Crossover operators are very important components in Evolutionary Computation. Here we are interested in crossovers for the permutation representation that find applications in combinatorial optimization problems such as the permutation flowshop scheduling and the traveling salesman problem. We introduce three families of permutation crossovers based on algebraic properties of the permutation space. In particular, we exploit the group and lattice structures of the space. A total of 34 new crossovers is provided. Algebraic and semantic properties of the operators are discussed, while their performances are investigated by experimentally comparing them with known permutation crossovers on standard benchmarks from four popular permutation problems. Three different experimental scenarios are considered and the results clearly validate our proposals.

中文翻译：

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置换问题的代数交叉算子的实验比较

交叉算子是进化计算中非常重要的组成部分。在这里，我们对排列表示的交叉感兴趣，该交叉在组合优化问题中找到了应用，例如排列流水车间调度和旅行商问题。我们基于排列空间的代数性质，介绍了三个排列交换的族。特别是，我们利用空间的群和格结构。总共提供了34个新的分频器。讨论了运算符的代数和语义特性，同时通过实验比较它们与已知基准的置换交叉，并从四个流行的置换问题按标准基准对它们的性能进行了研究。考虑了三种不同的实验方案，结果清楚地验证了我们的建议。