Crossover is one of the most important operators in a genetic algorithm by which offspring production for the next generation is performed. There are a number of crossover operators for each type of chromosome representation of solutions that are closely related to different types of optimisation problems. Crossover operation in genetic algorithms, aimed at solving permutation-based combinatorial optimisation problems, is more computationally expensive compared to other cases. This is mainly caused by the fact that no duplicate numbers are allowed in a chromosome and therefore offspring legalisation is needed after each substring exchange. Under these conditions, the time required for performing crossover operation increases significantly with increasing chromosome size, which may deeply affect the efficiency of these genetic algorithms. In this paper, a genetic algorithm that uses path representation for chromosomes and benefits from an alternative form of the well-known partially mapped crossover is proposed. The results of numerical experiments performed on a set of benchmark problems clearly show that the use of this crossover operator can significantly increase the efficiency of permutation-based genetic algorithms and also help in producing good quality solutions.

杂交是遗传算法中最重要的运算符之一，通过遗传运算可以进行下一代后代生产。对于每种类型的解决方案染色体表示，都有许多交叉算子，这些算子与不同类型的优化问题密切相关。遗传算法中的交叉运算旨在解决基于置换的组合优化问题，与其他情况相比，计算量更大。这主要是由于这样的事实，即染色体中不允许有重复的数字，因此每次子串交换后都需要将后代合法化。在这些条件下，执行交叉操作所需的时间会随着染色体大小的增加而显着增加，这可能会深刻影响这些遗传算法的效率。在本文中，提出了一种遗传算法，该算法使用染色体的路径表示，并受益于众所周知的部分映射交叉的另一种形式。针对一组基准问题进行的数值实验结果清楚地表明，使用此交叉算子可以显着提高基于置换的遗传算法的效率，还有助于产生高质量的解决方案。