Landscape produced by genetic programming where Constriction helps Particle Swarm Optimisation

Swarm of ten Particles without Constriction

No constriction 0.8+1.08*x-x*x

10 particles without constriction factor. In this run 116 generations were needed to find an optima. Note as time progresses particles become increasingly energetic and only stumble of maximum value by chance.

Swarm of ten Particles with Constriction factor of 0.7

No constriction 0.8+1.08*x-x*x
Swarm of 10 particles operating on the same landscape as above (note different scales) with the same initial consitions but this time with a constriction factor. Now only 11 generations are needed. Note as time progresses particles become increasingly more focused on the area containing the maximum value.

Example where constriction fails.

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W.B.Langdon 4 June 2005

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