Наблюдатель изменений в лесах кратчайших путей на динамических графах транспортных сетей

The purpose of the work is the development of basic data structures, speed-efficient and memoryefficient algorithms for tracking changes in predefined decisions about sets of shortest paths on transport networks, notifications about which are received by autonomous coordinated transport agents with centralized or collective control. A characteristic feature of transport operations is the independence and asynchrony of the emergence of perturbations of optimal solutions, as well as the lack of global influence of individual perturbations on the set of all processes on the network. This clearly determines the feasibility of realizing the idea of reoptimizing existing solutions in real time as information is received about disturbances in the structure and parameters of the transport network, various restrictions on the use of existing shortest paths. In contrast to the classical problems of finding shortest paths on static or dynamic graphs, it is proposed to supplement the set of situations controlled by the observer by taking into account the associations of shortest path trees with agents that actually use such paths. This will improve the responsiveness of agent notification processes for timely switching to a new path. The space of search states is a dynamically generated bipartite sparse graph of the transport network, represented by a list of arcs. The basic algorithm for finding the shortest paths uses Dijkstra's scheme, but implements a bootstrapping method to generate the search result. The compactness of the representation of the observed forest of shortest paths is achieved by mapping individual trees of such a forest onto the projection of tree vertices in memory, where the position of each vertex corresponds to the distance from the tree root. The proposed version of the construction of the search procedure is based on the mechanisms existing in database management systems for creating different relational representations of the physical data model. This eliminates the need to solve technological problems of complexing heterogeneous models of dynamic transport networks, memory allocation. As a result, the specification of various rules for the logistics of transport operations is simplified, since such operations in terms of object-oriented models are easily determined by polymorphic classes of transitions between nodes of the transport network.Цель работы – разработка базовых структур данных и эффективных по быстродействию и памяти алгоритмов слежения за изменениями предопределенных решений о множествах кратчайших путей на транспортных сетях, уведомления о которых получают автономные координируемые транспортные агенты с централизованным или коллективным управлением. Характерная особенность транспортных операций – независимость и асинхронность появления возмущений оптимальных решений, а также отсутствие глобального влияния отдельных возмущений на множество всех процессов на сети. Тем самым, очевидно, определяется целесообразность реализации идеи реоптимизации существующих решений в реальном времени по мере поступления информации о возмущениях структуры и параметров транспортной сети, различных ограничений на использование существующих кратчайших путей. В отличие от классических задач поиска кратчайших путей на статических или динамических графах, набор контролируемых наблюдателем ситуаций предлагается дополнить учетом ассоциаций деревьев кратчайших путей с фактически использующими такие пути агентами. Это позволит улучшить реактивность процессов уведомления агентов для своевременного переключения на новый путь. Пространство состояний поиска – динамически формируемый двудольный разреженный граф транспортной сети, представленный списком дуг. Базовый алгоритм поиска кратчайших путей использует схему Дейкстры, но реализует для формирования результата поиска метод бутстрэппинга. Компактность представления наблюдаемого леса кратчайших путей достигается отображением отдельных деревьев такого леса на проекцию вершин дерева в памяти, где позиция каждой вершины соответствует расстоянию от корня дерева. Предложенная версия построения процедуры поиска опирается на существующие в системах управления базами данных механизмы создания разных реляционных представлений физической модели данных. Это избавляет от необходимости решения технологических задач комплексирования гетерогенных моделей динамических транспортных сетей, распределения памяти. В результате спецификация различных правил логистики транспортных операций упрощается, так как такие операции в терминах объектно-ориентированных моделей легко определяются полиморфными классами переходов между узлами транспортной сети

A New Algorithm for Reoptimizing Shortest Paths When the Arc Costs Change

We propose an algorithm which reoptimizes shortest paths in a very general situation, that is when any subset of arcs of the input graph is aected by a change of the arc costs, which can be either lower or higher than the old ones. This situation is more general than the ones addressed in the literature so far

New approaches for determining greenest paths and efficient vehicle routes on transportation networks

