We propose a new memetic algorithm with optimal recombination for the asymmetric travelling salesman problem (ATSP). The optimal recombination problem (ORP) is solved in a crossover operator based on a new exact algorithm that solves the ATSP on cubic digraphs. A new mutation operator makes random jumps in 3-opt or 4-opt neighborhoods. The initial population is constructed by means of greedy constructive heuristics. The 3-opt local search is used to improve the initial and the final populations. A computational experiment on the TSPLIB instances shows that the proposed algorithm yields results competitive to those of other well-known algorithms for ATSP and confirms that the ORP may be used successfully in memetic algorithms.

中文翻译：

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非对称旅行商问题的最优重组模因算法

针对非对称旅行商问题（ATSP），我们提出了一种具有最佳重组的新模因算法。基于一种新的精确算法，在交叉算子中解决了最佳重组问题（ORP），该算法可解决三次有向图上的ATSP。一个新的变异算子在3或4邻域中随机跳跃。初始种群是通过贪婪的构造启发法构建的。3-opt本地搜索用于改善初始种群和最终种群。在TSPLIB实例上进行的计算实验表明，所提出的算法产生的结果与ATSP的其他知名算法相比具有竞争优势，并证实了ORP可以成功用于模因算法。