Consider the following model problem:
I want to use an evolutionary algorithm to optimize the starting point of particles for which it is apriori clear where they would start in state space, but not when. Once a particle is placed, it is part of the dynamics, which is stochastic, i.e. whether certain particles interact is modeled by a random variable. A mutation of the evolutionary algorithm corresponds to slightly changing the time when the particle is introduced in the system.
I have now two choices:
1) I let the stochastic dynamics evolve while the evolutionary algorithm is optimizing, i.e. after every mutation I draw a new interaction environment from the distribution. That means, the algorithm is evaluating every situation with a different environment (drawn from one fixed distribution).
2) I draw an interaction pattern for every particle apriori to have one fixed environment (we assume they can be drawn independently). Then I let the algorithm optimize my problem in that deterministic environment. I do that for several environments and take some statistic over the solution.
Does someone have experience with those two approaches and can tell me their advantages and disadvantages from a practical point of view?