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Direct hybrid algorithms directly integrate deep learning with heuristic algorithms, showcasing robust solving performance and generalization capability. LLM-based hybrid algorithms leverage LLMs to autonomously generate and refine heuristics, showing promising performance despite being in early developmental stages. In the future, further integration of deep learning techniques, particularly LLMs, with heuristic algorithms and advancements in interpretability and generalization will be pivotal trends in TSP algorithm design. These endeavors aim to tackle larger and more complex real-world instances while enhancing algorithm reliability and practicality. 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