An Analysis of Differential Evolution Parameters on Rotated Bi-objective Optimization Functions


Differential evolution (DE) is a very powerful and simple algorithm for single- and multi-objective continuous optimization prob- lems. However, its success is highly affected by the right choice of pa- rameters. Authors of successful multi-objective DE algorithms usually use parameters which do not render the algorithm invariant with re- spect to rotation of the coordinate axes in the decision space. In this work we try to see if such a choice can bring consistently good perfor- mance under various rotations of the problem. We do this by testing a DE algorithm with many combinations of parameters on a testbed of bi-objective problems with different modality and separability charac- teristics. Then, we explore how the performance changes when we rotate the axes in a controlled manner. We find out that our results are con- sistent with the single-objective theory but only for unimodal problems. On multi-modal problems, unexpectedly, parameter settings which do not render the algorithm rotationally invariant have a consistently good performance for all studied rotations.