This project seeks to demonstrate routing optimization that would allow pedestrian and micromobility user groups to select and prioritize different route features according to their preferences. Through the creation of a routing demonstrator that considers both static and dynamic parameters in the form of pavement quality, elevation climb, travel time, and air quality, along with user-specified weights for their prioritization of each of these parameters, a number of routes were created and mapped to qualitatively compare against routes representing only a shortest path. / <p>Examensarbetet är utfört vid Institutionen för teknik och naturvetenskap (ITN) vid Tekniska fakulteten, Linköpings universitet</p>

A stochastic shortest path (SSP) problem is an undiscounted Markov decision process with an absorbing and zero-cost target state, where the objective is to reach the target state with minimum expected cost. This problem provides a foundation for algorithms for decision-theoretic planning and probabilistic model checking, among other applications. This thesis describes an implementation and evaluation of recently developed error bounds for SSP problems. The bounds can be used in a test for convergence of iterative dynamic programming algorithms for solving SSP problems, as well as in action elimination procedures that can accelerate convergence by excluding provably suboptimal actions that do not need to be re-evaluated each iteration. The techniques are shown to be effective for both decision-theoretic planning and probabilistic model checking.

A major factor that negatively impacts flight operations globally is adverse weather. To reduce the impact of adverse weather, avoidance procedures such as finding an alternative flight path can usually be carried out. However, such procedures usually introduce extra costs such as flight delay. Hence, there exists a need for alternative flight paths that efficiently avoid adverse weather regions while minimising costs. Existing weather avoidance methods used techniques, such as Dijkstra’s and artificial potential field algorithms that do not scale adequately and have poor real time performance. They do not adequately consider the impact of weather and its avoidance on passengers. The contributions of this work include a new development of an improved integrated model for weather avoidance, that addressed the impact of weather on passengers by defining a corresponding cost metric. The model simultaneously considered other costs such as flight delay and fuel burn costs. A genetic algorithm (GA)-based rerouting technique that generates optimised alternative flight paths was proposed. The technique used a modified mutation strategy to improve global search. A discrete firefly algorithm-based rerouting method was also developed to improve rerouting efficiency. A data framework and simulation platform that integrated aeronautical, weather and flight data into the avoidance process was developed. Results show that the developed algorithms and model produced flight paths that had lower total costs compared with existing techniques. The proposed algorithms had adequate rerouting performance in complex airspace scenarios. The developed system also adequately avoided the paths of multiple aircraft in the considered airspace.

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This thesis examines the existence of a dominant route between a hub pair and factors that influence bike share cyclists route choices. This research collects 132,396 hub to-hub global positioning system (GPS) trajectories over a 12-month period between April 1, 2015 and March 31, 2016 from 750 bicycles provided by a bike share program (BSP) called SoBi (Social Bicycles) Hamilton. Then, a GIS-based map-matching toolkit is used to convert GPS points to map-matched trips and generate a series of route attributes. In order to create choice sets, unique routes between the same hub pair are extracted from all corresponding repeated trips using a link signature tool. The results from t statistics and Path-size logit models indicate that bike share cyclists are willing to detour for some positive features, such as bicycle facilities and low traffic volumes, but they also try to avoid too circuitous routes, turns, and steep slopes over 4% though detouring may come with a slight increase in turns. This research not only helps us understand BSP cyclist route preferences but also presents a GIS-based approach to determine potential road segments for additional bike facilities on the basis of such preferences. / Thesis / Master of Science (MSc)

