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. 2018 Sep 10;8:13513. doi: 10.1038/s41598-018-31902-8

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© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Pareto front-distance broken down into two dimensions: Inaccurary (ΔR) and slowness(Δt). The position of a competitor in a scatter plot reveals, in which direction a competitor should be improved, in order to be more competitive. For instance, BI is always very close to the Pareto front regarding the quality of solutions (small ΔR), but the running time should be reduced significantly (larger Δt). ND, on the other hand, should be improved to compute better attacks, in order to be more competitive.