Learning unified mutation operator for differential evolution by natural evolution strategies

Differential evolution (DE) is one of the widely studied algorithms in evolutionary computation. Recently, many adaptive mechanisms have been proposed for DE including adaptive operator selection and adaptive parameter control. Existing studies consider the two kinds of mechanisms independently. In this paper, we first propose a unified mutation operator with learnable parameters. With different parameter settings, the unified mutation operator degenerates into various classic mutation operators. As a result, by adapting the control parameters of the unified mutation operator, we can realize parameter control and operator selection simultaneously. We then present how to use a neural network to adaptively determine the control parameters. We use natural evolution strategies to train the neural network by modeling the evolutionary process as a Markov decision process. We then embed it into three DEs including classic DE, JADE and LSHADE. Experimental studies show that by embedding the learned unified mutation operator, the performances of these backbone DEs can be improved. Particularly, by embedding the unified mutation operator, LSHADE can perform competitively among state-of-the-art EAs including the winner algorithms in the past CEC competitions. Furthermore, we verify the effectiveness of the unified mutation operator through analyzing the population diversity theoretically.