On Optimal Coverage of a Tree with Multiple Robots

We study the algorithmic problem of optimally covering a tree with $k$ mobile robots. The tree is known to all robots, and our goal is to assign a walk to each robot in such a way that the union of these walks covers the whole tree. We assume that the edges have the same length, and that traveling along an edge takes a unit of time. Two objective functions are considered: the cover time and the cover length. The cover time is the maximum time a robot needs to finish its assigned walk and the cover length is the sum of the lengths of all the walks. We also consider a variant in which the robots must rendezvous periodically at the same vertex in at most a certain number of moves. We show that the problem is different for the two cost functions. For the cover time minimization problem, we prove that the problem is NP-hard when $k$ is part of the input, regardless of whether periodic rendezvous are required or not. For the cover length minimization problem, we show that it can be solved in polynomial time when periodic rendezvous are not required, and it is NP-hard otherwise

The Optimal Dispatch of Traffic and Patrol Police Service Platforms

The main goal of this paper is to present a minmax programming model for the optimal dispatch of Traffic and Patrol Police Service Platforms with single traffic congestion. The objective is to minimize the longest time of the dispatch for Traffic and Patrol Police Service Platforms. Some numerical experiments are carried out, and the optimal project is given

The Optimal Dispatch of Traffic and Patrol Police Service Platforms

The main goal of this paper is to present a minmax programming model for the optimal dispatch of Traffic and Patrol Police Service Platforms with single traffic congestion. The objective is to minimize the longest time of the dispatch for Traffic and Patrol Police Service Platforms. Some numerical experiments are carried out, and the optimal project is given

Modelación En Programación Matemática Y Resolución Del Problema De Localización-Ruteo En Logística Urbana

The implementation of urban distribution centers near to city centers to allow freight consolidation is a widely extended initiative worldwide, seeking to improve traffic congestion and quality of life in downtown, among others. This paper considers the problem of locating urban distribution centers and proposes an exact method, based on integer linear programming for strategic, tactical and operational decision-making. The aim is to solve, in an integer manner, location, sizing and operation (vehicle routing) problems in these logistics platforms. The model is validated using real-data taken from the city of SaintÉtienne, France. Computational experiments are also carried out in order to compare the proposed model with existing procedures from the literature. Results show the efficiency and effectiveness of the proposed model and its applicability in real decision-making for medium sized data sets

Modelación En Programación Matemática Y Resolución Del Problema De Localización-Ruteo En Logística Urbana

The implementation of urban distribution centers near to city centers to allow freight consolidation is a widely extended initiative worldwide, seeking to improve traffic congestion and quality of life in downtown, among others. This paper considers the problem of locating urban distribution centers and proposes an exact method, based on integer linear programming for strategic, tactical and operational decision-making. The aim is to solve, in an integer manner, location, sizing and operation (vehicle routing) problems in these logistics platforms. The model is validated using real-data taken from the city of SaintÉtienne, France. Computational experiments are also carried out in order to compare the proposed model with existing procedures from the literature. Results show the efficiency and effectiveness of the proposed model and its applicability in real decision-making for medium sized data sets

An Iterative Approach for Collision Feee Routing and Scheduling in Multirobot Stations

This work is inspired by the problem of planning sequences of operations, as welding, in car manufacturing stations where multiple industrial robots cooperate. The goal is to minimize the station cycle time, \emph{i.e.} the time it takes for the last robot to finish its cycle. This is done by dispatching the tasks among the robots, and by routing and scheduling the robots in a collision-free way, such that they perform all predefined tasks. We propose an iterative and decoupled approach in order to cope with the high complexity of the problem. First, collisions among robots are neglected, leading to a min-max Multiple Generalized Traveling Salesman Problem (MGTSP). Then, when the sets of robot loads have been obtained and fixed, we sequence and schedule their tasks, with the aim to avoid conflicts. The first problem (min-max MGTSP) is solved by an exact branch and bound method, where different lower bounds are presented by combining the solutions of a min-max set partitioning problem and of a Generalized Traveling Salesman Problem (GTSP). The second problem is approached by assuming that robots move synchronously: a novel transformation of this synchronous problem into a GTSP is presented. Eventually, in order to provide complete robot solutions, we include path planning functionalities, allowing the robots to avoid collisions with the static environment and among themselves. These steps are iterated until a satisfying solution is obtained. Experimental results are shown for both problems and for their combination. We even show the results of the iterative method, applied to an industrial test case adapted from a stud welding station in a car manufacturing line

Control and communication systems for automated vehicles cooperation and coordination

Mención Internacional en el título de doctorThe technological advances in the Intelligent Transportation Systems (ITS) are exponentially improving over the last century. The objective is to provide intelligent and innovative services for the different modes of transportation, towards a better, safer, coordinated and smarter transport networks. The Intelligent Transportation Systems (ITS) focus is divided into two main categories; the first is to improve existing components of the transport networks, while the second is to develop intelligent vehicles which facilitate the transportation process. Different research efforts have been exerted to tackle various aspects in the fields of the automated vehicles. Accordingly, this thesis is addressing the problem of multiple automated vehicles cooperation and coordination. At first, 3DCoAutoSim driving simulator was developed in Unity game engine and connected to Robot Operating System (ROS) framework and Simulation of Urban Mobility (SUMO). 3DCoAutoSim is an abbreviation for "3D Simulator for Cooperative Advanced Driver Assistance Systems (ADAS) and Automated Vehicles Simulator". 3DCoAutoSim was tested under different circumstances and conditions, afterward, it was validated through carrying-out several controlled experiments and compare the results against their counter reality experiments. The obtained results showed the efficiency of the simulator to handle different situations, emulating real world vehicles. Next is the development of the iCab platforms, which is an abbreviation for "Intelligent Campus Automobile". The platforms are two electric golf-carts that were modified mechanically, electronically and electrically towards the goal of automated driving. Each iCab was equipped with several on-board embedded computers, perception sensors and auxiliary devices, in order to execute the necessary actions for self-driving. Moreover, the platforms are capable of several Vehicle-to-Everything (V2X) communication schemes, applying three layers of control, utilizing cooperation architecture for platooning, executing localization systems, mapping systems, perception systems, and finally several planning systems. Hundreds of experiments were carried-out for the validation of each system in the iCab platform. Results proved the functionality of the platform to self-drive from one point to another with minimal human intervention.Los avances tecnológicos en Sistemas Inteligentes de Transporte (ITS) han crecido de forma exponencial durante el último siglo. El objetivo de estos avances es el de proveer de sistemas innovadores e inteligentes para ser aplicados a los diferentes medios de transporte, con el fin de conseguir un transporte mas eficiente, seguro, coordinado e inteligente. El foco de los ITS se divide principalmente en dos categorías; la primera es la mejora de los componentes ya existentes en las redes de transporte, mientras que la segunda es la de desarrollar vehículos inteligentes que hagan más fácil y eficiente el transporte. Diferentes esfuerzos de investigación se han llevado a cabo con el fin de solucionar los numerosos aspectos asociados con la conducción autónoma. Esta tesis propone una solución para la cooperación y coordinación de múltiples vehículos. Para ello, en primer lugar se desarrolló un simulador (3DCoAutoSim) de conducción basado en el motor de juegos Unity, conectado al framework Robot Operating System (ROS) y al simulador Simulation of Urban Mobility (SUMO). 3DCoAutoSim ha sido probado en diferentes condiciones y circunstancias, para posteriormente validarlo con resultados a través de varios experimentos reales controlados. Los resultados obtenidos mostraron la eficiencia del simulador para manejar diferentes situaciones, emulando los vehículos en el mundo real. En segundo lugar, se desarrolló la plataforma de investigación Intelligent Campus Automobile (iCab), que consiste en dos carritos eléctricos de golf, que fueron modificados eléctrica, mecánica y electrónicamente para darle capacidades autónomas. Cada iCab se equipó con diferentes computadoras embebidas, sensores de percepción y unidades auxiliares, con la finalidad de transformarlos en vehículos autónomos. Además, se les han dado capacidad de comunicación multimodal (V2X), se les han aplicado tres capas de control, incorporando una arquitectura de cooperación para operación en modo tren, diferentes esquemas de localización, mapeado, percepción y planificación de rutas. Innumerables experimentos han sido realizados para validar cada uno de los diferentes sistemas incorporados. Los resultados prueban la funcionalidad de esta plataforma para realizar conducción autónoma y cooperativa con mínima intervención humana.Programa Oficial de Doctorado en Ingeniería Eléctrica, Electrónica y AutomáticaPresidente: Francisco Javier Otamendi Fernández de la Puebla.- Secretario: Hanno Hildmann.- Vocal: Pietro Cerr

