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)).

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Problems affecting the transport of people or goods are plentiful in industry and commerce and they also appear to be at the origin of much more complex problems. In recent years, the logistics and transport sector keeps growing supported by technological progress, i.e. companies to be competitive are resorting to innovative technologies aimed at efficiency and effectiveness. This is why companies are increasingly using technologies such as Artificial Intelligence (AI), Blockchain and Internet of Things (IoT). Artificial intelligence, in particular, is often used to solve optimization problems in order to provide users with the most efficient ways to exploit available resources.In this work we present an overview of our current research activities concerning the development of new algorithms, based on Constraint Logic Programming (CLP) techniques, for route planning problems exploiting the geometric information intrinsically present in many of them or in some of their variants. The research so far has focused in particular on the Euclidean Traveling Salesperson Problem (Euclidean TSP) with the aim to exploit the results obtained also to other problems of the same category, such as the Euclidean Vehicle Routing Problem (Euclidean VRP), in the future.

The Traveling Salesperson Problem (TSP) is a well-known problem addressed in the literature through various techniques, including Integer Linear Programming, Constraint Programming (CP) and Local Search. Many real life instances belong to the subclass of Euclidean TSPs, in which the nodes to be visited are associated with points in the Euclidean plane, and the distance between them is the Euclidean distance. A well-known property of the Euclidean TSP is that no crossings can exist in an optimal solution. In a previous publication, we exploited this property to speedup the solution of Euclidean instances in CP, by imposing a number of so-called no-overlapping constraints. The number of imposed constraints is quadratic in the number of nodes of the TSP. In this work, we observe that not all the no-overlapping constraints are equally useful: by experimental analysis, some of them provide a speedup, while others only introduce overhead. We use a supervised machine learning approach on them to learn a binary classifier, with the objective to impose only those no-overlapping constraints that have been classified as effective. Preliminary experiments support the validity of the idea.