Local Search for the Resource Constrained Assignment Problem

The resource constrained assignment problem (RCAP) is to find a minimal cost cycle partition in a directed graph such that a resource constraint is fulfilled. The RCAP has its roots in an application that deals with the covering of a railway timetable by rolling stock vehicles. Here, the resource constraint corresponds to maintenance constraints for rail vehicles. Moreover, the RCAP generalizes several variants of vehicle routing problems. We contribute a local search algorithm for this problem that is derived from an exact algorithm which is similar to the Hungarian method for the standard assignment problem. Our algorithm can be summarized as a k-OPT heuristic, exchanging k arcs of an alternating cycle of the incumbent solution in each improvement step. The alternating cycles are found by dual arguments from linear programming. We present computational results for instances from our railway application at Deutsche Bahn Fernverkehr AG as well as for instances of the vehicle routing problem from the literature

Regional Search for the Resource Constrained Assignment Problem

The resource constrained assignment problem (RCAP) is to find a minimal cost partition of the nodes of a directed graph into cycles such that a resource constraint is fulfilled. The RCAP has its roots in rolling stock rotation optimization where a railway timetable has to be covered by rotations, i.e., cycles. In that context, the resource constraint corresponds to maintenance constraints for rail vehicles. Moreover, the RCAP generalizes variants of the vehicle routing problem (VRP). The paper contributes an exact branch and bound algorithm for the RCAP and, primarily, a straightforward algorithmic concept that we call regional search (RS). As a symbiosis of a local and a global search algorithm, the result of an RS is a local optimum for a combinatorial optimization problem. In addition, the local optimum must be globally optimal as well if an instance of a problem relaxation is computed. In order to present the idea for a standardized setup we introduce an RS for binary programs. But the proper contribution of the paper is an RS that turns the Hungarian method into a powerful heuristic for the resource constrained assignment problem by utilizing the exact branch and bound. We present computational results for RCAP instances from an industrial cooperation with Deutsche Bahn Fernverkehr AG as well as for VRP instances from the literature. The results show that our RS provides a solution quality of 1.4 % average gap w.r.t. the best known solutions of a large test set. In addition, our branch and bound algorithm can solve many RCAP instances to proven optimality, e.g., almost all asymmetric traveling salesman and capacitated vehicle routing problems that we consider

A Coarse-To-Fine Approach to the Railway Rolling Stock Rotation Problem

We propose a new coarse-to-fine approach to solve certain linear programs by column generation. The problems that we address contain layers corresponding to different levels of detail, i.e., coarse layers as well as fine layers. These layers are utilized to design efficient pricing rules. In a nutshell, the method shifts the pricing of a fine linear program to a coarse counterpart. In this way, major decisions are taken in the coarse layer, while minor details are tackled within the fine layer. We elucidate our methodology by an application to a complex railway rolling stock rotation problem. We provide comprehensive computational results that demonstrate the benefit of this new technique for the solution of large scale problems

A Hypergraph Model for Railway Vehicle Rotation Planning

We propose a model for the integrated optimization of vehicle rotations and vehicle compositions in long distance railway passenger transport. The main contribution of the paper is a hypergraph model that is able to handle the challenging technical requirements as well as very general stipulations with respect to the "regularity" of a schedule. The hypergraph model directly generalizes network flow models, replacing arcs with hyperarcs. Although NP-hard in general, the model is computationally well-behaved in practice. High quality solutions can be produced in reasonable time using high performance Integer Programming techniques, in particular, column generation and rapid branching. We show that, in this way, large-scale real world instances of our cooperation partner DB Fernverkehr can be solved

Ein Fallbeispiel aus der bayerischen Waldschadensforschung

Der Prozeß staatlicher Forschungförderung wird am Beispiel bayerischen Waldschadensforschung analysiert. Untersucht wird, welchen Einfluß die Forscher sowie die politischen Auftraggeber auf die Formulierung und Durchführung eines Forschungsprogrammes nehmen. Die Erkenntnisse über die Praxis der Forschungspolitik werden abschließend für Gestaltungsvorschläge zur Auftragsforschung genutzt. Theoretische Grundlage bietet die Politikfeld-Analyse, mit der ein Forschungsprogramm in die einzelnen Phasen des Policy-Zyklus zerlegt wird. Auf steuerungstheoretischer Grundlage können die Akteure aus Politik und Wissenschaft mit ihren jeweiligen Interessenlagen, Machtpotentialen und Handlungsstrategien beschrieben und ihre Handlungen erklärt werden. Ein zwischen 1984 und 1993 durchgeführtes, bayerisches Programm mit der Koordinierungsstelle "Projektgruppe Bayern zur Erforschung der Wirkung von Umweltschadstoffen" (PBWU) wird als Fallstudie gewählt. Mit Hilfe der teilnehmenden Beobachtung, D! okumenten- und Inhaltsanalyse kann der Förderprozeß erhoben werden. Als Ergebnis der empirischen Darstellung und politikwissenschaftlichen Analyse werden Faktoren aufgezeigt, welche die Entwicklung und Steuerung des Forschungsprojektes maßgeblich beeinflussen. Politischer Handlungsdruck stellt die treibende Kraft zur Durchsetzung des Forschungsprogramms dar und bestimmt Etablierung und Beendigung des Programms. Während der Programmdurchführung dominiert die Wissenschaft die Programmssteuerung. Zur Verbesserung anwendungsorientierter Forschungsförderung werden geeignete Forschungsstrukturen empfohlen und Strategievorschläge zur Beteiligung von Politik und Wissenschaft an Programmerstellung und Förderverfahren geliefert, um zu möglichst optimaler Programmplanung, -durchführung, -koordination und -evaluation zu gelangen

