Varying the Population Size of Artificial Foraging Swarms on Time Varying Landscapes

ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”

Varying the Population Size of Artificial Foraging Swarms on Time Varying Landscapes

Carlos Fernandes

Vitorino Ramos

Agostinho Rosa

•LaSEEB-ISR-IST, Technical Univ. of Lisbon (IST)•CVRM-IST, Technical Univ. of Lisbon (IST)


Previous Models

Chialvo and Millonas, 1995

Models the formation of trails and networks in a collection of insect-like agents. The agents interact in simple ways inspired in experiments with real ants.

Agents evolve over “flat” (or homogeneous) surfaces


Previous Models

Ramos and Almeida, 2000

A swarm model based on Chialvo’s work evolves over grey-level digital images.

The swarm builds pheromone trails that reflect the edges of the image.


Previous Models

Ramos and Fernandes, 2005 – Swarm With Fixed Population Size (SFPS)

Ants are randomly placed on the landscape/function.

All ants move on each time step: the direction is chosen according to the pheromone levels around the ant and it is constrained by a directional bias.

Environment is NxN toroidal grid with different values according to a function.

Each time step, all ants deposit a certain amount of pheromone that is proportional to the value of the function on that site.

t = 0 t=1000 t = 50 t = 100 t = 500


Deciding where to go - Chialvo Model

Normalised Transition probabilitieson the lattice to go from cell k to cell i:

kj jj

iiik wW

wWP

Measures the magnitude of thedifference in orientation:

w (0) = 1w (1) = 1/2w (2) = 1/4w (3) = 1/12w (4) = 1/20

Measures the relative probabilities ofmoving to cell i with pheromone density,

e.g.: Coming from North

w = 1/12

w = 1/4

w = 1/2w = 1/2

w = 1

w = 1/4

w = 1/12

Indicates the sum over all the cells jwhich are in local neighbourhood of k.

4 3

2

1

3

2

01

11W


Deciding where to go - Chialvo Model

Transition rule between cells by use ofa pheromone weighting function:

11W

Measures the relative probabilities ofmoving to cell r with pheromone density, r

This parameter is associated with theosmotropotaxic sensitivity. Controls thedegree of randomness with which the antfollows the gradient of pheromone.

For low values the pheromone concentrationdoes not greatly affect its choice, while highvalues cause it to follow pheromone gradientwith more certainty.

1 can be seen as the sensory

capacity. This parameter describes the fact that the ant’sability to sense pheromone decreases athigh concentrations.


T

Chialvo, 1995 Ramos, 2000Ramos and Fernandes, 2005

max

ipT

P(c)= P(c)+T

Pheromone update of cell c

255glpT

represents the difference between the median grey-levels of previous cell and its neighbors, and current cell and its neighbors

represents the difference between the median grey-levels of previous cell and its neighbors, and current cell and its neighbors

Ramos and Fernandes Model:

Pheromone evaporation, k


The Swarm Model with Varying Population Size (SVPS)

Aging process

Each ant is born with energy = 1

Each generation its energy is decreased by a constant amount = 0.1

When energy = 0, ant dies

Reproduction process (when ant meets ant)

Pr = P*(n) [Δ(c)/Δmax]

/* P*(0) = P*(8) =0; P*(4) = 1; P*(5) = P*(3) =0.75; P*(6) = P*(2) =0.5; P*(7) = P*(1) = 0.25 */

n is the number of surrounding cells occupied


For all ants do place agent at randomly selected cell End For For t = 1 to tmax do /* Main loop */

For all ants do Decrease energy If energy = 0 Kill ant Compute W(σ) and Pik

Move to a selected neighboring cell not occupied by other agent Increase pheromone at cell c P(c)= P(c)+[+p(Δ(c)/Δmax)]) End For Evaporate pheromone by K, at all cells For all ants do If ant meets ant do Compute n Determine P*(n) Compute reproduction probability Pr = P*(n) [Δ(c)/Δmax] If random [0, 1] < Pr Create an ant End If End For End For

Decide where to go

Update pheromone level on each cell

Aging process

Reproduction process

The Swarm Model with Varying Population Size (SVPS)


Results

t=0 t=50t=20 t=300 t=500

SFPS

SVPS

β = 7; = 0.2; = 0.07; k = 1.0; p=1,9; IPS = 10%

Max F0a


Results

SFPS

SVPS

β = 7; = 0.2; = 0.07; k = 1.0; p=1,9; IPS = 10%

min Passino F1


0

0,2

0,4

0,6

0,8

1

0 50 100 150 200 250 300 350 400 450 500

1

2

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4

-3000000

-2500000

-2000000

-1500000

-1000000

-500000

0

500000

0 50 100 150 200 250 300 350 400 450 500

1

2

3

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1-SFPS

2,3,4 – SVPS with different parameters

Median height of ants on landscape

Max F0a

min Passino F1

SVPS converges massively to the desired regions


0

0,2

0,4

0,6

0,8

1

0 50 100 150 200 250 300 350 400 450 500

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3.5

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-3000000

-2500000

-2000000

-1500000

-1000000

-500000

0

500000

0 50 100 150 200 250 300 350 400 450 500

1

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7

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15

Median height of ants on landscape

min Passino F1

Max F0a

SVPS with different values for β (IPS = 20%)

β =1 means that the swarm is practically ignoring pheromone

Higher performance is attained by pheromone following and varying population size


0

1000

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7000

0 50 100 150 200 250 300 350 400 450 500

10%

20%

30%

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0 50 100 150 200 250 300 350 400 450 500

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3.5

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Max F0a

min Passino F1

Population growth in SVPS

Populations with different initial size converge to the same size

Populations with different β converge to the same size, except for β=1.


Mediumvalleys

Highestpeak

Mediumvalley

Lowestvalley

MediumpeakMedium

peaks

Mediumvalley


Conclusions

SVPS converges faster than SFPS to desired regions

The way the ants become distributed along the landscape is clearly different in both models

SVPS self-regulates the population size according to the shape of the landscape

SFPS – PassinoF1 SVPS – PassinoF1

SVPS – F0a SVPS – PassinoF1


Future work

Optimization (????)

Multi-Objective Optimization (?)

Genetic Algorithms

Image ProcessingWatershed Watershed+SVPSWatershed+SFPS

Varying the Population Size of Artificial Foraging Swarms on Time Varying Landscapes

Education

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