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An analysis of differential evolution parameters on rotated bi-objective optimization functions

Abstract:

Differential evolution (DE) is a very powerful and simple algorithm for single- and multi-objective continuous optimization problems. However, its success is highly affected by the right choice of parameters. Authors of successful multi-objective DE algorithms usually use parameters which do not render the algorithm invariant with respect 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 performance 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 characteristics. Then, we explore how the performance changes when we rotate the axes in a controlled manner. We find out that our results are consistent 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.