Road transportation has hazardous and threatening impacts on the environment. However, the traditional logistics models and approaches used in transportation planning have mainly focused on minimizing the internal costs and lack the environmental aspect. Therefore, new planning techniques and approaches are needed in road transport by explicitly accounting for these negative impacts. In this thesis, we address these issues by first concentrating on solution methods for the Greenest Path Problem (GPP) where fuel consumption and GHG emission objectives are incorporated to find the least GHG generating path, namely the greenest path, and propose a fast and effective heuristic. Taking the strong relation between the speed and the GHG emission into account, we also address the speed embedded minimum cost path problem in the most general case where the speed is also a decision variable as well as the departure time Within this context, we develop a new networkconsistent (which implies spatially and temporally consistent speeds) time-dependent speed and travel time layer generation scheme since real data is difficult to acquire. In the second part, we mainly focus on Vehicle Routing Problems (VRP). First, we propose an Ant Colony Optimization (ACO) approach for solving the Vehicle Routing Problem with Time Windows (VRPTW). Then, we adapt this method to solve the environment friendly VRP, namely the Green VRP, where the greenest paths between all customer pairs are used as input. Finally, we extend the ACO algorithm to a parallel matheuristic approach for solving a class of VRP variants

Improved methods for solving traffic flow problems in dynamic networks

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2002.Includes bibliographical references (p. 107-109).by Nathaniel J. Grier.S.M

Applications of mathematical network theory

This thesis is a collection of papers on a variety of optimization problems where network structure can be used to obtain efficient algorithms. The considered applications range from the optimization of radiation treatment plkans in cancer therapy to maintenance planning for maximizing the throughput in bulk good supply chains

Machine Learning Solutions for Transportation Networks

This thesis brings a collection of novel models and methods that result from a new look at practical problems in transportation through the prism of newly available sensor data. There are four main contributions: First, we design a generative probabilistic graphical model to describe multivariate continuous densities such as observed traffic patterns. The model implements a multivariate normal distribution with covariance constrained in a natural way, using a number of parameters that is only linear (as opposed to quadratic) in the dimensionality of the data. This means that learning these models requires less data. The primary use for such a model is to support inferences, for instance, of data missing due to sensor malfunctions. Second, we build a model of traffic flow inspired by macroscopic flow models. Unlike traditional such models, our model deals with uncertainty of measurement and unobservability of certain important quantities and incorporates on-the-fly observations more easily. Because the model does not admit efficient exact inference, we develop a particle filter. The model delivers better medium- and long- term predictions than general-purpose time series models. Moreover, having a predictive distribution of traffic state enables the application of powerful decision-making machinery to the traffic domain. Third, two new optimization algorithms for the common task of vehicle routing are designed, using the traffic flow model as their probabilistic underpinning. Their benefits include suitability to highly volatile environments and the fact that optimization criteria other than the classical minimal expected time are easily incorporated. Finally, we present a new method for detecting accidents and other adverse events. Data collected from highways enables us to bring supervised learning approaches to incident detection. We show that a support vector machine learner can outperform manually calibrated solutions. A major hurdle to performance of supervised learners is the quality of data which contains systematic biases varying from site to site. We build a dynamic Bayesian network framework that learns and rectifies these biases, leading to improved supervised detector performance with little need for manually tagged data. The realignment method applies generally to virtually all forms of labeled sequential data

The dynamic, resource-constrained shortest path problem on an acyclic graph with application in column generation and literature review on sequence-dependent scheduling

