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 Technology13 © 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