Improved Filtering for the Euclidean Traveling Salesperson Problem in CLP(FD)

Abstract

The Traveling Salesperson Problem (TSP) is one of the best-known problems in computer science. The Euclidean TSP is a special case in which each node is identified by its coordinates on the plane and the Euclidean distance is used as cost function. Many works in the Constraint Programming (CP) literature addressed the TSP, and use as benchmark Euclidean instances; however the usual approach is to build a distance matrix from the points coordinates, and then address the problem as a TSP, disregarding the information carried by the points coordinates for constraint propagation. In this work, we propose to use geometric information, present in Euclidean TSP instances, to improve the filtering power. In order to have a declarative approach, we implemented the filtering algorithms in Constraint Logic Programming on Finite Domains (CLP(FD)).