Lifetime maximization for Wireless Sensor Networks ... - Lab-STICC

Lifetime maximization for Wireless Sensor Networks using video cameras Andr´e Rossi⋆ , Alok Singh† , Marc Sevaux⋆ ⋆

Universit´ e de Bretagne-Sud, Lab-STICC, Lorient, France {andre.rossi,marc.sevaux}@univ-ubs.fr

†

University of Hyderabad, School of Computer and Information Sciences, India [email protected]

July 3, 2013 A. Rossi, A. Singh, M. Sevaux (UBS)

Lifetime maximization for camera sensors

July 3 2013

1 / 22

Plan 1

Omni-directional wireless sensor networks

2

Overview

3

Directional wireless sensor networks

4

Column generation approach

5

Comparing the two problem versions

6

Results

7

Camera sensor networks

8

Conclusions

A. Rossi, A. Singh, M. Sevaux (UBS)


July 3 2013

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July 3 2013

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July 3 2013

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July 3 2013

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Omni-directional wireless sensor networks c X

Maximize

(1)

tj

j=1

c X

ai,j tj ≤ bi

∀i ∈ {1, . . . , n}

tj ≥ 0

∀j ∈ {1, . . . , c}

[πi ]

(2)

j=1

Maximize 1 −

n X

(3)

(4)

ai,c+1 πi

i=1

1≤

X

ai,c+1

(5)

∀k ∈ {1, . . . , m}

i∈Ck n X

(6)

ai,c+1 ≤ m

i=1

ai,c+1 ∈ {0, 1}


∀i ∈ {1, . . . , n}


(7)

July 3 2013

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Overview 3

3

4

2 4

1 si

3

s

2 si

6 5

Omni-directional sensor

2 θ

1

4 0

6 5

Directional sensor

θ

1 si

0

6 5

Camera sensor

Decide when to set the sensor to active state θ Set working direction θ Set focal distance s A. Rossi, A. Singh, M. Sevaux, A column generation algorithm for sensor coverage scheduling under bandwidth constraints, Networks, 60 (3), pp. 141-154, 2012. A. Rossi, A. Singh, M. Sevaux (UBS)


July 3 2013

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Directional wireless sensor networks Each sensor has a given sensing angle ϕ Each active sensor has a working direction θ in [0, 2π) 5π 8

