Artificial Social Insects in Dynamic Environments, Warsaw, 2005. Emergent behavior of an artificial swarm when searching for optimon dynamic landscapes.

1. 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)
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

2. 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
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

3. 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.
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

4. Previous Models
Ramos and Fernandes, 2005 – Swarm With Fixed Population Size (SFPS)
t=0 t = 50 t = 100 t = 500 t=1000
Environment is Ants are Each time step, all All ants move on
NxN toroidal randomly ants deposit a each time step: the
grid with placed on the certain amount of direction is chosen
different landscape/fun pheromone that is according to the
values ction. proportional to the pheromone levels
according to a value of the around the ant and it
function. function on that is constrained by a
site. directional bias.
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

5. Deciding where to go - Chialvo Model
Measures the relative β
Normalised Transition probabilities  σ 
on the lattice to go from cell k to cell i:
probabilities of
W ( σ ) = 1 +
 1 + δσ 
moving to cell i with
pheromone density, 
Measures the magnitude of the
W ( σ i ) w( ∆ i )
difference in orientation:
Pik =
∑ j W (σ j ) w( ∆ j )
w (0) = 1
w (1) = 1/2
k w (2) = 1/4 3 4 3
w (3) = 1/12
w (4) = 1/20 2 2
1 0 1
Indicates the sum over all the cells j
which are in local neighbourhood of k.
w = 1/12 w = 1/12
w = 1/4 w = 1/4
w = 1/2 w = 1/2
w=1
e.g.: Coming from North
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

6. Deciding where to go - Chialvo Model
Transition rule between cells by use of
a pheromone weighting function:
β
 σ 
W ( σ ) = 1 +
 1 + δσ 

Measures the relative probabilities of
moving to cell r with pheromone density, σ (r)
This parameter is associated with the
osmotropotaxic sensitivity. Controls the
degree of randomness with which the ant 1 can be seen as the sensory
follows the gradient of pheromone. δ
capacity. This parameter
describes the fact that the
For low values the pheromone concentration
ant’s
does not greatly affect its choice, while high
ability to sense pheromone
values cause it to follow pheromone gradient
decreases at
with more certainty.
high concentrations.
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

7. Ramos and Fernandes Model:
Ramos and
Chialvo, 1995 Ramos, 2000
Fernandes, 2005
T =η ∆ gl ∆[ i ]
T =η + p T =η + p
255 ∆ max
Pheromone update of cell c
represents the represents the
P(c)= P(c)+T difference between difference between
the median grey- the median grey-
levels of previous levels of previous
cell and its cell and its
neighbors, and neighbors, and
Pheromone evaporation, k current cell and its current cell and its
neighbors neighbors
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

8. 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
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

9. The Swarm Model with Varying Population Size (SVPS)
For all ants do place agent at randomly selected cell
End For
For t = 1 to tmax do /* Main loop */
For all ants do
Aging Decrease energy
process If energy = 0 Kill ant
Compute W(σ) and Pik
Decide where to go
Move to a selected neighboring cell not occupied by other agent
Increase pheromone at cell c
P(c)= P(c)+[η+p(Δ(c)/Δmax)]) Update pheromone level on each cell
End For
Evaporate pheromone by K, at all cells
For all ants do
If ant meets ant do
Compute n
Reproduction Determine P*(n)
process Compute reproduction probability Pr = P*(n) [Δ(c)/Δmax]
If random [0, 1] < Pr Create an ant
End If
End For
End For
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

10. Results
β = 7; σ = 0.2;
η = 0.07; k = 1.0; p=1,9; IPS = 10%
Max F0a
SFPS
SVPS
t=0 t=20 t=50 t=300 t=500
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

11. Results
β = 7; σ = 0.2;
η = 0.07; k = 1.0; p=1,9; IPS = 10%
min Passino F1
SFPS
SVPS
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

12. Median height of ants on landscape 1
1-SFPS
0,8
2,3,4 – SVPS with different parameters
0,6 1
2
3
0,4 4
Max F0a
0,2
0
0 50 100 150 200 250 300 350 400 450 500
500000
SVPS converges massively
to the desired regions 0
-500000
1
-1000000
2
3
-1500000 4
-2000000
min Passino F1
-2500000
-3000000
0 50 100 150 200 250 300 350 400 450 500
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

13. Median height of ants on landscape 1
SVPS with different values for β (IPS = 20%)
0,8
1
0,6
3.5
7
β =1 means that the 10
swarm is practically 0,4 15
ignoring pheromone
Max F0a
0,2
0
0 50 100 150 200 250 300 350 400 450 500
500000
Higher performance is attained
by pheromone following and 0
varying population size
-500000
1
-1000000
3.5
7
-1500000 10
15
-2000000
min Passino F1
-2500000
-3000000
0 50 100 150 200 250 300 350 400 450 500
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

14. Population growth in SVPS
7000
6000
5000
Populations with different initial
size converge to the same size 4000 10%
20%
30%
3000
2000
Max F0a
1000
0
0 50 100 150 200 250 300 350 400 450 500
9000
8000
Populations with different 7000
β converge to the same
size, except for β=1. 6000
1
5000
3.5
7
4000 10
3000
2000
min Passino F1
1000
0
0 50 100 150 200 250 300 350 400 450 500
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

15. Medium
valleys
Highest Medium
peak valley
Medium
Medium peak
peaks
Medium
valley
Lowest
valley
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

16. Conclusions
SVPS converges faster than SFPS to
desired regions
SFPS – PassinoF1 SVPS – PassinoF1
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
SVPS – F0a SVPS – PassinoF1
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

17. Future work
Optimization (????)
Multi-Objective Optimization (?)
Genetic Algorithms
Watershed Watershed+SFPS Watershed+SVPS
Image Processing
Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw