Improving the Asymmetric TSP by Considering Graph Structure

Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based on general graph properties. We experimentally show that such implied propagators bring robustness to pathological instances and highlight the fact that graph structure can significantly improve search heuristics behavior. Finally, we show that our approach outperforms current state of the art results.Comment: Technical repor

A new exact algorithm for the multi-depot vehicle routing problem under capacity and route length constraints

This article presents an exact algorithm for the multi-depot vehicle routing problem (MDVRP) under capacity and route length constraints. The MDVRP is formulated using a vehicle-flow and a set-partitioning formulation, both of which are exploited at different stages of the algorithm. The lower bound computed with the vehicle-flow formulation is used to eliminate non-promising edges, thus reducing the complexity of the pricing subproblem used to solve the set-partitioning formulation. Several classes of valid inequalities are added to strengthen both formulations, including a new family of valid inequalities used to forbid cycles of an arbitrary length. To validate our approach, we also consider the capacitated vehicle routing problem (CVRP) as a particular case of the MDVRP, and conduct extensive computational experiments on several instances from the literature to show its effectiveness. The computational results show that the proposed algorithm is competitive against stateof-the-art methods for these two classes of vehicle routing problems, and is able to solve to optimality some previously open instances. Moreover, for the instances that cannot be solved by the proposed algorithm, the final lower bounds prove stronger than those obtained by earlier methods

School bus selection, routing and scheduling.

The aim of this thesis is to develop formulations and exact algorithms for the school bus routing and scheduling problem and to develop an integrated software implementation using Xpress-MP/CPLEX and ArcGIS of ESRI, a geographical information system software package. In this thesis, bus flow, single commodity flow, two-commodity flow, multi-commodity flow, and time window formulations have been developed. They capture all of the important elements of the School Bus Routing and Scheduling Problem (SBRSP) including homogeneous or heterogeneous bus fleets, the identification of bus stops from a large set of potential bus stops, and the assignment of students to stops and stops to routes. They allow for the one stop-one bus and one stop-multi bus scenarios. Each formulation of the SBRSP has a linear programming relaxation and we present the relationships among them. We present a Branch-and-Cut exact algorithm which makes use of new linearization techniques, new valid inequalities, and the first valid equalities. We develop an integrated software package that is based on Geographical Information System (GIS) map-based interface, linking to an Xpress-MP/CPLEX solver. The interface between GIS and Xpress-MP is written in VBA and VC++.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2005 .K4. Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 6250. Thesis (Ph.D.)--University of Windsor (Canada), 2005

Constraint Programming Algorithms for Route Planning Exploiting Geometrical Information

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 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.Comment: In Proceedings ICLP 2020, arXiv:2009.0915

Layered graph approaches for combinatorial optimization problems

Extending the concept of time-space networks, layered graphs associate information about one or multiple resource state values with nodes and arcs. While integer programming formulations based on them allow to model complex problems comparably easy, their large size makes them hard to solve for non-trivial instances. We detail and classify layered graph modeling techniques that have been used in the (recent) scientific literature and review methods to successfully solve the resulting large-scale, extended formulations. Modeling guidelines and important observations concerning the solution of layered graph formulations by decomposition methods are given together with several future research directions

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

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))