Efficient nonlinear optimization by differential evolution with a rotation-invariant local sampling operation

Differential Evolution (DE) is a newly proposed evolutionary algorithm. DE has been successfully applied to optimization problems including non-linear, non-differentiable, non-convex and multimodal functions. However, the performance of DE degrades in problems having strong dependence among variables, where variables are strongly related to each other. One of the desirable properties of optimization algorithms for solving the problems with the strong dependence is rotation invariant property. In DE, the mutation operation is rotation invariant, but the crossover operation is not rotation-invariant usually. In this study, we propose a new operation, called local sampling operation that is rotation-invariant. In the operation, independent points are selected from the population, difference vectors from a parent to the points span a local area centered at the parent, and a new point is generated around the area. Also, the operation is used for judging whether intensive search or extensive search is desirable in each generation. The effect of the proposed method is shown by solving some benchmark problems.