This dissertation contributes to the ongoing national project concerning the \emph{Next Generation Air Transportation System} (NextGen) that endeavors, in particular, to reshape the management of air traffic in the continental United States. Our work is part of this effort and mainly concerns modeling and algorithmic enhancements to the Airspace Planning and Collaborative Decision-Making Model (APCDM). First, we augment the APCDM to study an \emph{Airspace Flow Program} (AFP) in the context of weather-related disruptions. The proposed model selects among alternative flight plans for the affected flights while simultaneously (a) integrating slot-exchange mechanisms induced by multiple Ground Delay Programs (GDPs) to permit airlines to improve flight efficiencies through a mediated bartering of assigned slots, and (b) considering issues related to sector workloads, airspace conflicts, as well as overall equity concerns among the involved airlines in regard to accepted slot trades and flight plans. More specifically, the APCDM is enhanced to include the following: a. The revised model accommodates continuing flights, where some flight cannot depart until a prerequisite flight has arrived. Such a situation arises, for example, when the same aircraft will be used for the departing flight. b. We model a slot-exchange mechanism to accommodate flights being involved in multiple trade offers, and to permit slot trades at multiple GDP airports (whence the flight connection constraints become especially relevant). We also model flight cancelations whereby, if a flight assigned to a particular slot is canceled, the corresponding vacated slot would be made available for use in the slot-exchange process. c. Alternative equity concepts are presented, which more accurately reflect the measures used by the airlines. d. A reduced variant of the APCDM, referred to as \textbf{APCDM-Light}, is also developed. This model serves as a fast-running version of APCDM to be used for quick-turn analyses, where the level of modeling detail, as well as data requirements, are reduced to focus only on certain key elements of the problem. e. As an alternative for handling large-scale instances of APCDM more effectively, we present a \emph{sequential variable fixing heuristic} (SFH). The list of flights is first partitioned into suitable subsets. For the first subset, the corresponding decision variables are constrained to be binary-valued (which is the default for these decision variables), while the other variables are allowed to vary continuously between 0 and 1. If the resulting solution to this relaxed model is integral, the algorithm terminates. Otherwise, the binary variables are fixed to their currently prescribed values and another subset of variables is designated to be binary constrained. The process repeats until an integer solution is found or the heuristic encounters infeasibility. f. We experiment with using the APCDM model in a \emph{dynamic, rolling-horizon framework}, where we apply the model on some periodic basis (e.g., hourly), and where each sequential run of the model has certain flight plan selections that are fixed (such as flights that are already airborne), while we consider the selection among alternative flight plans for other imminent flights in a look-ahead horizon (e.g., two hours). These enhancements allow us to significantly expand the functionality of the original APCDM model. We test the revised model and its variants using realistic data derived from the \emph{Enhanced Traffic Management System} (ETMS) provided by the \emph{Federal Aviation Administration} (FAA). One of the new equity methods, which is based on average delay per passenger (or weighted average delay per flight), turns out to be a particularly robust way to model equity considerations in conjunction with sector workloads, conflict resolution, and slot-exchanges. With this equity method, we were able to solve large problem instances (1,000 flights) within 30 seconds on average using a 1\% optimality tolerance. The model also produced comparable solutions within about 20 seconds on average using the Sequential Fixing Heuristic (SFH). The actual solutions obtained for these largest problem instances were well within 1\% of the best known solution. Furthermore, our computations revealed that APCDM-Light can be readily optimized to a 0.01\% tolerance within about 5 seconds on average for the 1,000 flight problems. Thus, the augmented APCDM model offers a viable tool that can be used for tactical air traffic management purposes as an airspace flow program (particularly, APCDM-Light), as well as for strategic applications to study the impact of different types of trade restrictions, collaboration policies, equity concepts, and airspace sectorizations. The modeling of slot ownership in the APCDM motivates another problem: that of generating detoured flight plans that must arrive at a particular slot time under severe convective weather conditions. This leads to a particular class of network flow problems that seeks a shortest path, if it exists, between a source node and a destination node in a connected digraph $G(N,A)$, such that we arrive at the destination at a specified time while leaving the source no earlier than a lower bounding time, and where the availability of each network link is time-dependent in the sense that it can be traversed only during specified intervals of time. We refer to this problem as the \emph{reverse time-restricted shortest path problem} (RTSP). We show that RTSP is