Large-scale mixed integer optimization approaches for scheduling airline operations under irregularity

Perhaps no single industry has benefited more from advancements in computation, analytics, and optimization than the airline industry. Operations Research (OR) is now ubiquitous in the way airlines develop their schedules, price their itineraries, manage their fleet, route their aircraft, and schedule their crew. These problems, among others, are well-known to industry practitioners and academics alike and arise within the context of the planning environment which takes place well in advance of the date of departure. One salient feature of the planning environment is that decisions are made in a frictionless environment that do not consider perturbations to an existing schedule. Airline operations are rife with disruptions caused by factors such as convective weather, aircraft failure, air traffic control restrictions, network effects, among other irregularities. Substantially less work in the OR community has been examined within the context of the real-time operational environment. While problems in the planning and operational environments are similar from a mathematical perspective, the complexity of the operational environment is exacerbated by two factors. First, decisions need to be made in as close to real-time as possible. Unlike the planning phase, decision-makers do not have hours of time to return a decision. Secondly, there are a host of operational considerations in which complex rules mandated by regulatory agencies like the Federal Administration Association (FAA), airline requirements, or union rules. Such restrictions often make finding even a feasible set of re-scheduling decisions an arduous task, let alone the global optimum. The goals and objectives of this thesis are found in Chapter 1. Chapter 2 provides an overview airline operations and the current practices of disruption management employed at most airlines. Both the causes and the costs associated with irregular operations are surveyed. The role of airline Operations Control Center (OCC) is discussed in which serves as the real-time decision making environment that is important to understand for the body of this work. Chapter 3 introduces an optimization-based approach to solve the Airline Integrated Recovery (AIR) problem that simultaneously solves re-scheduling decisions for the operating schedule, aircraft routings, crew assignments, and passenger itineraries. The methodology is validated by using real-world industrial data from a U.S. hub-and-spoke regional carrier and we show how the incumbent approach can dominate the incumbent sequential approach in way that is amenable to the operational constraints imposed by a decision-making environment. Computational effort is central to the efficacy of any algorithm present in a real-time decision making environment such as an OCC. The latter two chapters illustrate various methods that are shown to expedite more traditional large-scale optimization methods that are applicable a wide family of optimization problems, including the AIR problem. Chapter 4 shows how delayed constraint generation and column generation may be used simultaneously through use of alternate polyhedra that verify whether or not a given cut that has been generated from a subset of variables remains globally valid. While Benders' decomposition is a well-known algorithm to solve problems exhibiting a block structure, one possible drawback is slow convergence. Expediting Benders' decomposition has been explored in the literature through model reformulation, improving bounds, and cut selection strategies, but little has been studied how to strengthen a standard cut. Chapter 5 examines four methods for the convergence may be accelerated through an affine transformation into the interior of the feasible set, generating a split cut induced by a standard Benders' inequality, sequential lifting, and superadditive lifting over a relaxation of a multi-row system. It is shown that the first two methods yield the most promising results within the context of an AIR model.PhDCommittee Co-Chair: Clarke, John-Paul; Committee Co-Chair: Johnson, Ellis; Committee Member: Ahmed, Shabbir; Committee Member: Clarke, Michael; Committee Member: Nemhauser, Georg

Three Puzzles on Mathematics, Computation, and Games

In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear programming. The second puzzle is about errors made when votes are counted during elections. The third puzzle is: are quantum computers possible?Comment: ICM 2018 plenary lecture, Rio de Janeiro, 36 pages, 7 Figure

Neuere Entwicklungen der deklarativen KI-Programmierung : proceedings

The field of declarative AI programming is briefly characterized. Its recent developments in Germany are reflected by a workshop as part of the scientific congress KI-93 at the Berlin Humboldt University. Three tutorials introduce to the state of the art in deductive databases, the programming language Gödel, and the evolution of knowledge bases. Eleven contributed papers treat knowledge revision/program transformation, types, constraints, and type-constraint combinations

