  Among many evolutionary algorithms, differential evolution (DE) has received
much attention over the last two decades. DE is a simple yet powerful
evolutionary algorithm that has been used successfully to optimize various
real-world problems. Since it was introduced, many researchers have developed
new methods for DE, and one of them makes use of a mutation based on the Cauchy
distribution to increase the convergence speed of DE. The method monitors the
results of each individual in the selection operator and performs the Cauchy
mutation on consecutively failed individuals, which generates mutant vectors by
perturbing the best individual with the Cauchy distribution. Therefore, the
method can locate the consecutively failed individuals to new positions close
to the best individual. Although this approach is interesting, it fails to take
into account establishing a balance between exploration and exploitation. In
this paper, we propose a sigmoid based parameter control that alters the
failure threshold for performing the Cauchy mutation in a time-varying
schedule, which can establish a good ratio between exploration and
exploitation. Experiments and comparisons have been done with six conventional
and six advanced DE variants on a set of 30 benchmark problems, which indicate
that the DE variants assisted by the proposed algorithm are highly competitive,
especially for multimodal functions.
