Differential evolution with polymorphic schemes

In recent years a new evolutionary algorithm for optimization in continuous spaces called Differential Evolution (DE) has developed. If one wants to apply DE one has to specify several parameters as well as to select a scheme. Several schemes being widely used can be found in literature. This raises the question, which one fits best to your application at hand. To get rid of this scheme selection problem, a new concept called Polymorphic Differential Evolution (PolyDE) is proposed. PolyDE generalizes the standard schemes by a polymorphic scheme. The mathematical expression of this polymorphic scheme can be changed on symbolic level. This polymorphic scheme is an adaptive scheme changing symbols based on accumulative histograms and roulette-wheel sampling. PolyDE is applied to four typical benchmark functions known from literature and its performance is ranked between the top and middle region compared to all standard DE schemes. Since PolyDE performs not worse than the other schemes it can be used as alternative to them solving this way the scheme selection problem. The best performance is obtained for the multimodal functions.