Apesar de serem utilizados com sucesso em problemas de roteirização clássicos como o do caixeiro-viajante e o de roteirização de veículos com janelas de tempo, os algoritmos genéticos não apresentavam bons resultados nos problemas de roteirização de veículos sem janelas de tempo. Utilizando-se de uma tendência recente de hibridização de algoritmos genéticos, Prins (2004) elaborou um algoritmo para o problema de roteirização de veículos sem janelas de tempo, monoperíodo, e que obrigatoriamente atenda a todos os clientes cujos resultados, quando aplicado a instâncias de Christofides et al. (1979) e de Golden et al. (1998), são comparáveis aos melhores códigos elaborados com base na busca tabu. Diferentemente da maioria dos algoritmos genéticos apresentados para solução de problemas de roteirização de veículos, no método desenvolvido por Prins (2004) o cromossomo é composto apenas pelos pontos a serem atendidos, não contendo delimitadores de rotas. Estas são definidas a partir de um método de particionamento do cromossomo. Este trabalho implementa o algoritmo descrito por Prins (2004) e propõe a este melhorias em diversas de suas etapas, como inicialização, operação de crossover, operação de mutação, reinicialização e particionamento do cromossomo. As alterações implantadas são aplicadas às instâncias de Christofides et al. (1979) e comparadas com o algoritmo inicial em termos de qualidade de solução e tempo de processamento. Finalmente, é elaborado um algoritmo genético que contempla as alterações que obtiveram resultados positivos. / In the Vehicle Routing Problem (VRP) we seek for a set of minimum-cost vehicle routes for a fleet of identical vehicles, each starting and ending at a depot, such that each customer is visited exactly once and the total demand of any route does not exceed the vehicle capacity. Several families of heuristics have been proposed for the VRP. They can be broadly classified into two main classes: classical heuristics developed between 1960 and 1990, and, more recently, metaheuristics. Among them, tabu search plays an key role, being acknowledged by most authors as the most successful approach for the VRP. In the literature some successful implementations of metaheuristic Genetic Algorithm (GA) can be found for classic routing problems such as the traveling salesman and vehicle routing problems with time windows. However, until recently, the same did not apply for the VRP. In this thesis we develop a genetic algorithm without trip delimiters, and hybridized with a local search procedure, for the solving the VRP, which is based on the work of Prins (2004). At any time, a chromosome can be converted into an optimal VRP solution (subject to chromosome sequence) by means of a splitting procedure, in which the chromosome sequence, representing a giant tour, is partitioned into feasible routes in terms of vehicle capacities. Starting with the procedure originally proposed Prins (2004), we then introduce new improvements in terms of the different components of the GA, aiming to obtain improved solutions. These include how we determine the initial population, different partitioning approaches, alternative reproduction (crossover) processes, a granular tabu mechanism similar to the one proposed by Toth and Vigo (2003 and, finally, in changes in the reinitialization process, aiming to reestablish diversity. Computational experiments are presented, based on the 14 classical Christofides instances for the VRP. The results show that the proposed improved versions of the GA allow us to obtain better solutions when compared to the original approach by Prins (2004).

