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When there are several methods to solve a given problem, it is always fruitful looking for some "links" between these methods. We consider here "classical" PSO, with random modifications of positions and velocities, on the one hand, and, on the other hand
We know the first one is already quite powerful, but random choices don't use all the information we have, and also it doesn't take into account the fact that computers use only approximations of real values. Sometimes results are then strange (negative,
As we will see, it is also interesting to make use of gradient evaluations, at least from time to time.