Does Laziness Pay Off? - A Lazy-Constraint Approach to Timetabling

Timetabling is a classical and complex task for public transport operators as well as for railway undertakings. The general question is: Which vehicle is taking which route through the transportation network in which order? In this paper, we consider the special setting to find optimal timetables for railway systems under a moving block regime. We directly set up on our work of [T. Schlechte et al., 2022], i.e., we consider the same model formulation and real-world instances of a moving block headway system. In this paper, we present a repair heuristic and a lazy-constraint approach utilizing the callback features of Gurobi, see [Gurobi Optimization, 2022]. We provide an experimental study of the different algorithmic approaches for a railway network with 100 and up to 300 train requests. The computational results show that the lazy-constraint approach together with the repair heuristic significantly improves our previous approaches

Disorder trapping by rapidly moving phase interface in an undercooled liquid

Non-equilibrium phenomena such as the disappearance of solute drag, the origin of solute trapping and evolution of disorder trapping occur during fast transformations with originating metastable phases [D.M. Herlach, P.K. Galenko, D. Holland-Moritz, Metastable solids from undrercooled melts (Elsevier, Amsterdam, 2007)]. In the present work, a theoretical investigation of disorder trapping by a rapidly moving phase interface is presented. Using a model of fast phase transformations, a system of governing equations for the diffusion of atoms, and the evolution of both long-range order parameter and phase field variable is formulated. First numerical solutions are carried out for a congruently melting binary alloy system

Parts of Me : Identity-Relevance Moderates Self-Prioritization

Recent research has revealed a pervasive bias for self-relevant information during decision-making, a phenomenon termed the self-prioritization effect. Focusing almost exclusively on between-target (e.g., self vs. friend) differences in task performance, however, this work has overlooked the influence stimulus factors potentially exert during decisional processing. Accordingly, based on pertinent socialpsychological theorizing (i.e., Identity-Based Motivation Theory), here we explored the possibility that self-prioritization is sensitive to the identity-based relevance of stimuli. The results of three experiments supported this hypothesis. In a perceptual-matching task, stimulus enhancement was greatest when geometric shapes were associated with identity-related information that was important (vs. unimportant) to participants. In addition, hierarchical drift-diffusion modeling revealed this effect was underpinned by differences in the efficiency of visual processing. Specifically, evidence was extracted more rapidly from stimuli paired with consequential compared to inconsequential identityrelated components. These findings demonstrate how identity-relevance moderates self-prioritization

