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I'm experimenting with particle swarm optimisation and am trying to determine the best approach for the following simple scenario:

  • Optimizing a 1-dimensional function (i.e. particles are moving along a single line)
  • The function to be optimised can be sampled at any point on the line
  • The "value" sampled for each position is very noisy
  • The underlying function to optimise (excluding the noise) is quite simple (e.g. a pyramid with a single global maximum, or two humps with different heights)

What would be the best particle swarm design to solve this problem, i.e to efficiently discover the optimum with the minimum number of samples?