Les problèmes de tournées de véhicules sont des problèmes d’optimisation combinatoire épineux avec des enjeux économiques et environnementaux importants au sein de la chaîne logistique. Le problème fondamental est de desservir des clients avec un ensemble de véhicules de façon à minimiser la distance totale parcourue. En pratique, il y a une grande variété d’objectifs et de contraintes additionnelles, liées à la législation et à la diversité des domaines d’applications. Ces problèmes de tournées sont très fréquents pour de nombreuses industries et la conception d’approches de résolution génériques est devenue une question de recherche importante.Cette thèse porte sur la conception et le développement d’un nouveau moteur de résolution pour les logiciels de tournées de véhicules proposés par l’entreprise GEOCONCEPT. Le solveur mis au point s’appuie sur la programmation par contraintes (PPC) pour améliorer la flexibilité (prise en compte de contraintes additionnelles), la déclarativité et la maintenance qui sont les limites des solveurs actuels de GEOCONCEPT fondés sur la recherche locale.Dans un premier temps, un modèle de graphe est établi pour la représentation unifiée des données et de nombreuses contraintes métiers. La résolution s’effectue par des approches à base de voisinage large disponibles dans les solveurs de PPC modernes. On peut ainsi traiter des instances de très grandes tailles efficacement tout en conservant une approche déclarative pour exprimer une classe très large de problèmes de tournées de véhicules. Dans un second temps, des modèles PPC s’appuyant sur des représentations redondantes du problème sont proposés afin de renforcer le filtrage. Nous nous intéressons en détails aux mécanismes de filtrage c’est-à-dire aux processus d’élimination des valeurs infaisables ou sous-optimales dans les domaines des variables. Ces algorithmes permettent de simplifier rapidement le problème et de fournir des bornes inférieures afin d’évaluer la qualité des solutions obtenues. Les bornes inférieures sont obtenues en résolvant des relaxations du plus célèbre des problèmes de la Recherche Opérationnelle : le problème du voyageur de commerce (TSP). Ce problème est le cœur de la contrainte globale weightedcircuit permettant de modéliser les problèmes de tournées en PPC. Nous proposons de nouveaux mécanismes de filtrage pour cette contrainte s’appuyant sur trois relaxations du TSP. Ces relaxations sont comparées sur les plans théorique et expérimental. L’originalité de ce travail est de proposer un nouvel algorithme de filtrage permettant de raisonner à la fois sur les successeurs directs d’un client et sur sa position dans la tournée. Ces raisonnements sont particulièrement utiles en présence de contraintes de fenêtres de temps, très communes dans les problèmes industriels.Le nouveau moteur de résolution offre d’excellentes performances sur des problèmes académiques et industriels tout en proposant des bornes inférieures informatives à des problèmes industriels réels. / Vehicle routing problems are very hard combinatorial optimization problems with significant economic and environmental challenges. The fundamental problem is to visit a set of customers with a given fleet of vehicles in order to minimize the total distance travelled. Moreover, these problems arise with a wide variety of objectives and additional constraints, related to the legislation and the diversity of industrial sectors. They are very common for many industries and the design of generic solvers has become an important research issue.This thesis focuses on the design and implementation of a new solver for the vehicle routing services offered by the company GEOCONCEPT. The proposed solver is based on constraint programming (CP) to improve flexibility (ability to take additional constraints into account), declarative modelling and maintenance, which are the limits of current GEOCONCEPT solvers based on local search.Firstly, a graph model is established to provide a common representation of the input-data and the numerous business constraints. The resolution is performed using large neighbourhood search methods available in modern CP solvers. It is thus possible to deal with large instances efficiently with a declarative approach where a broad class of vehicle routing problems can be modelled. Secondly, several CP models based on redundant views of the problem are proposed to strengthen the filtering. We focus on the filtering mechanisms for removing infeasible or suboptimal values in the domains of the variables. These algorithms can quickly simplify the problem and derive lower bounds to assert the quality of the solutions found. The lower bounds are obtained by solving relaxations of the most famous problem in Operations Research: the Traveling Salesman Problem (TSP). This problem is the core of the global constraint WEIGTEHDCIRCUIT for modelling routing problems in CP. We propose new filtering algorithms for this constraint based on three relaxations of the TSP. These relaxations are compared theoretically and experimentally. The originality of this work is to propose a new filtering algorithm for reasoning on the direct successors of a customer as well as his position in the tour. It is particularly useful in the presence of time window constraints, which are very common in industrial problems.The new solver shows excellent performance on academic and industrial problems and can compute informative lower bounds for real-life problems.

