A Population Adaptation Mechanism for Differential Evolution Algorithm

In the original Differential Evolution algorithm three different control parameter values must be pre-specified by a user. These parameters are the population size, the crossover constant and the mutation scale factor. Control parameters affect strongly the performance and reliability of the algorithm. However, choosing good parameters can be very difficult for a user. In this paper a new adaptive Differential Evolution algorithm called Cumu-DE is proposed. The aim of the algorithm is to be a user friendly and reliable algorithm with moderate convergence speed. In the proposed algorithm, the so called effective population size is adapted automatically using mechanism based on probability mass function. The actual population size is kept fixed. Even though we talk about two different population sizes, we have only one population. The effective population size describes the effective part of the actual population. The more we get successful trials, the smaller the effective population is and vice versa. The algorithm was initially evaluated by using the set of 25 benchmark functions provided by CEC2005 special session on real-parameter optimization. It was compared with the results of standard DE/rand/1/bin. The proposed algorithm Cumu-DE proved to be significantly faster due to its average of FES in four cases and significantly slower in six cases. Additionally, Cumu-DE was significantly more reliable in six cases and significantly less reliable in none. These results are demonstrating the potential of the proposed adaptation approach.