Learning Adaptive Subspace Differential Evolution by Evolution Strategies

The subspace method is one of the most used optimization methods, which means optimizing not all elements of the decision variable but only part of it. Subspace methods can obtain a faster convergence rate on objective functions with special structures, such as sparse objective functions. The core idea of the subspace method is selecting the proper subspace (i.e. elements) to be optimized in each iteration, which is always selected by hand. Recently the idea has been borrowed in some studies of evolutionary algorithms, however, the subspace-selecting mechanism is still handcrafted. In our opinion, the selecting mechanism can be learned from optimizing related optimization problems. In this paper, we propose an adaptive subspace differential evolution algorithm, whose subspace is selected by a graph neural network (GNN). The GNN is trained by Natural Evolution Strategies. The experiments on the CEC 2018 test suite show that the proposed method can perform significantly better than classic differential evolution and the proposed method can generalize on problems with different dimensions.