Interactive Theorem Proving with Indexed Formulas

Since more than two decades research in interactive theorem proving (ITP) has attracted growing interest. The primary application domains for ITPs range from hard- and software verification tools to mathematical tutor systems. To support communication with the user in an adequate way these systems depend on calculi that allow for the construction of human understandable and readable proofs. However, most calculi that are used in current ITPs fall still short of supporting the user in an optimal way. The reason is that they enforce the user to construct proofs at a level that is far more detailed than the one that can be found in human constructed proofs. Autexier [Aut03] has recently proposed a new theorem proving framework that allows to model different logics and calculi in an uniform way. In CORE, a proof-state is always represented as a single formula that can be manipulated by the application of replacement rules that are generated from the logical context of the subformula under transformation. This approach also facilitates proof construction at the assertion level which is considered as more closely matching the level at which humans construct proofs (see for instance [Hua94]). Together with COREs window inference technique this makes CORE a potentially well suited basis for interactive theorem proving. This thesis tries to excerpt COREs potential for interactive theorem proving by mapping important concepts of the established proof system ΩMEGA to CORE. A task structure is developed to present the context of a subformula in an intuitive way to the user and to assist him in structuring proofs. The development of a method interpreter makes it possible to specify abstract inference steps declaratively and to encode proof strategies for the use in CORE. The adaptation of ΩMEGAS agent-based suggestion mechanism ΩANTS to CORE helps the user with the identification of applicable methods and replacement rules.Interaktives Theorembeweisen hat in den letzten zwei Jahrzehnten zunehmend an Bedeutung gewonnen. Die Anwendungsbereiche von Systemen mit denen sich Beweise interaktiv führen lassen reichen von der Hard- und Software Verifikation bis zu mathematischen Tutor-Systemen. Die genannten Anwendungsgebiete machen es erforderlich das der Anwender bei der Beweisführung adequat untersützt wird. Um eine entsprechende Kommunikation mit dem Benutzer zu ermöglichen verwenden interaktive Beweissysteme Kalküle, in denen Beweise in einer für den Benutzer nachvollziehbaren Art und Weise, geführt werden können. Trotzdem kann man noch nicht davon sprechen, dass interaktive Beweiser den Benutzer optimal unterstützen. Der Hauptrgund hierfür ist, dass die eingesetzten Kalküle automatisch dazu führen, dass Beweise auf einer viel detailliertern Ebene geführt werden müssen, als man typischerweise in einem mathematischen Beweis finden würde. Autexier [Aut03]hat kürzlich eine neue logische Umgebung für die Beweissuche entwickelt, welche es ermöglicht verschiedene Logiken und Kalküle einheitlich zu modellieren. In CORE ist ein Beweiszustand immer als eine einzige Formel repräsentiert, welche durch das Anwenden von Ersetzungsregeln, die aus dem Kontext einer Teilformel abgeleitet werden, transformiert werden kann. Diese Herangehensweise erleichtert es auch, Beweise auf der sogenannten Assertion-Ebene (vgl. [Hua94]) zu führen, welche allgemein als eine natürlichere Ebene für die Beweisführung angesehen wird. Zusammen mit der Window-Inferenz Technik, die von CORE unterstützt, wird stellt CORE ein System dar das potentiell als eine verbesserte Grundlage für die interaktive Beweissuche angesehen werden kann. In dieser Arbeit geht es darum, das Potential von CORE im Hinblick auf die interaktive Beweiskonstruktion auszunutzen. Dieses geschieht zum einen dadurch, dass etablierte Konzepte im Bereich des interaktiven Beweisens, wie sie auch im Beweis-System ΩMEGA verwendet werden, auf das CORE-System abgebildet werden. Desweiteren wird eine Task-Srukture entwickelt, die es zum einen ermöglicht, den logischen Kontext einer Teilformel für den Benutzer verständlich aufzubereiten und darzustellen; zum anderen untersützt sie den Anwender auch darin, Beweise strukturiert zu führen. Der Entwurf eines Methoden-Interpreters ermöglicht es, abstrakte Beweisschritte zu kodieren und im System anzuwenden. Die Anpassung des Vorschlags-Mechanismus ΩANTS an CORE stellt eine weitere Unterstützung für den Benutzer bereit, indem sie automatisch Vorschläge über mögliche Fortsetzungen eines Beweises generiert

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th

Computer Science & Technology Series : XXI Argentine Congress of Computer Science. Selected papers

CACIC’15 was the 21thCongress in the CACIC series. It was organized by the School of Technology at the UNNOBA (North-West of Buenos Aires National University) in Junín, Buenos Aires. The Congress included 13 Workshops with 131 accepted papers, 4 Conferences, 2 invited tutorials, different meetings related with Computer Science Education (Professors, PhD students, Curricula) and an International School with 6 courses. CACIC 2015 was organized following the traditional Congress format, with 13 Workshops covering a diversity of dimensions of Computer Science Research. Each topic was supervised by a committee of 3-5 chairs of different Universities. The call for papers attracted a total of 202 submissions. An average of 2.5 review reports werecollected for each paper, for a grand total of 495 review reports that involved about 191 different reviewers. A total of 131 full papers, involving 404 authors and 75 Universities, were accepted and 24 of them were selected for this book.Red de Universidades con Carreras en Informática (RedUNCI

Computer Science & Technology Series : XXI Argentine Congress of Computer Science. Selected papers

CACIC’15 was the 21thCongress in the CACIC series. It was organized by the School of Technology at the UNNOBA (North-West of Buenos Aires National University) in Junín, Buenos Aires. The Congress included 13 Workshops with 131 accepted papers, 4 Conferences, 2 invited tutorials, different meetings related with Computer Science Education (Professors, PhD students, Curricula) and an International School with 6 courses. CACIC 2015 was organized following the traditional Congress format, with 13 Workshops covering a diversity of dimensions of Computer Science Research. Each topic was supervised by a committee of 3-5 chairs of different Universities. The call for papers attracted a total of 202 submissions. An average of 2.5 review reports werecollected for each paper, for a grand total of 495 review reports that involved about 191 different reviewers. A total of 131 full papers, involving 404 authors and 75 Universities, were accepted and 24 of them were selected for this book.Red de Universidades con Carreras en Informática (RedUNCI