This dissertation discusses two independent topics: a resource-constrained shortest-path problem (RCSP) and a literature review on scheduling problems involving sequence-dependent setup (SDS) times (costs). RCSP is often used as a subproblem in column generation because it can be used to solve many practical problems. This dissertation studies RCSP with multiple resource constraints on an acyclic graph, because many applications involve this configuration, especially in column genetation formulations. In particular, this research focuses on a dynamic RCSP since, as a subproblem in column generation, objective function coefficients are updated using new values of dual variables at each iteration. This dissertation proposes a pseudo-polynomial solution method for solving the dynamic RCSP by exploiting the special structure of an acyclic graph with the goal of effectively reoptimizing RCSP in the context of column generation. This method uses a one-time âÂÂpreliminaryâ phase to transform RCSP into an unconstrained shortest path problem (SPP) and then solves the resulting SPP after new values of dual variables are used to update objective function coefficients (i.e., reduced costs) at each iteration. Network reduction techniques are considered to remove some nodes and/or arcs permanently in the preliminary phase. Specified techniques are explored to reoptimize when only several coefficients change and for dealing with forbidden and prescribed arcs in the context of a column generation/branch-and-bound approach. As a benchmark method, a label-setting algorithm is also proposed. Computational tests are designed to show the effectiveness of the proposed algorithms and procedures. This dissertation also gives a literature review related to the class of scheduling problems that involve SDS times (costs), an important consideration in many practical applications. It focuses on papers published within the last decade, addressing a variety of machine configurations - single machine, parallel machine, flow shop, and job shop - reviewing both optimizing and heuristic solution methods in each category. Since lot-sizing is so intimately related to scheduling, this dissertation reviews work that integrates these issues in relationship to each configuration. This dissertation provides a perspective of this line of research, gives conclusions, and discusses fertile research opportunities posed by this class of scheduling problems. since, as a subproblem in column generation, objective function coefficients are updated using new values of dual variables at each iteration. This dissertation proposes a pseudo-polynomial solution method for solving the dynamic RCSP by exploiting the special structure of an acyclic graph with the goal of effectively reoptimizing RCSP in the context of column generation. This method uses a one-tim

Approches générales de résolution pour les problèmes multi-attributs de tournées de véhicules et confection d'horaires

