  This paper presents several types of evolutionary algorithms (EAs) used for
global optimization on real domains. The interest has been focused on
multimodal problems, where the difficulties of a premature convergence usually
occurs. First the standard genetic algorithm (SGA) using binary encoding of
real values and its unsatisfactory behavior with multimodal problems is briefly
reviewed together with some improvements of fighting premature convergence. Two
types of real encoded methods based on differential operators are examined in
detail: the differential evolution (DE), a very modern and effective method
firstly published by R. Storn and K. Price, and the simplified real-coded
differential genetic algorithm SADE proposed by the authors. In addition, an
improvement of the SADE method, called CERAF technology, enabling the
population of solutions to escape from local extremes, is examined. All methods
are tested on an identical set of objective functions and a systematic
comparison based on a reliable methodology is presented. It is confirmed that
real coded methods generally exhibit better behavior on real domains than the
binary algorithms, even when extended by several improvements. Furthermore, the
positive influence of the differential operators due to their possibility of
self-adaptation is demonstrated. From the reliability point of view, it seems
that the real encoded differential algorithm, improved by the technology
described in this paper, is a universal and reliable method capable of solving
all proposed test problems.