Models and algorithms for the capacitated location-routing problem

Le problème de localisation-routage avec capacités (PLRC) apparaît comme un problème clé dans la conception de réseaux de distribution de marchandises. Il généralisele problème de localisation avec capacités (PLC) ainsi que le problème de tournées de véhicules à multiples dépôts (PTVMD), le premier en ajoutant des décisions liées au routage et le deuxième en ajoutant des décisions liées à la localisation des dépôts. Dans cette thèse on dévelope des outils pour résoudre le PLRC à l’aide de la programmation mathématique. Dans le chapitre 3, on introduit trois nouveaux modèles pour le PLRC basés sur des flots de véhicules et des flots de commodités, et on montre comment ceux-ci dominent, en termes de la qualité de la borne inférieure, la formulation originale à deux indices [19]. Des nouvelles inégalités valides ont été dévelopées et ajoutées aux modèles, de même que des inégalités connues. De nouveaux algorithmes de séparation ont aussi été dévelopés qui dans la plupart de cas généralisent ceux trouvés dans la litterature. Les résultats numériques montrent que ces modèles de flot sont en fait utiles pour résoudre des instances de petite à moyenne taille. Dans le chapitre 4, on présente une nouvelle méthode de génération de colonnes basée sur une formulation de partition d’ensemble. Le sous-problème consiste en un problème de plus court chemin avec capacités (PCCC). En particulier, on utilise une relaxation de ce problème dans laquelle il est possible de produire des routes avec des cycles de longueur trois ou plus. Ceci est complété par des nouvelles coupes qui permettent de réduire encore davantage le saut d’intégralité en même temps que de défavoriser l’apparition de cycles dans les routes. Ces résultats suggèrent que cette méthode fournit la meilleure méthode exacte pour le PLRC. Dans le chapitre 5, on introduit une nouvelle méthode heuristique pour le PLRC. Premièrement, on démarre une méthode randomisée de type GRASP pour trouver un premier ensemble de solutions de bonne qualité. Les solutions de cet ensemble sont alors combinées de façon à les améliorer. Finalement, on démarre une méthode de type détruir et réparer basée sur la résolution d’un nouveau modèle de localisation et réaffectation qui généralise le problème de réaffectaction [48].The capacitated location-routing problem (CLRP) arises as a key problem in the design of distribution networks. It generalizes both the capacitated facility location problem (CFLP) and the multiple depot vehicle routing problem (MDVRP), the first by considering additional routing decisions and the second by adding the location decision variables. In this thesis we use different mathematical programming tools to develop and specialize new models and algorithms for solving the CLRP. In Chapter 3, three new models are presented for the CLRP based on vehicle-flow and commodity-flow formulations, all of which are shown to dominate, in terms of the linear relaxation lower bound, the original two-index vehicle-flow formulation [19]. Known valid inequalities are complemented with some new ones and included using separation algorithms that in many cases generalize extisting ones found in the literature. Computational experiments suggest that flow models can be efficient for dealing with small or medium size instances of the CLRP (50 customers or less). In Chapter 4, a new branch-and-cut-and-price exact algorithm is introduced for the CLRP based on a set-partitioning formulation. The pricing problem is a shortest path problem with resource constraints (SPPRC). In particular, we consider a relaxation of such problem in which routes are allowed to contain cycles of length three or more. This is complemented with the development of new valid inequalities that are shown to be effective for closing the optimality gap as well as to restrict the appearance of cycles. Computational experience supports the fact that this method is now the best exact method for the CLRP. In Chapter 5, we introduce a new metaheuristic with the aim of finding good quality solutions in short or moderate computing times. First, a bundle of good solutions is generated with the help of a greedy randomized adaptive search procedure (GRASP). Following this, a blending procedure is applied with the aim of producing a better upper bound as a combination of all the others in the bundle. An iterative destroy-and-repair method is then applied using a location-reallocation model that generalizes the reallocation model due to de Franceschi et al. [48]