Thèse réalisée en cotutelle entre l'Université de Montréal et l'Université de Technologie de TroyesLe problème de tournées de véhicules (VRP) implique de planifier les itinéraires d'une flotte de véhicules afin de desservir un ensemble de clients à moindre coût. Ce problème d'optimisation combinatoire NP-difficile apparait dans de nombreux domaines d'application, notamment en logistique, télécommunications, robotique ou gestion de crise dans des contextes militaires et humanitaires. Ces applications amènent différents contraintes, objectifs et décisions supplémentaires ; des "attributs" qui viennent compléter les formulations classiques du problème. Les nombreux VRP Multi-Attributs (MAVRP) qui s'ensuivent sont le support d'une littérature considérable, mais qui manque de méthodes généralistes capables de traiter efficacement un éventail significatif de variantes. Par ailleurs, la résolution de problèmes "riches", combinant de nombreux attributs, pose d'importantes difficultés méthodologiques. Cette thèse contribue à relever ces défis par le biais d'analyses structurelles des problèmes, de développements de stratégies métaheuristiques, et de méthodes unifiées. Nous présentons tout d'abord une étude transversale des concepts à succès de 64 méta-heuristiques pour 15 MAVRP afin d'en cerner les "stratégies gagnantes". Puis, nous analysons les problèmes et algorithmes d'ajustement d'horaires en présence d'une séquence de tâches fixée, appelés problèmes de "timing". Ces méthodes, développées indépendamment dans différents domaines de recherche liés au transport, ordonnancement, allocation de ressource et même régression isotonique, sont unifiés dans une revue multidisciplinaire. Un algorithme génétique hybride efficace est ensuite proposé, combinant l'exploration large des méthodes évolutionnaires, les capacités d'amélioration agressive des métaheuristiques à voisinage, et une évaluation bi-critère des solutions considérant coût et contribution à la diversité de la population. Les meilleures solutions connues de la littérature sont retrouvées ou améliorées pour le VRP classique ainsi que des variantes avec multiples dépôts et périodes. La méthode est étendue aux VRP avec contraintes de fenêtres de temps, durée de route, et horaires de conducteurs. Ces applications mettent en jeu de nouvelles méthodes d'évaluation efficaces de contraintes temporelles relaxées, des phases de décomposition, et des recherches arborescentes pour l'insertion des pauses des conducteurs. Un algorithme de gestion implicite du placement des dépôts au cours de recherches locales, par programmation dynamique, est aussi proposé. Des études expérimentales approfondies démontrent la contribution notable des nouvelles stratégies au sein de plusieurs cadres méta-heuristiques. Afin de traiter la variété des attributs, un cadre de résolution heuristique modulaire est présenté ainsi qu'un algorithme génétique hybride unifié (UHGS). Les attributs sont gérés par des composants élémentaires adaptatifs. Des expérimentations sur 26 variantes du VRP et 39 groupes d'instances démontrent la performance remarquable de UHGS qui, avec une unique implémentation et paramétrage, égalise ou surpasse les nombreux algorithmes dédiés, issus de plus de 180 articles, révélant ainsi que la généralité ne s'obtient pas forcément aux dépends de l'efficacité pour cette classe de problèmes. Enfin, pour traiter les problèmes riches, UHGS est étendu au sein d'un cadre de résolution parallèle coopératif à base de décomposition, d'intégration de solutions partielles, et de recherche guidée. L'ensemble de ces travaux permet de jeter un nouveau regard sur les MAVRP et les problèmes de timing, leur résolution par des méthodes méta-heuristiques, ainsi que les méthodes généralistes pour l'optimisation combinatoire.The Vehicle Routing Problem (VRP) involves designing least cost delivery routes to service a geographically-dispersed set of customers while taking into account vehicle-capacity constraints. This NP-hard combinatorial optimization problem is linked with multiple applications in logistics, telecommunications, robotics, crisis management in military and humanitarian frameworks, among others. Practical routing applications are usually quite distinct from the academic cases, encompassing additional sets of specific constraints, objectives and decisions which breed further new problem variants. The resulting "Multi-Attribute" Vehicle Routing Problems (MAVRP) are the support of a vast literature which, however, lacks unified methods capable of addressing multiple MAVRP. In addition, some "rich" VRPs, i.e. those that involve several attributes, may be difficult to address because of the wide array of combined and possibly antagonistic decisions they require. This thesis contributes to address these challenges by means of problem structure analysis, new metaheuristics and unified method developments. The "winning strategies" of 64 state-of-the-art algorithms for 15 different MAVRP are scrutinized in a unifying review. Another analysis is targeted on "timing" problems and algorithms for adjusting the execution dates of a given sequence of tasks. Such methods, independently studied in different research domains related to routing, scheduling, resource allocation, and even isotonic regression are here surveyed in a multidisciplinary review. A Hybrid Genetic Search with Advanced Diversity Control (HGSADC) is then introduced, which combines the exploration breadth of population-based evolutionary search, the aggressive-improvement capabilities of neighborhood-based metaheuristics, and a bi-criteria evaluation of solutions based on cost and diversity measures. Results of remarkable quality are achieved on classic benchmark instances of the capacitated VRP, the multi-depot VRP, and the periodic VRP. Further extensions of the method to VRP variants with constraints on time windows, limited route duration, and truck drivers' statutory pauses are also proposed. New route and neighborhood evaluation procedures are introduced to manage penalized infeasible solutions w.r.t. to time-window and duration constraints. Tree-search procedures are used for drivers' rest scheduling, as well as advanced search limitation strategies, memories and decomposition phases. A dynamic programming-based neighborhood search is introduced to optimally select the depot, vehicle type, and first customer visited in the route during local searches. The notable contribution of these new methodological elements is assessed within two different metaheuristic frameworks. To further advance general-purpose MAVRP methods, we introduce a new component-based heuristic resolution framework and a Unified Hybrid Genetic Search (UHGS), which relies on modular self-adaptive components for addressing problem specifics. Computational experiments demonstrate the groundbreaking performance of UHGS. With a single implementation, unique parameter setting and termination criterion, this algorithm matches or outperforms all current problem-tailored methods from more than 180 articles, on 26 vehicle routing variants and 39 benchmark sets. To address rich problems, UHGS was included in a new parallel cooperative solution framework called "Integrative Cooperative Search (ICS)", based on problem decompositions, partial solutions integration, and global search guidance. This compendium of results provides a novel view on a wide range of MAVRP and timing problems, on efficient heuristic searches, and on general-purpose solution methods for combinatorial optimization problems