5π 8

π 4

3 7π 8

4

1 si

1 si

6

First problem

π 9

2 4

0 5


7π 8

π 9

2

π 4

3

15π 8 16π 9

0 6 5

15π 8 16π 9

Second problem


July 3 2013

6 / 22


5π 8

π 4

3 7π 8

4

1 si

1 si

6

First problem

π 9

2 4

0 5


7π 8

π 9

2

π 4

3

15π 8 16π 9

0 6 5

15π 8 16π 9

Second problem


July 3 2013

6 / 22


5π 8

π 4

3 7π 8

4

1 si

1 si

6

First problem

π 9

2 4

0 5


7π 8

π 9

2

π 4

3

15π 8 16π 9

0 6 5

15π 8 16π 9

Second problem


July 3 2013

6 / 22


5π 8

π 4

3 7π 8

4

1 si

1 si

6

First problem

π 9

2 4

0 5


7π 8

π 9

2

π 4

3

15π 8 16π 9

0 6 5

15π 8 16π 9

Second problem


July 3 2013

6 / 22


5π 8

π 4

3 7π 8

4

1 si

1 si

6

First problem

π 9

2 4

0 5


7π 8

π 9

2

π 4

3

15π 8 16π 9

0 6 5

15π 8 16π 9

Second problem


July 3 2013

6 / 22


5π 8

π 4

3 7π 8

4

1 si

1 si

6

First problem

π 9

2 4

0 5


7π 8

π 9

2

π 4

3

15π 8 16π 9

0 6 5

15π 8 16π 9

Second problem


July 3 2013

6 / 22


5π 8

π 4

3 7π 8

4

1 si

1 si

6

First problem

π 9

2 4

0 5


7π 8

π 9

2

π 4

3

15π 8 16π 9

0 6 5

15π 8 16π 9

Second problem


July 3 2013

6 / 22


5π 8

π 4

3 7π 8

4

1 si

1 si

6

First problem

π 9

2 4

0 5


7π 8

π 9

2

π 4

3

15π 8 16π 9

0 6 5

15π 8 16π 9

Second problem


July 3 2013

6 / 22


5π 8

π 4

3 7π 8

4

1 si

1 si

6

First problem

π 9

2 4

0 5


7π 8

π 9

2

π 4

3

15π 8 16π 9

0 6 5

15π 8 16π 9

Second problem


July 3 2013

6 / 22


5π 8

π 4

3 7π 8

4

1 si

1 si

6

First problem

π 9

2 4

0 5


7π 8

π 9

2

π 4

3

15π 8 16π 9

0 6 5

15π 8 16π 9

Second problem


July 3 2013

6 / 22


5π 8

π 4

3 7π 8

4

1 si

1 si

6

First problem

π 9

2 4

0 5


7π 8

π 9

2

π 4

3

15π 8 16π 9

0 6 5

15π 8 16π 9

Second problem


July 3 2013

6 / 22

Directional wireless sensor networks A normalized direction is associated with each target 3 2 4

1 si

6 5

Non-normalized direction A (normalized) direction is dominated if the targets it covers are a strict subset of the targets covered by another direction



July 3 2013

7 / 22

Directional wireless sensor networks A normalized direction is associated with each target 3 2 4

1 si

6 5

Non-normalized direction A (normalized) direction is dominated if the targets it covers are a strict subset of the targets covered by another direction



July 3 2013

7 / 22

Directional wireless sensor networks A normalized direction is associated with each target 3

3 2

4

2 4

1 si

1 si

6 5

6 5

Non-normalized direction Normalized direction A (normalized) direction is dominated if the targets it covers are a strict subset of the targets covered by another direction



July 3 2013

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3 2

4

2 4

1 si

1 si

6 5

6 5

Non-normalized direction Normalized direction A (normalized) direction is dominated if the targets it covers are a strict subset of the targets covered by another direction 3 2 4

1 si

6 5

Dominated direction A. Rossi, A. Singh, M. Sevaux (UBS)


July 3 2013

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3 2

4

2 4

1 si

1 si

6

6

5

5

Non-normalized direction Normalized direction A (normalized) direction is dominated if the targets it covers are a strict subset of the targets covered by another direction 3

3 2

4

2 4

1 si

6 5

Dominated direction A. Rossi, A. Singh, M. Sevaux (UBS)

1 si

6 5

Non-dominated direction


July 3 2013

7 / 22

Directional wireless sensor networks



July 3 2013

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Column generation approach

1

Group encoding

2

Subproblem

3

Global strategy of the column generation algorithm

4

Benefits of the genetic algorithm for addressing the subproblem



July 3 2013

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Group encoding Sensor si has σi directions, for all i in {1, . . . , n}. i−1 X σℓ , and ∀q ∈ {1, . . . , σi }, Agi +q,j = 1 iff sensor si is active gi = ℓ=1

and is working in its q th direction. 5π 8

π 4

3 7π 8

π 9

2 4

1 si

0

Aj =

6 5


.. .

15π 8 16π 9


0 0 0 .. .

1 gi + 1 gi + σi

gn + σn

July 3 2013

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π 4

3 7π 8

π 9

2 4

1 si

0

Aj =

6 5


.. .

15π 8 16π 9


1 0 0 .. .

1 gi + 1 gi + σi

gn + σn

July 3 2013

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π 4

3 7π 8

π 9

2 4

1 si

0

Aj =

6 5


.. .

15π 8 16π 9


0 1 0 .. .

1 gi + 1 gi + σi

gn + σn

July 3 2013

10 / 22



π 4

3 7π 8

π 9

2 4

1 si

0

Aj =

6 5


.. .

15π 8 16π 9


0 0 1 .. .

