Learning to Mutate for Differential Evolution

Adaptive parameter control and mutation operator selection are two important research avenues in differential evolution (DE). Existing works consider the two avenues independently. In this paper, we propose to unify the two modules and develop a unified parameterized mutation operator. With different settings of the parameters, different mutation operators can be retrieved. Further, the settings of the parameters closely relate to the control parameters of the DE. By determining the parameters we can achieve adaptive parameter control and mutation operator selection simultaneously. We propose to use a neural network to output the parameters and learn the network parameter by the natural evolution strategies algorithm under the consideration of modeling the evolution process as a Markov Decision Process. Experimental results on the CEC 2018 test suite show that the proposed method performs significantly better than traditional DEs with different operators and an advanced adaptive DE. We further analyze the time complexity and population diversity of the proposed method. The analysis shows that our method can achieve a balanced exploration and exploitation with a properly learned network.