Apesar de serem utilizados com sucesso em problemas de roteirização clássicos como o do caixeiro-viajante e o de roteirização de veículos com janelas de tempo, os algoritmos genéticos não apresentavam bons resultados nos problemas de roteirização de veículos sem janelas de tempo. Utilizando-se de uma tendência recente de hibridização de algoritmos genéticos, Prins (2004) elaborou um algoritmo para o problema de roteirização de veículos sem janelas de tempo, monoperíodo, e que obrigatoriamente atenda a todos os clientes cujos resultados, quando aplicado a instâncias de Christofides et al. (1979) e de Golden et al. (1998), são comparáveis aos melhores códigos elaborados com base na busca tabu. Diferentemente da maioria dos algoritmos genéticos apresentados para solução de problemas de roteirização de veículos, no método desenvolvido por Prins (2004) o cromossomo é composto apenas pelos pontos a serem atendidos, não contendo delimitadores de rotas. Estas são definidas a partir de um método de particionamento do cromossomo. Este trabalho implementa o algoritmo descrito por Prins (2004) e propõe a este melhorias em diversas de suas etapas, como inicialização, operação de crossover, operação de mutação, reinicialização e particionamento do cromossomo. As alterações implantadas são aplicadas às instâncias de Christofides et al. (1979) e comparadas com o algoritmo inicial em termos de qualidade de solução e tempo de processamento. Finalmente, é elaborado um algoritmo genético que contempla as alterações que obtiveram resultados positivos. / In the Vehicle Routing Problem (VRP) we seek for a set of minimum-cost vehicle routes for a fleet of identical vehicles, each starting and ending at a depot, such that each customer is visited exactly once and the total demand of any route does not exceed the vehicle capacity. Several families of heuristics have been proposed for the VRP. They can be broadly classified into two main classes: classical heuristics developed between 1960 and 1990, and, more recently, metaheuristics. Among them, tabu search plays an key role, being acknowledged by most authors as the most successful approach for the VRP. In the literature some successful implementations of metaheuristic Genetic Algorithm (GA) can be found for classic routing problems such as the traveling salesman and vehicle routing problems with time windows. However, until recently, the same did not apply for the VRP. In this thesis we develop a genetic algorithm without trip delimiters, and hybridized with a local search procedure, for the solving the VRP, which is based on the work of Prins (2004). At any time, a chromosome can be converted into an optimal VRP solution (subject to chromosome sequence) by means of a splitting procedure, in which the chromosome sequence, representing a giant tour, is partitioned into feasible routes in terms of vehicle capacities. Starting with the procedure originally proposed Prins (2004), we then introduce new improvements in terms of the different components of the GA, aiming to obtain improved solutions. These include how we determine the initial population, different partitioning approaches, alternative reproduction (crossover) processes, a granular tabu mechanism similar to the one proposed by Toth and Vigo (2003 and, finally, in changes in the reinitialization process, aiming to reestablish diversity. Computational experiments are presented, based on the 14 classical Christofides instances for the VRP. The results show that the proposed improved versions of the GA allow us to obtain better solutions when compared to the original approach by Prins (2004).

Les problèmes de tournées de véhicules (VRPs) ont fait l’objet de plusieurs travaux de recherche depuis maintenant plus de 50 ans. La plupart des approches trouvées dans la littérature s’appuient sur un graphe complet ou un nœud est introduit pour tout point d’intérêt du réseau routier (typiquement les clients et le dépôt). Cette modélisation est, implicitement, basée sur l’hypothèse que le meilleur chemin entre toute paire de points du réseau routier est bien défini. Cependant, cette hypothèse n’est pas toujours valide dans de nombreuses situations. Souvent, plus d’informations sont nécessaires pour modéliser et résoudre correctement le problème. Nous commençons par examiner ces situations et définir les limites de la modélisation basée sur un graphe complet. Nous proposons un état de l’art des travaux qui examinent ces limites et qui traitent des VRPs en considérant plus d’informations issues du réseau routier. Nous décrivons les approches alternatives proposées, à savoir la modélisation utilisant un multi-graphe et celle utilisant la résolution directe sur un graph représentant le réseau routier. Dans une seconde étude, nous nous intéressons à l’approche basée sur la construction d’un multi-graphe. Nous proposons, d’abord, un algorithme qui permet de calculer d’une manière efficace la représentation par multi-graph du réseau routier. Puis, nous présentons une analyse empirique sur l’impact de cette modélisation sur la qualité de la solution. Pour ce faire, nous considérons le problème classique VRPTW comme un problème de pilote. Par la suite, nous développons une méthode heuristique efficace afin