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.
Solving large-scale instances of the Traveling Salesman Problem (TSP) exactly is computationally expensive. Researchers often employ graph sparsification methods to improve computational efficiency. Traditional sparsification methods typically rely on fixed heuristics and fail to fully exploit instance-specific structural information. In this paper, we propose Graph Edge Sparsification (GES), a learning-based sparsification approach for Euclidean TSP. By incorporating geometric structural information and combinatorial optimization technology, our proposed method adaptively generates a sparsification graph for different instances, significantly reducing the graph size and accelerating the solving process. Experimental results demonstrate that our sparsification method can prune up to 95% of edges on the MATILDA dataset, while keeping the solution gap within 1% of the optimal value. Moreover, our approach exhibits strong generalization capability on the TSPLIB benchmark.In some large-scale instances, the pruning rate exceeds 99%, while the optimality gap remains below 1%.