Sorting unsigned permutations by reversals is a difficult problem; indeed, it was proved to be NP-hard by Caprara (1997). Because of its high complexity, many approximation algorithms to compute the minimal reversal distance were proposed until reaching the nowadays best-known theoretical ratio of 1.375. In this article, two memetic algorithms to compute the reversal distance are proposed. The first one uses the technique of opposition-based learning leading to an opposition-based memetic algorithm; the second one improves the previous algorithm by applying the heuristic of two breakpoint elimination leading to a hybrid approach. Several experiments were performed with one-hundred randomly generated permutations, single benchmark permutations, and biological permutations. Results of the experiments showed that the proposed OBMA and Hybrid-OBMA algorithms achieve the best results for practical cases, that is, for permutations of length up to 120. Also, Hybrid-OBMA showed to improve the results of OBMA for permutations greater than or equal to 60. The applicability of our proposed algorithms was checked processing permutations based on biological data, in which case OBMA gave the best average results for all instances.

中文翻译：

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基于对立的模因算法和混合方法通过反转对排列进行排序

通过反转对无符号排列进行排序是一个难题；事实上，Caprara (1997) 证明它是 NP-hard 的。由于其高度复杂性，人们提出了许多计算最小反转距离的近似算法，直到达到当今最著名的理论比率 1.375。在本文中，提出了两种计算反转距离的模因算法。第一个使用基于对立的学习技术，导致基于对立的模因算法；第二个通过应用两个断点消除的启发式方法改进了先前的算法，从而产生了一种混合方法。使用一百个随机生成的排列、单个基准排列和生物排列进行了几个实验。