Is Differential Evolution Rotationally Invariant?

In this paper, we study a problem of the control parameter settings in Differential Evolution algorithm and test a novel variant of the algorithm called CoBiDE. Although Differential Evolution with basic setting (i.e., CR=0.5; F =0.5) works quite well, it starts to fail on rotated functions. In general, we want to improve the convergence of algorithm primarily on rotated functions. It is done by adapting crossover parameter CR whereas parameter F is fixed to 0.5. There is a recommendation to set CR = 1 for rotated functions. It means that trial vectors are essentially composed from mutant. However, it is not easy task to set the parameters appropriately for solving optimization problem but it is crucial for obtaining good results. Moreover, the quality of points produced in evolution is highly affected by the coordinate system. In CoBiDE, the authors proposed a new coordinate system based on the current distribution of points in the population. We test these two approaches by running both algorithms on six pairs of rotated and non-rotated functions from CEC 2013 benchmark set in two levels of dimension space. This experimental study aims to reveal if such algorithm’s setting is invariant under a rotation.