Adaptive differential evolution with optimization state estimation

Abstract

The performance of differential evolution (DE) largely depends on an appropriate selection of the values of the algorithmic parameters. Usually, it is difficult to choose optimal parameter values, because they are often ad hoc to the specific problem in question and also related to the optimization states that the DE is in during its search process. In this paper, a novel adaptive parameter control scheme is proposed for DE. Improving from existing parameter control schemes, the parameters F and CR in DE are adaptively controlled according to the optimization states, namely, exploration state and exploitation state in each generation. These optimization states are estimated by measuring the population distribution. During the optimization process of DE, the distribution of population varies and reflects the search maturity. In the exploration state, individuals in the population distribute evenly in the search space. As the optimization matures, the population gradually converges on a global or local optimum in the exploitation state. This feature enables parameter adaptation with a fuller utilization of the prevailing optimization information and hence reduces inappropriate adjustments. The proposed adaptive parameter control scheme is applied to the famous DE/rand/1 algorithm. Experimental results show that this scheme can effectively improve the efficiency and robustness of the algorithm.