Improvements of real coded genetic algorithms based on differential operators preventing premature convergence

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.