de résoudre le VRPTW basée sur une représentation par un multi-graphe.Dans une troisième étape, nous nous concentrons sur l’approche basée sur la résolution directe du problème sur un graphe représentant le réseau routier. Nous développons un algorithme de type branch-and-price pour la résolution de cette variante du problème. Une étude expérimentale est, ensuite, menée afin d’évaluer l’efficacité relative des deux approches. Enfin, nous étudions les problèmes de tournées de véhicules dans lesquels les temps de parcours varient au cours de la journée. Nous proposons un algorithme de type branch-and-price afin de résoudre le problème avec des fenêtres de temps directement sur le graphe représentant le réseau routier. Une analyse empirique sur l’impact de l’approche proposée sur la qualité de la solution est proposée. / Vehicle routing problems (VRPs) have drawn many researchers’ attention for more than fifty years. Most approaches found in the literature are, implicitly, based on the key assumption that the best path between each two points of interest in the road network (customers, depot, etc.) can be easily defined. Thus, the problem is tackled using the so-called customer-based graph, a complete graph representation of the road network. In many situations, such a graph may fail to accurately represent the original road network and more information are needed to address correctly the routing problem.We first examine these situations and point out the limits of the traditional customer-based graph. We propose a survey on works investigating vehicle routing problems by considering more information from the road network. We outline the proposed alternative approaches, namely the multigraph representation and the road network approach.Then, we are interested in the multigraph approach. We propose an algorithm that efficiently compute the multigraph representation for large sized road networks. We present an empirical analysis on the impact of the multigraph representation on the solution quality for the VPR with time windows (VRPTW) when several attributes are defined on road segments. Then, we develop an efficient heuristic method for the multigraph-based VRPTW.Next, we investigate the road network approach. We develop a complete branch-and-price algorithm that can solve the VRPTW directly on the original road network. We evaluate the relative efficiency of the two approaches through an extensive computational study.Finally, we are interested in problems where travel times vary over the time of the day, called time dependent vehicle routing problems (TDVRPs). We develop a branch-and-price algorithm that solves the TDVRP with time windows directly on the road network and we analyze the impact of the proposed approach on the solution quality.

La thèse porte sur l’étude de problèmes réels de transport et de distribution par voie routière. Il s’agit plus précisément de deux problèmes distincts d’optimisation des tournées de véhicules ; la distribution de produits pétroliers et le transfert des conteneurs. La résolution du premier problème, identifié comme le problème de tournées de véhicules avec compartiments multiples et fenêtres de temps ou MCVRP-TW (Multi-Compartment Vehicle Routing Problem with Time Windows), est basée sur une méthode de recherche tabou. Une adaptation de la méthode de résolution a été appliquée à deux autres problématiques annexes, la première intègre des contraintes supplémentaires liées à l’opération de chargement des produits pétroliers dans les compartiments, et la seconde inclut le concept d’ajustement des quantités demandées. Par ailleurs, dans l’optique d’une transition énergétique, nous nous sommes intéressés au problème de transfert des conteneurs par camions électriques dans la zone industrialo-portuaire du Havre. L’optimisation se situe à deux niveaux, un niveau stratégique pour le dimensionnement de l’infrastructure électrique et un niveau opérationnel pour la construction des tournées de véhicules. Seul le niveau stratégique a été abordé dans le cadre d’un projet de recherche grâce à un couplage de l’optimisation et la simulation. / The thesis focuses on the study of real road transportation and distribution pro-blems. The question concerns in particular the optimization of two different vehicle routing problems arising in the distribution of petroleum products and the transfer of containers. The first problem, modelled as an application of the multi-compartment vehicle routing problem with time windows (MCVRPTW), is solved by using a tabu search method. The same method is then applied to two other variants. One introduces additional constraints related to loading operations for petroleum products on the compartments, while the other one includes the ad-justment concept in quantities applied for. Moreover, in the context of an energy transition, we addressed the container transfer problem using a fleet of electric trucks in the industrial port zone of Le Havre. The optimization involves two levels : the strategic level for dimensioning electrical infrastructures and the operational level for constructing the vehicle routes. Only the strategic level is tackled with a research project thanks to a coupling of optimization and simulation.

