Two standard convergence tests are used to terminate ES searches.
One is that the * absolute* difference in the objective function values
of the
best and worst members of the post-selection population is less than a
user-specified limit, i.e.

The other is that the * relative* difference in the objective function
values of
the best and worst members of the post-selection population is less than a
user-specified limit, i.e.

Thus, absolutely or relatively, the objective function values of the parents must lie close together before the algorithm is deemed to have converged.