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），旨在最小化最长路径的长度。该遗传算法采用TSP序列作为每个个体的表示，并利用动态规划算法评估个体，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，从而为种群提供较高的多样性。对于部分生成的子代，我们检测并移除路径之间的交叉点，以获得无交叉的解决方案。这对最小最大化mTSP尤为有用。通过自适应随机局部搜索和彻底邻域搜索进一步优化生成的子代。在多个文献中常见的基准测试集上，与现有算法相比，我们的算法在相同截止时间阈值下平均表现更优。此外，在四个基准测试集的89个实例中，我们改进了其中21个实例的当前最优解。