The Traveling Salesman Problem is a fundamental combinatorial optimization problem widely studied in operations research. Despite its simple formulation, it remains computationally challenging due to the exponential growth of the search space and the large number of constraints required to eliminate subtours. This paper introduces a preprocessing strategy that significantly reduces the size of the optimization model by restricting the set of candidate arcs and retaining only the lowest-cost neighbors for each vertex. Computational experiments on TSPLIB benchmark instances demonstrate that the proposed approach substantially reduces the number of decision variables. The method is evaluated using both classical and quantum optimization techniques, showing improvements in computational time and reductions in optimality gaps. Overall, the results indicate that the proposed preprocessing enhances the scalability of the formulations and makes them more suitable for both classical solvers and emerging quantum optimization frameworks.

翻译：旅行商问题是运筹学中广泛研究的基本组合优化问题。尽管其表述简单，但由于搜索空间呈指数级增长且需要大量约束条件来消除子回路，该问题在计算上仍然具有挑战性。本文提出一种预处理策略，通过限制候选弧的集合并仅保留每个顶点的最低成本邻居，显著缩小了优化模型的规模。基于TSPLIB基准实例的计算实验表明，所提方法大幅减少了决策变量的数量。该方法在经典与量子优化技术下均进行了评估，结果显示其在计算时间与最优性差距方面均有所改进。总体而言，实验结果说明所提预处理增强了模型的可扩展性，使其更适用于经典求解器与新兴的量子优化框架。