问题
I am using the differential evolution optimizer in scipy and I don't understand the intuition behind the tol argument. Specifically is say in the documentation:
tol: float, optional
When the mean of the population energies, multiplied by tol, divided by the standard deviation of the population energies is greater than 1 the solving process terminates:
convergence = mean(pop) * tol / stdev(pop) > 1
What does setting tol represent from a user perspective?
回答1:
Maybe the formula in the documentation is easier to understand in the following form (see lines 508 and 526 in the code):
std(population_energies) / mean(population_energies) < tol
It means that convergence is reached when the standard deviation of the energies for each individual in the population, normed by the average, is smaller than the given tolerance value.
The optimization algorithm is iterative. At every iteration a better solution is found. The tolerance parameters is used to define a stopping condition. The stopping condition is actually that all the individuals (parameter sets) have approximately the same energy, i.e. the same cost function value. Then, the parameter set giving the lowest energy is returned as a solution.
It also implies that all the individuals are relatively close to each other in the parameter space. So, no better solution can be expected on the following generations.
来源：https://stackoverflow.com/questions/52142965/explain-the-intuition-for-the-tol-paramer-in-scipy-differential-evolution