Varying the Population Size of Artificial Foraging Swarms on Time Varying Landscapes
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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)
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
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
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
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.
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
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
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
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
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
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.
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
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
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
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
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
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)
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
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
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
Results
SFPS
SVPS
β = 7; = 0.2; = 0.07; k = 1.0; p=1,9; IPS = 10%
min Passino F1
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
0
0,2
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1
0 50 100 150 200 250 300 350 400 450 500
1
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-3000000
-2500000
-2000000
-1500000
-1000000
-500000
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500000
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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
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
0
0,2
0,4
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0,8
1
0 50 100 150 200 250 300 350 400 450 500
1
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
3.5
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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
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
0
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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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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.
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
Mediumvalleys
Highestpeak
Mediumvalley
Lowestvalley
MediumpeakMedium
peaks
Mediumvalley
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
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
ICANN´2005 - WarsawFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes”
Future work
Optimization (????)
Multi-Objective Optimization (?)
Genetic Algorithms
Image ProcessingWatershed Watershed+SVPSWatershed+SFPS
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