Abstract: The multiple traveling salesmen problem (mTSP) generalizes the classical TSP by involving multiple travelers who must collectively visit all cities, starting and ending at a common depot. This work focuses on the min-max variant, where the objective is to minimize the length of the longest subtour, ensuring a balanced workload among travelers, which is a crucial factor in many real-world applications, such as emergency response and logistics. This paper proposes a novel Ant Colony System (ACS)-based approach that effectively addresses the min-max mTSP, designed to construct well-balanced tours while optimizing the maximum tour length. The method integrates two key strategies: a sector-based heuristic for guiding city assignments, and a dynamic traveler selection criterion to promote equitable route construction. The method was evaluated on 33 two-dimensional Euclidean benchmark instances and compared with four state-of-the-art ACO-based approaches, demonstrating consistently better fitness under the min-max objective.
