Varying the Population Size of Artificial Foraging          Swarms on Time Varying Landscapes        Carlos Fernandes     ...
Previous Models          Chialvo and Millonas, 1995        Models the formation of        trails and networks in a        ...
Previous Models          Ramos and Almeida, 2000          A swarm model based on          Chialvo’s work evolves over grey...
Previous Models          Ramos and Fernandes, 2005 – Swarm With Fixed Population Size (SFPS)                           t=0...
Deciding where to go - Chialvo Model                                                        Measures the relative         ...
Deciding where to go - Chialvo Model   Transition rule between cells by use of   a pheromone weighting function:          ...
Ramos and Fernandes Model:                                                                          Ramos and         Chia...
The Swarm Model with Varying Population Size (SVPS)      Aging process                 Each ant is born with energy = 1   ...
The Swarm Model with Varying Population Size (SVPS)             For all ants do place agent at randomly selected cell     ...
Results                                                                       β = 7; σ = 0.2;                             ...
Results                                                                     β = 7; σ = 0.2;                               ...
Median height of ants on landscape                     1    1-SFPS                                                       0...
Median height of ants on landscape                    1   SVPS with different values for β (IPS = 20%)                    ...
Population growth in SVPS                                                       7000                                      ...
Medium  valleys  Highest                                                                        Medium  peak              ...
Conclusions      SVPS converges faster than SFPS to      desired regions                                                  ...
Future work                 Optimization (????)                 Multi-Objective Optimization (?)                 Genetic A...
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Varying the Population Size of Artificial Foraging Swarms on Time Varying Landscapes

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

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

  1. 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. 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) surfacesFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw
  3. 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. 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. 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 NorthFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw
  6. 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. 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 neighborsFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw
  8. 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 occupiedFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw
  9. 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 nReproduction 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 ForFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw
  10. 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=500Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw
  11. 11. Results β = 7; σ = 0.2; η = 0.07; k = 1.0; p=1,9; IPS = 10% min Passino F1 SFPS SVPSFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw
  12. 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 500Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw
  13. 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 500Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw
  14. 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 500Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw
  15. 15. Medium valleys Highest Medium peak valley Medium Medium peak peaks Medium valleyLowestvalleyFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw
  16. 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 – PassinoF1Fernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw
  17. 17. Future work Optimization (????) Multi-Objective Optimization (?) Genetic Algorithms Watershed Watershed+SFPS Watershed+SVPS Image ProcessingFernandes, Ramos and Rosa – “VPS Swarms on Time Varying Landscapes” ICANN´2005 - Warsaw

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