monitor the same area.


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Mansour and Dessouky (2010) S.Kilic, IFORS 2014, Barcelona

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DPSP of the SPOT5 satellite • Components

– A set P = {p1, p2, . . . , pn} of candidate photographs

• can be scheduled to be taken on the “next day” under appropriate conditions of the satellite trajectory and oblique viewing capability.

– A “profit” associated with each photograph pi • result of the aggregation of several criteria (client importance, the demand urgency, the meteorological forecasts)

– A “size” associated with each photograph pi

• represents the amount of memory required to record pi when it is taken.

– A set of capturing possibilities associated with each photograph pi • for a mono pi , there are three possibilities (front/middle/rear) • for a stereo pi , there is one single possibility (front and rear)

– Objective is to maximize profit


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DPSP of the SPOT5 satellite • A set of constraints • Binary constraint: for some couples (photo, camera), it is forbidden to schedule simultaneously pi on the camera x and pj on y. • Ternary constraint: for some couples (photo, camera), it is forbidden to schedule simultaneously pi on the camera x, pj on y and pk on z. • Capacity (or knapsack) constraint: the sum of the sizes of the selected photos cannot exceed the recording capacity on board.


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DPSP of the SPOT5 satellite • The DPSP can be seen as a kind of multi-dimensional knapsack problem and belongs to the class of Discrete Constrained Optimization Problems. • NP-hard problem, according to the complexity theory.


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Previous Works • Variable Valued Constraint Satisfaction Problem (VVCSP) formulation and an integer linear programming model of the problem, Bensana et al. (1996) • Russian Doll Search (RDS) algorithm, Verfaillie et al.(1996) • 20 benchmark instances from SPOT5 order book, Bensana et al.(1999). ftp://ftp.cert.fr/pub/Lemaitre/LVCSP/Pbs/SPOT5.tgz • Knapsack model formulation and a TS algorithm, Vasques and HAO (2001) • Divide and conquer principle to find tight upper bounds for the multi-orbit instances of the Vasques and HAO(2003) • A genetic algorithm with a multi-criteria objective, Mansour and Dessouky (2010)


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Ant Colony Optimization Algorithm for DPSP • Inspired by the ants’ foraging behavior. • Indirect communication between ants by means of pheromone trails • A modified version of the hyper-cube framework for ACO (Blum and Dorigo, 2004) is applied to the DPSP.


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Begin

Parameter Setting and pheromone initialization

Artificial ants construct solutions biased by pheromone

Solution feasible

no

Repair by eliminating some photos

yes Local Search

Save iteration best, restart best and global best solutions

Calculate convergence factor (cf)

Update pheromones according to cf

no

End condition satisfied feasible yes End


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Initialization • A binary decision variable xij is defined for i={1,2,…,n} and j={1,2,3,4,5}. • Solutions are represented by (n x 5) 0-1 matrices. • A sample solution for a problem where n=3 i

Cam-1

Cam-2

Cam-3

No Cam

0

Cam-13 (stereo) 0

1

0

1

2

0

0

0

1

0

3

0

0

0

0

1


0

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Initialization and Construction • Each ant aims to generate a complete solution for the problem. • At each step of 1 to n, each ant selects one of the alternatives for each photograph. • Alternative sets are defined for each photograph at the initialization phase of the algorithm and defined by Ai. • Pheromone values represents the desirability of alternative j for photograph i at iteration t. • At the beginning of the algorithm all pheromone values are equal to each other and determined by

1  ij (0)  number of alternatives S.Kilic, IFORS 2014, Barcelona

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Construction • Ants select one of the alternative for a photograph according to the probabilities defined by

 ij (t ) P (t )    ij (t ) k ij

jAi

Pijk (t )

: denotes the probability of selection alternative j for the photograph i by ant k at iteration t.

• Infeasible solutions are repaired by using a greedy rule. • After repair phase a local improvement process is applied on to solutions. S.Kilic, IFORS 2014, Barcelona

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Pheromone Update • Different pheromone update strategies depending on the convergence status of the algorithm. • The convergence status of the algorithm is monitored through a convergence factor (cf), which is defined as

  max    min    n

cf 

i 1

jA

ij

jA

ij

n

• When the algorithm has converged the cf value will be close to 1. S.Kilic, IFORS 2014, Barcelona

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Pheromone Update • Pheromone update procedure consists of two parts: • pheromone evaporation • pheromone intensification

 ij (t  1)  1    ij  t   

 is the evaporation parameter.



xij Supd

wx

Supd : set of solutions to be intensified in the pheromone update procedure

wx(0,1): intensification weight for a solution


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Pheromone Update • Supd consists of three components; – The global best solution, Sgb – The iteration best solution, Sib – The restart best solution, Srb

• wib, wrb, and wgb are intensification weights for solution Sib, Srb, and Sgb, respectively. • cfr (r = 1, . . . , 5) are the threshold parameters for the division of the five stages, cfr = [0.3, 0.5, 0.7, 0.9, 0.95] wib wrb wgb

cf