Cette thèse porte sur la résolution de problèmes de transport qui intègrent des contraintes temporelles considérant les fenêtres de temps, la synchronisation des visites et l’équilibrage des services. Ces problèmes trouvent plusieurs applications dans le monde réel.L’objectif de nos recherches est l’élaboration de nouvelles méthodes de résolution pour les problèmes considérés en examinant leur performance avec une étude comparative par rapport aux différentes approches de la littérature. Deux variantes sont traitées. Le premier cas étudie le Problème de Tournées de Véhicules avec Fenêtres de Temps (VRPTW). Nous proposons de nouveaux prétraitements et bornes inférieures pour déterminer le nombre de véhicules nécessaires en s’inspirant de travaux menés en ordonnancement (raisonnement énergétique) et d’autres problèmes combinatoires comme la clique maximum et les problèmes de bin-packing. Nous présentons également un algorithme d’optimisation par essaim particulaire qui traite de la minimisation du nombre de véhicules puis de celle du temps de trajet total. Le deuxième cas étudie le Problème de Tournées de Véhicules avec des Fenêtres de Temps et des Visites Synchronisées (VRPTWSyn). Nous proposons plusieurs méthodes basées sur des approches heuristiques et des formulations linéaires avec l’incorporation d’inégalités valides pour tenir compte de la contrainte de synchronisation. / This dissertation focuses on vehicle routing problems, one of the major academic problems in logistics. We address NP-Hard problems that model some realworld situations particularly those with different temporal constraints including time windows, visit synchronization and service balance.The aim of this research is to develop new algorithms for the considered problems,investigate their performance and compare them with the literature approaches.Two cases are carried out. The first case studies the Vehicle Routing Problem with Time Windows (VRPTW). We propose new lower bound methods for the number of vehicles. Then we present a Particle Swarm Optimization algorithm dealing with the Solomon objective. The second case studies the VehicleRouting Problem with Time Windows and Synchronized Visits (VRPTWsyn).Both exact methods and heuristics are proposed and compared to the literature approaches.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第18621号 / 情博第545号 / 新制||情||96(附属図書館) / 31521 / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 永持 仁, 教授 太田 快人, 教授 髙橋 豊 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Submitted by Aelson Maciera (aelsoncm@terra.com.br) on 2017-05-22T20:04:01Z No. of bitstreams: 1 TeseALS.pdf: 2588373 bytes, checksum: 85ce391accc868c711a33c83006ee738 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-05-31T13:43:27Z (GMT) No. of bitstreams: 1 TeseALS.pdf: 2588373 bytes, checksum: 85ce391accc868c711a33c83006ee738 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-05-31T13:43:34Z (GMT) No. of bitstreams: 1 TeseALS.pdf: 2588373 bytes, checksum: 85ce391accc868c711a33c83006ee738 (MD5) / Made available in DSpace on 2017-05-31T13:52:08Z (GMT). No. of bitstreams: 1 TeseALS.pdf: 2588373 bytes, checksum: 85ce391accc868c711a33c83006ee738 (MD5) Previous issue date: 2017-03-07 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Vehicle routing problems occur in many practical situations where the distribution of goods and / or services to different demand points is necessary. In this context, this research aims to study a ship routing and scheduling problem that arises at the collection and delivery operations of different types of crude oil from offshore platforms to coastal terminals. In the paradigm adopted for the representation of the problem, the transportation is largely the result of the need to maintain inventories at each supply point (platforms) between minimum and maximum levels, considering production rates on these operating points and the demand attendance of each product in the coastal terminals. The routing and scheduling of the fleet aims to achieve minimum variable cost solutions, and considers various operational constraints, such as the maximum cargo volume transported on each ship, the ships mooring in the operational points ports, the simultaneous unloading of the ships in terminals with more than one berth, among many others. In this research, Inventory Constrained Routing Problem (ICRP) models in the maritime context have been modified and extended for appropriately representating and solving real problems based on data collected in a case study performed on a Brazilian oil company, involving relatively short distances and time horizons. Small sized instances are solved by a mathematical programming software. Given the difficulties of solving larger examples, this study proposes a multistart heuristic method that includes a metaheuristic GRASP and improvement procedures, and also a rolling horizon heuristic. Both methods provide feasible good quality solutions in reasonable computing times. In order to improve the quality of the solutions found by these constructive methods, it is also discussed a procedure that combines the mathematical programming software and local search heuristic methods (matheuristic). The results show the potential of the proposed models and solution methods to tackle the problem and produce competitive solutions. / Problemas de