M esd PSO Conceptual Development E5. 77 How do large numbers of birds produce seamless, gracefu flocking choreography, while often, but suddenly changing direction, scattering and regrouping? Decentralized"local processes Manipulation of inter-individual distances(keep pace and avoid collision) Are there any advantages to the swarming behavior for an individual in a swarm? Can profit from the discoveries and previous experience of other swarm members in search for food, avoiding predators, adjusting to the environment, i.e. information sharing yields evolutionary advantage Do humans exhibit social interaction similar to the swarming behavior in other species? Absolutely, humans learn to imitate physical motion early on; as they grow older, they imitate their peers on a more abstract level by adjusting their beliefs and attitudes to conform with societal standards ⊙ Rania hassan3/2004 Engineering Systems Division -Massachusetts Institute of Technology
11 © Rania Hassan 3/2004 Engineering Systems Division - Massachusetts Institute of Technology PSO Conceptual Development PSO Conceptual Development • How do large numbers of birds produce seamless, graceful flocking choreography, while often, but suddenly changing direction, scattering and regrouping? – “Decentralized” local processes. – Manipulation of inter-individual distances (keep pace and avoid collision). • Are there any advantages to the swarming behavior for an individual in a swarm? – Can profit from the discoveries and previous experience of other swarm members in search for food, avoiding predators, adjusting to the environment, i.e. information sharing yields evolutionary advantage. • Do humans exhibit social interaction similar to the swarming behavior in other species? – Absolutely, humans learn to imitate physical motion early on; as they grow older, they imitate their peers on a more abstract level by adjusting their beliefs and attitudes to conform with societal standards
M esd PSO Conceptual Development E5. 77 Phase l Randomly generated particle positions in 2-d space Randomly generated velocity vectors for each particle in 2-d space For each swarm movement(iteration), each particle(agent) matches the velocity of its nearest neighbor to provide synchrony Random changes in velocities(craziness)are added in each iteration to provide variation in motion and" life-like"appearance-artificial ⊙ Rania hassan3/2004 Engineering Systems Division -Massachusetts Institute of Technology
12 © Rania Hassan 3/2004 Engineering Systems Division - Massachusetts Institute of Technology PSO Conceptual Development PSO Conceptual Development • Phase I: – Randomly generated particle positions in 2-d space. – Randomly generated velocity vectors for each particle in 2-d space. – For each swarm movement (iteration), each particle (agent) matches the velocity of its nearest neighbor to provide synchrony. – Random changes in velocities (craziness) are added in each iteration to provide variation in motion and “life-like” appearance – artificial
M esd PSO Conceptual Development E5. 77 Phase ll Heppner's simulation used a roost (cornfield), that the birds flocked around before landing there -eliminating the need for craziness The mathematical formulation for the roosting model included each particle evaluates its current fitness by comparing its position to the roost position(100, 100) ith particle kth time unit 100J+ 100 each particle remembers its best ever fitness value f, and the position associated with it,p=[x'y'j, and adjusts its velocity accordingly k+1 Uniformly distributed if xk<x ∴Vxk+1= Vxk +c rand random number update the velocity in the y-direction in the same manner ⊙ Rania hassan3/2004 Engineering Systems Division -Massachusetts Institute of Technology
13 © Rania Hassan 3/2004 Engineering Systems Division - Massachusetts Institute of Technology PSO Conceptual Development PSO Conceptual Development • Phase II: – Heppner’s simulation used a roost (cornfield), that the birds flocked around before landing there – eliminating the need for “craziness “. – The mathematical formulation for the roosting model included: • each particle evaluates its current fitness by comparing its position to the roost position (100, 100). • each particle remembers its best ever fitness value, , and the position associated with it, , and adjusts its velocity accordingly. ( ) ( ) = − + − ik ik ik kth time unit f x y ith particle i f > @ i i i p = x y x x Vx Vx c rand x x Vx Vx c rand i k i k i i k i k i k i i k LI LI < ∴ = + > ∴ = − + + Uniformly distributed random number update the velocity in the y-direction in the same manner
M esd PSo Conceptual Development E50. 7 Phase‖ each particle knows the position of the best particle in the current swarm,Pi=[xi yi]. This is the particle with the lowest fitness value f (closest to the roost) if Vxl=vxl -co rand global best ifxk<xg∴改xk+1=xk+C2rnd in the simulation, when c and c, are set high, the flock is sucked swirls around the cornfield and slowly approach it, the flock violently into the cornfield; whereas if they are set low, the flock The simulation with the known cornfield position appeared real and raised the question of how do birds find"optimal food sources in reality without knowing the"cornfield "location Example 1: scientists proved that parks in affluent neighborhoods attract more birds than parks in poor neighborhoods Example 2: put a bird feeder in your balcony and see what happens in few hours ⊙ Rania hassan3/2004 Engineering Systems Division -Massachusetts Institute of Technology
14 © Rania Hassan 3/2004 Engineering Systems Division - Massachusetts Institute of Technology PSO Conceptual Development PSO Conceptual Development • Phase II: • each particle knows the position of the best particle in the current swarm, . This is the particle with the lowest fitness value, (closest to the roost). • in the simulation, when and are set high, the flock is sucked violently into the cornfield; whereas if they are set low, the flock swirls around the cornfield and slowly approach it. – The simulation with the known cornfield position appeared real and raised the question of how do birds find “optimal” food sources in reality without knowing the “cornfield” location? • Example 1: scientists proved that parks in affluent neighborhoods attract more birds than parks in poor neighborhoods. • Example 2: put a bird feeder in your balcony and see what happens in few hours. global best g kf > @ gk gk gk p = x y x x Vx Vx c rand x x Vx Vx c rand i k i k g k i k i k i k g k i k LI LI < ∴ = + > ∴ = − + + c c