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Article . 2025 . Peer-reviewed
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Article . 2025
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Hisom: Hierarchical Self‐Organizing Map for Solving Multiple Traveling Salesman Problems

HiSOM: hierarchical self-organizing map for solving multiple traveling salesman problems
Authors: Qingshu Guan; Hui Cao; Xianjing Zhong; Dapeng Yan; Shuangsi Xue;

Hisom: Hierarchical Self‐Organizing Map for Solving Multiple Traveling Salesman Problems

Abstract

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%.

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Keywords

hierarchical self-organizing map, path intersection, Combinatorial optimization, multiple traveling salesman problem, convex hull

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Top 10%
Average
Average
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