  Many Differential Evolution (DE) algorithms with various parameter control
methods (PCMs) have been proposed. However, previous studies usually considered
PCMs to be an integral component of a complex DE algorithm. Thus the
characteristics and performance of each method are poorly understood. We
present an in-depth review of 24 PCMs for the scale factor and crossover rate
in DE and a large scale benchmarking study. We carefully extract the 24 PCMs
from their original, complex algorithms and describe them according to a
systematic manner. Our review facilitates the understanding of similarities and
differences between existing, representative PCMs. The performance of DEs with
the 24 PCMs and 16 variation operators is investigated on 24 black-box
benchmark functions. Our benchmarking results reveal which methods exhibit high
performance when embedded in a standardized framework under 16 different
conditions, independent from their original, complex algorithms. We also
investigate how much room there is for further improvement of PCMs by comparing
the 24 methods with an oracle-based model, which can be considered to be a
conservative lower bound on the performance of an optimal method.
