Finding Social Landscapes for PSOs via Kernels

W. B. Langdon and Riccardo Poli
XPS Computer Science
University of Essex Logo

Paper presented at CEC-2006 Pages 6118-6125


Individual landscape→Social Landscape

Evolution of Social Landscape

finding fitness of evolved kernel

Top: original landscape
Below: Equivalent social landscape given by convolution of evolved kernel and original landscape

Genetic Programming of Kernel

Hill Climber



One dimensional Rastrigin (maximisation)
Rastrigin set up as a maximisation problem. Global optimum at the origin.

five PSO runs and corresponding 5 hill climber positions

Rastrigin PSO Kernel

Evolved kernel for PSO on Rastrigin

PSO Test error 0.66 (sd 0.29)

Movie showing movement of a five member PSO on Rastrigin and the corresponding movement of the hill climber on the equivalent social landscape. Note the RMS error between the center of the PSO and the position of the hill climber (both shown with blue squares) is on average only 0.66 when started from random positions not used in training the GP.

GA Test Error 0.86 (sd 0.35)

Movie showing the location of every GA individual (and the values of its bits, red or blue) versus the location of the hill climber on the equivalent social landscape. Again note closeness of match of the two squares.



Extended Particle Swarms
W.B.Langdon 25 July 2006