约束逻辑编程中欧几里得旅行商问题及其变体的增强过滤算法
Enhanced Filtering Algorithms for the Euclidean Traveling Salesperson Problem and its variants in Constraint Logic Programming
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中文总结 AI 辅助
本研究针对约束逻辑编程，提出利用几何信息的欧几里得旅行商问题增强过滤算法，可扩展至其变体，实验验证了该方法的计算优势。
中文摘要 AI 辅助
旅行商问题（TSP）是计算机科学中最知名的问题之一，广泛应用于智能车辆、智能交通系统等众多工程应用场景。在“欧几里得”情形下，每个节点由平面内的坐标定义，距离通过欧几里得度量计算。在约束规划（CP）文献中，欧几里得TSP通常通过计算完整距离矩阵并将其作为一般情形处理，但该方法忽略了点坐标所携带的几何信息。本研究提出在约束逻辑编程（CLP）中实现的新过滤算法，该算法利用此类几何信息实现比现有方法更强的约束传播。此外，我们展示了该方法如何扩展到TSP的其他欧几里得变体，包括欧几里得广义旅行商问题（EGTSP），其在实际路由和物流应用中具有相关性。实验结果证明了所提方法的计算优势。
英文摘要
The Traveling Salesperson Problem (TSP) is one of the best-known problems in computer science and arises in many engineering applications, such as smart vehicles and intelligent transportation systems. In the "Euclidean" case, each node is defined by its coordinates in the plane and distances are computed using the Euclidean metric. In the Constraint Programming (CP) literature, the Euclidean TSP is typically addressed by computing the full distance matrix and treating it as a general case; however this approach ignores the geometric information carried by the points' coordinates. In this work, we propose new filtering algorithms, implemented in Constraint Logic Programming (CLP), that exploit such geometric information to achieve stronger constraint propagation than existing approaches. Moreover, we show how this methodology can be extended to other Euclidean variants of the TSP, including the Euclidean Generalized Traveling Salesperson Problem (EGTSP), which is relevant in practical routing and logistics applications. Experimental results demonstrate the computational advantages of the proposed approach.
