
doi: 10.1002/net.22268
ABSTRACTRecently, routing problems have made significant progress and exhibited remarkable performance across various domains. However, they still suffer from severe issues, including high computational complexity and path intersection phenomenon, which curtail their broader applicability. This study focuses on the challenging and practical Single Depot‐Multiple Traveling Salesman Problem (SD‐MTSP) with a min‐max objective, which aims to minimize the maximum tour length among all salesmen. To tackle these challenges, we propose a Hierarchical Self Organizing Map (HiSOM) based on a divide‐and‐conquer framework to decompose the complex scheduling of SD‐MTSP into task allocation and route planning subproblems, with a strong emphasis on reducing computational complexity. Specifically, in the task allocation stage, we introduce the concept of soft labels to precisely characterize the strength of association between salesmen and their traversal cities, and devise an SGD‐SOM framework to optimize the sum square error with smooth gradient descents. In the route planning stage, we design a TOSOM framework to generate a topologically ordered tour with minimal length, ensuring strict adherence to the convex hull property and effectively mitigating path intersection. Comprehensive experiments on both synthetic and real‐world datasets demonstrate that our proposed HiSOM outperforms numerous baseline methods by up to 6.91%.
hierarchical self-organizing map, path intersection, Combinatorial optimization, multiple traveling salesman problem, convex hull
hierarchical self-organizing map, path intersection, Combinatorial optimization, multiple traveling salesman problem, convex hull
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