NP-hard in general and propose a dynamic programming algorithm for finding an optimal solution in pseudo-polynomial time. Moreover, under a special regularity condition, we prove that the problem is polynomially solvable with a complexity of order $O(|N / A|)$. Computational results using real flight generation test cases as well as random simulated problems are presented to demonstrate the efficiency of the proposed solution procedures. The current airspace configuration consists of sectors that have evolved over time based on historical traffic flow patterns. \citet{kopardekar_dyn_resect_2007} note that, given the current airspace configuration, some air traffic controller resources are likely under-utilized, and they also point out that the current configuration limits flexibility. Moreover, under the free-flight concept, which advocates a relaxation of waypoint traversals in favor of wind-optimized trajectories, the current airspace configuration will not likely be compatible with future air traffic flow patterns. Accordingly, one of the goals for the \emph{NextGen Air Transportation System} includes redesigning the airspace to increase its capacity and flexibility. With this motivation, we present several methods for defining sectors within the \emph{National Airspace System} (NAS) based on a measure of sector workload. Specifically, given a convex polygon in two-dimensions and a set of weighted grid points within the region encompassed by the polygon, we present several mixed-integer-programming-based algorithms to generate a plane (or line) bisecting the region such that the total weight distribution on either side of the plane is relatively balanced. This process generates two new polygons, which are in turn bisected until some target number of regions is reached. The motivation for these algorithms is to dynamically reconfigure airspace sectors to balance predicted air-traffic controller workload. We frame the problem in the context of airspace design, and then present and compare four algorithmic variants for solving these problems. We also discuss how to accommodate monitoring, conflict resolution, and inter-sector coordination workloads to appropriately define grid point weights and to conduct the partitioning process in this context. The proposed methodology is illustrated using a basic example to assess the overall effect of each algorithm and to provide insights into their relative computational efficiency and the quality of solutions produced. A particular competitive algorithmic variant is then used to configure a region of airspace over the U.S. using realistic flight data. The development of the APCDM is part of an ongoing \emph{NextGen} research project, which envisages the sequential use of a variety of models pertaining to three tiers. The \emph{Tier 1} models are conceived to be more strategic in scope and attempt to identify potential problematic areas, e.g., areas of congestion resulting from a severe convective weather system over a given time-frame, and provide aggregate measures of sector workloads and delays. The affected flow constrained areas (FCAs) highlighted by the results from these \emph{Tier 1} models would then be analyzed by more detailed \emph{Tier 2} models, such as APCDM, which consider more specific alternative flight plan trajectories through the different sectors along with related sector workload, aircraft conflict, and airline equity issues. Finally, \emph{Tier 3} models are being developed to dynamically examine smaller-scaled, localized fast-response readjustments in air traffic flows within the time-frame of about an hour prior to departure (e.g., to take advantage of a break in the convective weather system). The APCDM is flexible, and perhaps unique, in that it can be used effectively in all three tiers. Moreover, as a strategic tool, analysts could use the APCDM to evaluate the suitability of potential airspace sectorization strategies, for example, as well as identify potential capacity shortfalls under any given sector configuration. / Ph. D.

This thesis deals with shortest paths problem in graphs. Shortest paths problem is the basic issue of graph theory with many pracitcal applications. We can divide this problem into two following generalizations: single-source shortest path problem and all-pairs shortest paths problem. This text introduces principles and algorithms for generalizations. We describe both classical and new more efficient methods. It contains information about how some of these algorithms were implemented and offers an experimental comparison of these algorithms.

Cette thèse apporte plusieurs contributions dans le domaine des langages formels. Notre premier travail a été de montrer la pertinence des grammaires de graphes comme outil de démonstration de résultats fondamentaux sur les langages algébriques. Nous avons ainsi reformulé avec un point de vue géométrique les démonstrations du lemme des paires itérantes et du lemme de Parikh. Nous avons ensuite étendu aux graphes réguliers des algorithmes de base sur les graphes finis, notamment pour calculer des problèmes de plus court chemin. Ces extensions ont été faites par calcul de plus petits points fixes sur les grammaires de graphes. Enfin, nous avons caractérisé des familles générales de systèmes de récriture de mots dont la dérivation préserve la régularité ou l’algébricité. Ces familles ont été obtenues par décomposition de la dérivation en une substitution régulière suivie de la dérivation du système de Dyck / Pas de résumé en anglais