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Comparing black-box differential evolution and classic differential evolution

Recently, black-box differential evolution (BBDE) has been proposed to overcome the search biases and sensitivity to rotation of the classic differential evolution (DE). To date, BBDE has been studied only for the 'rand' strategy and even for this strategy, no systematic experimental study has been published yet. In this paper we provide such a study and further examine whether the idea from BBDE can be extended to two other DE strategies, 'best' and 'target-to-best'. We compare in detail these DE and BBDE variants using the COCO (Comparing Continuous Optimizers) platform to assess their overall performance and invariance to rotation. The results show that BBDE with the 'rand' strategy performs better than the original algorithm, but this is not true for the other two strategies. We also demonstrate that while the BBDE variants are less sensitive to rotation than the DE variants, some sensitivity to this transformation still persists and remains currently unexplained.