This paper proposes a hybrid genetic algorithm for solving the Multiple Traveling Salesman Problem (mTSP) to minimize the length of the longest tour. The genetic algorithm utilizes a TSP sequence as the representation of each individual, and a dynamic programming algorithm is employed to evaluate the individual and find the optimal mTSP solution for the given sequence of cities. A novel crossover operator is designed to combine similar tours from two parents and offers great diversity for the population. For some of the generated offspring, we detect and remove intersections between tours to obtain a solution with no intersections. This is particularly useful for the min-max mTSP. The generated offspring are also improved by a self-adaptive random local search and a thorough neighborhood search. Our algorithm outperforms all existing algorithms on average, with similar cutoff time thresholds, when tested against multiple benchmark sets found in the literature. Additionally, we improve the best-known solutions for 21 out of 89 instances on four benchmark sets.

翻译：本文提出了一种混合遗传算法，用于求解多旅行商问题（mTSP），以最小化最长路径的长度。该遗传算法采用旅行商问题（TSP）序列作为每个个体的表示形式，并利用动态规划算法评估个体，从而为给定的城市序列找到最优的mTSP解。设计了一种新型交叉算子，用于组合两个父代中的相似路径，并为种群提供高度多样性。对于部分生成的子代，我们检测并消除路径之间的交叉，以获得无交叉的解。这对于最小化最长路径的mTSP尤为有效。生成的子代还通过自适应随机局部搜索和彻底的邻域搜索进行改进。在多个文献中的基准测试集上，设定类似的截止时间阈值时，我们的算法在平均性能上优于所有现有算法。此外，在四个基准测试集的89个实例中，我们改进了其中21个实例的已知最优解。