1 gi + 1 gi + σi

gn + σn

July 3 2013

10 / 22

Group encoding One column of the master problem may represent different groups  p X    Maximize tj     j=1    p σi X X    Agi +q,j tj ≤ bi ∀i ∈ {1, . . . , n}     q=1 j=1   tj ≥ 0 ∀j ∈ {1, . . . , p} 1

Aj = s1

s2 2


}s }s

1

2


July 3 2013

11 / 22


Aj = s1

s2 2


1 0 0 1

}s }s

1

2


July 3 2013

11 / 22


Aj = s1

s2 2


1 0 0 1

}s }s

1

1

Aj = 2

s1

s2 2


0 1 1 0

}s }s

July 3 2013

1

2

11 / 22

Subproblem Subproblem:    σi n X X      Maximize 1 − Agi +q,j  πi     q=1 i=1   σi  X    Agi +q,j ≤ 1    q=1 X  Ah,j ≥ 1    h∈C  k   σi n X  X    Agi +q,j ≤ m       i=1 q=1 Agi +q,j ∈ {0, 1}

∀i ∈ {1, . . . , n} ∀k ∈ {1, . . . , m}

∀i ∈ {1, . . . , n}, ∀q ∈ {1, . . . , σi }

A genetic algorithm is used for returning many attractive groups The ILP formulation is solved only upon failure of the genetic algorithm



July 3 2013

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Global strategy of the column generation algorithm Start

Master problem

Subproblem with GA Yes

Yes

Attractive group found?

No Yes Fourth attempt?

No Subproblem with ILP

Attractive group found?

No End



July 3 2013

13 / 22

Benefits of GA for addressing the subproblem

n 50

100

ϕ

ILP alone

GA + ILP

2π 3 π 2 π 3 2π 3 π 2 π 3

0.250 0.312 0.234

0.046 0.062 0.063

Speedup factor 5.435 5.032 3.714

1.840 3.713 5.273

0.281 0.265 0.281

6.548 14.011 18.765

CPU time in seconds Problem is more difficult when sensing angle ϕ is small The benefit of GA is more visible with hard problem instances



July 3 2013

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Comparing the two problem versions LM-PDS: predefined directions, LM-CDS: contextual directions LM-PDS may be infeasible while LM-CDS is feasible π 4

π 4

1 si

1 0

2

si

0 2

15π 8

LM-PDS

15π 8

LM-CDS

Lifetime with LM-CDS is larger than with LM-PDS. A. Rossi, A. Singh, M. Sevaux (UBS)


July 3 2013

15 / 22


π 4

1 si

1 0

2

si

0 2

15π 8

LM-PDS

15π 8

LM-CDS



July 3 2013

15 / 22


π 4

1 si

1 0

2

si

0 2

15π 8

LM-PDS

15π 8

LM-CDS



July 3 2013

15 / 22


π 4

1 si

1 0

2

si

0 2

15π 8

LM-PDS

15π 8

LM-CDS



July 3 2013

15 / 22


π 4

1 si

1 0

2

si

0 2

15π 8

LM-PDS

15π 8

LM-CDS



July 3 2013

15 / 22


π 4

1 si

1 0

2

si

0 2

15π 8

LM-PDS

15π 8

LM-CDS



July 3 2013

15 / 22

Results n

LM-PDS

ϕ # opt.

50

100

200

400

2π 3 π 2 π 3 2π 3 π 2 π 3 2π 3 π 2 π 3 2π 3 π 2 π 3

LM-CDS

avg. LT

avg. CPU

5 5 5

2.94 2.91 2.65

0.14 0.10 0.17

5 5 4

5.97 5.49 4.82

4 1 0 0 0 0

# opt.

From LM-PDS to LM-CDS

avg. LT

avg. CPU

5 5 5

3.60 3.60 3.21

0.06 0.12 0.11

avg. LT +22.58% +23.75% +20.91%

avg. CPU −56.91% +18.06% −35.91%

248.13 87.46 336.69

5 4 2

6.60 6.35 5.71

1.98 0.72 0.36

+10.63% +15.62% +18.39%

−99.20% −97.63% −31.29%

12.93 11.30 9.42

14.26 6.05 dnf

4 3 1

13.82 13.01 10.95

6.09 15.24 11.03

+6.88% +15.13% +16.22%

−57.31% −55.16% -

25.90 20.68 16.19

dnf dnf dnf

1 0 0

29.58 24.58 18.38

1085.15 dnf dnf

+14.21% +18.87% +13.53%

-

LM-CDS allows for more than 10% longer lifetime than LM-PDS LM-CDS is not more difficult than LM-PDS A. Rossi, A. Singh, M. Sevaux (UBS)


