Differential evolution with generalized differentials

In this paper, we study the mutation operation of the differential evolution (DE) algorithm. In particular, we propose the differential of scaled vectors, called the ‘generalized differential’, as opposed to the existing scaled differential vector in the mutation of DE. We derive the probability distribution of points generated by the mutation with ‘generalized differentials’. We incorporate a vector-projection-based exploratory method within the new mutation scheme. The vector projection is not mandatory and it is only invoked if trial points continue to be unsuccessful. An algorithm is then proposed which implements the mutation strategy based on the difference of the scaled vectors as well as the vector projection technique. A numerical study is carried out using a set of 50 test problems, many of which are inspired by practical applications. Numerical results suggest that the new algorithm is superior to DE.