Rotation Invariance and Rotated Problems: An Experimental Study on Differential Evolution

This paper presents an experimental study on the efficacy of a rotation-invariant Differential Evolution (based on current-to-rand mutation) on a benchmark of test problems in its non-rotated and rotated version. Numerical results show that standard Differential Evolution outperforms rotation-invariant Differential Evolution on the benchmark under consideration for both non-rotated and rotated problems. In other words, the rotation-invariant Differential Evolution does not seem to be more efficient than its standard counterpart to address rotated problems. According to our interpretation, these experimental results show that rotated problems are simply different problems with respect to the non-rotated problems. Furthermore, rotation-invariant Differential Evolution is characterised by its moving operator: it generates an offspring by perturbing all the design variables of a candidate solution at the same time. This logic does not appear to guarantee a better performance on rotated problems.