July 3 2013

16 / 22

Camera sensor networks CCD

LENS SHARP ZONE

Optical axis

Dn (s) s: focal distance A. Rossi, A. Singh, M. Sevaux (UBS)

s

Df (s)

f : focal length

H: Hyperfocal distance


July 3 2013

17 / 22


LENS SHARP ZONE

Optical axis

Dn (s) s: focal distance A. Rossi, A. Singh, M. Sevaux (UBS)

s

Df (s)

f : focal length



July 3 2013

17 / 22


LENS SHARP ZONE

Optical axis

Dn (s) f s: focal distance A. Rossi, A. Singh, M. Sevaux (UBS)

f : focal length

s

Df (s)



July 3 2013

17 / 22

Camera sensor networks Camera sensor networks can be modeled by LM-CDS plus a specific constraint due to focal distance. s(H − f ) Dn (s) = is the near distance of acceptable sharpness H + s − 2f s(H − f ) Df (s) = is the far distance of acceptable sharpness H −s 100

Df (s)

SHARP ZONE Dn (s)

30

s

0 1


45


July 3 2013

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Camera sensor networks: normalized pairs For all sensors, a pair (θ, s) is a working direction and a focal distance. A normalized pair is such that ◮ ◮ ◮

there exists k such that disti,k ≤ Rs and θ = θk Dn (s) ≤ disti,k ≤ Df (s) there exists k ′ such that disti,k ′ = Df (s)

1

1

3

1

3

4

4 2

si

si


3

4 2

Non-normalized

1

3 4 2 si

Normalized

Non-normalized


2 si

Normalized

July 3 2013

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Camera sensor networks: non-dominated pairs A non-dominated pair is such that the set of targets it covers is not a strict subset of targets covered by another pair.

1 3 4 2 si

{1, 3}



July 3 2013

20 / 22


1

1

3

3

4

4 2

si

2 si

{1, 3}


{2, 3}


July 3 2013

20 / 22


1

1

3

1

3

4

3

4 2

si

4 2

si

{1, 3}


2 si

{2, 3}


{1, 2, 3}

July 3 2013

20 / 22


1

1

3

1

3

4

3

4 2

4 2

si

si

{1, 3}

2 si

{2, 3}

{1, 2, 3}

1 3 4 2 si

{3, 4} A. Rossi, A. Singh, M. Sevaux (UBS)


July 3 2013

20 / 22


1

1

3

1

3

4

3

4

4

2

2

si

si

{1, 3}

2 si

{2, 3}

1

{1, 2, 3}

1

3

3

4

4 2

si

2 si


{4} Lifetime maximization for camera sensors

{3, 4} July 3 2013

20 / 22


1

1

3

1

3

4

3

4

4

2

2

si

2

si

{1, 3}

si

{2, 3}

1

{1, 2, 3}

1

3

1

3

4

3

4 2

si

4 2

si


2 si

{4} Lifetime maximization for camera sensors

{3, 4} July 3 2013

20 / 22

Camera sensor networks: occlusion and obstacles Target k is occluded if there exists a target k ′ such that disti,k ′ < disti,k that prevents form fully seeing target k from si .

1

1

3

3

4

4 2

2

si

si

Target 3 is occluded by target 4

An obstacle hides target 1

Occlusions and obstacles make the problem easier as less targets can be covered by si .



July 3 2013

21 / 22

Conclusions Lifetime maximization for directional sensors ◮ ◮

with predefined directions with contextual directions

Contextual directions makes much more sense than predefined directions Column generation algorithm enhanced with genetic algorithm Extension to focal distance for camera wireless sensors Efficient and flexible Matheuristic based on open source code Exact approach that can be used as a heuristic Camera wireless sensors with zoom (angle ϕ is variable) Toward more realistic consumption models



July 3 2013

22 / 22

Lifetime maximization for Wireless Sensor Networks ... - Lab-STICC

Lifetime maximization for Wireless Sensor Networks ... - Lab-STICC

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