Mathematische Optimierung von Eisenbahnumläufen

We show how to optimize rolling stock rotations that are required for the operation of a passenger timetable. The underlying mathematical ptimization problem is called rolling stock rotation problem (RSRP) and the leitmotiv of the thesis is RotOR, i.e., a highly integrated optimization algorithm for the RSRP. RotOR is used by DB Fernverkehr AG (DBF) in order to optimize intercity express (ICE) rotations for the European high-speed network. In this application, RSRPs have to be solved which (A) require many different aspects to be simultaneously considered, (B) are typically of large scale, and (C) include constraints that have a difficult combinatorial structure. This thesis suggests answers to these issues via the following concepts. (A) The main model, which RotOR uses, relies on a hypergraph. The hypergraph provides an easy way to model manifold industrial railway requirements in great detail. This includes well known vehicle composition requirements as well as relatively unexplored regularity stipulations. At the same time, the hypergraph directly leads to a mixed-integer programming (MIP) model for the RSRP. (B) The main algorithmic ingredient to solve industrial instances of the RSRP is a coarse-to-fine (C2F) column generation procedure. In this approach, the hypergraph is layered into coarse and fine layers that distinguish different levels of detail of the RSRP. The coarse layers are algorithmically utilized while pricing fine columns until proven optimality. Initially, the C2F approach is presented in terms of pure linear programming in order to provide an interface for other applications. (C) Rolling stock rotations have to comply to resource constraints in order to ensure, e.g., enough maintenance inspections along the rotations. These constraints are computationally hard, but are well known in the literature on the vehicle routing problem (VRP). We define an interface problem in order to bridge between the RSRP and the VRP and derive a straightforward algorithmic concept, namely regional search (RS), from their common features and, moreover, differences. Our RS algorithms show promising results for classical VRPs and RSRPs. In the first part of the thesis we present these concepts, which encompass its main mathematical contribution. The second part explains all modeling and solving components of RotOR that turn out to be essential in its industrial application. The thesis concludes with a solution to a complex re-optimization RSRP that RotOR has computed successfully for DBF. In this application all ICE vehicles of the ICE-W fleets of DBF had to be redirected past a construction site on a high-speed line in the heart of Germany.Wir zeigen wie man Eisenbahnumläufe optimiert. Diese sind unerlässlich für die Produktion eines Fahrplans für den Personenverkehr. Das zugrundeliegende mathematische Optimierungsproblem ist das Rolling Stock Rotation Problem (RSRP) und RotOR - ein stark integrierter Optmierungsalgorithmus für das RSRP - bildet den roten Faden der Arbeit. RotOR wird bei der DB Fernverkehr AG (DBF) eingesetzt um Intercity-Express (ICE) Umläufe für das europäische Hochgeschwindigkeitsnetz zu optimieren. Diese Anwendung erfordert das Lösen von Szenarien in denen (A) viele verschiedene Anforderungen simultan, (B) typischer Weise große RSRP Instanzen und (C) Bedingungen mit einer schwierigen kombinatorischen Struktur zu betrachten sind. In dieser Arbeit schlagen wir die folgenden Konzepte für diese Gegebenheiten vor: (A) Das Gesamtmodell von RotOR basiert auf einem Hypergraphen. Dieser Hypergraph ermöglicht einen einfachen aber dennoch sehr detailierten Umgang mit vielfältigen Anforderungen des Eisenbahnbetriebs. Derartige Anforderungen sind die Fahrzeugkomposition und die noch relativ unerforschte Gleichförmigkeit. Gleichzeitig führt der Hypergraph direkt zu einem gemischt-ganzzahligen Program für das RSRP. (B) Unser algorithmischer Hauptansatz ist ein Coarse-to-fine (C2F) Spaltengenerierungsverfahren. Dazu wird der Hypergraph in feine und gröbere Schichten, sogenannte Layer, unterteilt. Die Layer entsprechen verschiedenen Detailierungsgraden. Gröbere Layer werden algorithmisch ausgenutzt um Spalten für den feinsten Layer zu erzeugen bis ein Optimalitätsbeweis gefunden ist. Die C2F Methode wird zunächst autonom für lineare Programme erklärt um eine Schnittstelle für andere Probleme bereit zu stellen. (C) Eisenbahnumläufe müssen sogenannten Ressourcenbedingungen genügen, sodass z.B. ausreichend viele Wartungsmaßnahmen überdeckt sind. Derartige Bedingungen sind schwierig, allerdings vom Vehicle Routing Problem (VRP) in der Literatur bekannt. Wir definieren eine Schnittstelle zwischen RSRP und VRP und entwickeln aus deren Gemeinsamkeiten und vorallem Unterschieden ein geradliniges algorithmisches Konzept das wir Regionale Suche (RS) nennen. Unsere RS Algorithmen zeigen vielversprechende Ergebnisse für klassische VRP und RSRP Instanzen. Diese drei Konzepte bilden den mathematischen Hauptbeitrag und den ersten Teil der Arbeit. Der zweite Teil erklärt alle Modellierungs- und Lösungskomponenten welche für die Optimierung von ICE Umläufen bei der DBF notwendig sind. Die Arbeit schließt mit einem komplexen Anwendungsfall bei dem RotOR von der DBF benutzt wurde um ICE Umläufe für eine Sperrung der Hochgeschwindigkeitstrecke zwischen Frankfurt (Main) und Köln zu berechnen. Aufgrund dieser Baustelle mussten nahezu alle Fahrzeuge der Kategorie ICE-W umgeleitet werden

A Coarse-To-Fine Approach to the Railway Rolling Stock Rotation Problem *

Abstract We propose a new coarse-to-fine approach to solve certain linear programs by column generation. The problems that we address contain layers corresponding to different levels of detail, i.e., coarse layers as well as fine layers. These layers are utilized to design efficient pricing rules. In a nutshell, the method shifts the pricing of a fine linear program to a coarse counterpart. In this way, major decisions are taken in the coarse layer, while minor details are tackled within the fine layer. We elucidate our methodology by an application to a complex railway rolling stock rotation problem. We provide comprehensive computational results that demonstrate the benefit of this new technique for the solution of large scale problems. 1998 ACM Subject Classification G.1.6 Optimizatio