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），目标是最小化最长路线的长度。该遗传算法采用旅行商问题（TSP）序列作为每个个体的编码表示，并运用动态规划算法对个体进行评估，从而在给定的城市序列中找到最优的mTSP解决方案。一种新型交叉算子被设计用于组合两个父代中的相似路线，为种群提供了良好的多样性。针对部分生成的子代个体，我们检测并移除路线之间的交叉点，以获得无交叉的解决方案。这一操作对最小化最长路线的多旅行商问题尤为有效。生成的子代个体进一步通过自适应随机局部搜索与全面邻域搜索进行优化。在与文献中多个基准测试集进行对比时，在相近的截止时间阈值下，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个实例的当前最优解。