roteirização de veículos ocorrem em diversas situações práticas onde se faz necessária a distribuição de bens e/ou serviços a pontos dispersos de demanda. Nesse contexto, a presente pesquisa visa o estudo de um problema de roteirização e programação de navios presente em operações de coleta e entrega de diferentes tipos de óleo cru de diversas plataformas offshore para vários terminais costeiros. No paradigma adotado para representação do problema, o transporte dos produtos é em grande parte o resultado da necessidade de manutenção dos estoques em cada ponto de suprimento (plataformas) entre níveis mínimos e máximos, considerando-se as taxas de produção nesses pontos operacionais, assim como o atendimento da demanda de cada produto nos terminais costeiros para abastecer as refinarias. A roteirização e programação da frota visa a obtenção de soluções de mínimo custo variável e considera várias restrições operacionais, tais como o volume máximo de carga transportada em cada navio, a viabilidade de atracação de navios em portos dos pontos operacionais, os descarregamentos simultâneos de navios em terminais com mais de um berço, dentre várias outras. Nesse sentido, modelos de otimização da literatura de roteirização veículos com restrições de estoque (Inventory Constrained Routing Problem – ICRP) no contexto marítimo foram modificados e estendidos para representação do problema e resolução de exemplares de uma situação real, definidos a partir de dados coletados em um estudo de caso realizado em uma empresa petrolífera nacional, envolvendo distâncias relativamente curtas e com horizontes de planejamento de curto prazo (poucas semanas). Exemplares de pequeno porte são resolvidos por meio da utilização de um software de programação matemática. Dada a dificuldade de resolução dos exemplos de maior porte, é proposto um método heurístico de múltiplos reinícios composto por uma metaheurística GRASP e procedimentos de melhoria, além de uma heurística de horizonte rolante, que proporcionaram a obtenção de soluções factíveis de boa qualidade em tempos computacionais aceitáveis. Com intuito de melhorar a qualidade das soluções encontradas pelos métodos construtivos, é também discutido um procedimento que combina o software de programação matemática e métodos heurísticos com busca local (mateheurística). Os resultados mostram o potencial dos modelos e métodos de solução aqui desenvolvidos e propostos para abordar o problema e produzir soluções competitivas em relação às soluções da empresa.

The consumer market of today is characterized by emphasis on superior customer satisfaction and personalization of services. This entails higher customer expectations on organizations, which also includes the workforce scheduling processes in which the consumers expect more decision-power to dictate what they want, when and where they want services to be delivered. For organizations that deliver on-site services, the routing aspect becomes an important part of the scheduling process. Literature on Workforce Scheduling and Routing Problems (WSRP) seldom relate to characteristics of the more dynamic consumer market. As the markets and consumer needs become more flexible, the relevance for research concerning these characteristics increases. This study addresses this by reviewing current literature and present common solution methodologies applied to WSRP, as well as the effects of the online scheduling characteristics. With this as a foundation, a discussion is provided of how WSRP and online scheduling can be combined in order to improve resource utilization and minimize travel time for an on-site service provider. The overall aim of the study is to investigate how an online WSRP with exact time windows can be formulated and solved. The result is a four-stage hybrid method including linear integer programming and constructive heuristics with the objective to minimize travel time, idle time, and the makespan in the schedules. A case study has been conducted on an on-site service provider, and by applying the proposed hybrid methodology on the case company’s scheduling process, results have been obtained that demonstrates improvements of travel time and resource utilization. The study also demonstrate that the appliance of flexible travel times and product dependent service times have positive impact on the quality of the generated schedules. A key insight is that organizations working with exact time windows have to be aware of the trade-off between customer preferences and operational efficiency in day-to-day operations. Thus, organizations have to decide what holds most importance to the organization’s long-term success.

The thesis deals with application of models of routing problems on a real problem, beer distribution in Jesenicko region provided by Viden plus, a.s. The goal of the thesis is to optimize daily distributional routes for two vehicles with different capacities. Total distance has to be minimized respecting time and capacity limits. In case the optimal solution is not found, sub-optimal solution will be accepted. Solutions are calculated with use of the optimization software LINGO and some heuristic methods. Models of travelling salesman problem and vehicle routing problem are used to find the solutions. Results are compared to the current state of distributional routes in conclusion of the thesis.