A Gradient-based Method for Differential Evolution Parameter Control by Smoothing

Differential evolution (DE) is one of the most studied algorithms in evolutionary computation. However, the parameters in DE need to be tuned carefully, which costs much computational resources. The reason is that the basic paradigm of DE (mutation, crossover, bound constraint and selection) contains non-differentiable operators. In this paper, we propose a DE paradigm called "smoDE"for the first time by smoothing the crossover operator and the bound constraint operator to make them differentiable with respect to the parameters. The experiments show that we can tune the parameters of smoDE by gradient descent with much fewer computational resources than commonly used tools such as the Bayesian optimization algorithm (BOA). Then we analyze the population diversity of smoDE theoretically and prove that smoDE can converge faster than DE. A simple experiment also validates that. We further propose the "ada-smoDE"by embedding a neural network in smoDE to output parameters of smoDE adaptively and test ada-smoDE on the CEC 2018 test suite. The results show that ada-smoDE can perform competitively on the whole test suite and significantly better than DE on some problems.