Structure Optimization of Mixed-Speed Train Traffic for Cyclic Timetable: Model and Algorithm Development

Trains can be optimally spread over the period of the cyclic timetable. By integrating sequencing issue with headway time together, this paper studies the structure optimization of mixed-speed train traffic for a cyclic timetable. Firstly, by taking it as a job-shop problem with sequence-dependent setup times on one machine, in the type of infinite capacity resource with headway (ICR + H), the problem is transformed to alternative graph (AG) and then recast to the mixed-speed train traffic planning (MSTTP) model. For the multiobjective in MSTTP, three indicators are optimized, i.e., heterogeneity, cycle time, and buffer time, which correspond to diversity of train service toward passenger, capacity consumption of rail network, and stability of train operation, respectively. Secondly, the random-key genetic algorithm (RKGA) is proposed to tackle the sequence and headway simultaneously. Finally, RKGA is coded with visual studio C# and the proposed method is validated with a case study. The rail system considered is a line section encompassing a territory of 180 km with 15 mixed-speed trains in each cycle of the timetable. Results indicate the comprehensively balanced train plan for all stakeholders from random variations of train sequence and headway time. Both the quantitative proportion of heterogeneity/homogeneity (e.g., 2.5) about the optimized distribution of the mixed train traffic and the link between train headway time and the sequence for each traffic scenario are found. All the findings can be used to arrange the mixed-speed train traffic more scientifically.

Regular graph-based free route flight planning approach

Purpose The purpose of this study is to provide an alternative graph-based airspace model for more effective free-route flight planning. Design/methodology/approach Based on graph theory and available data sets describing airspace, as well as weather phenomena, a new FRA model is proposed. The model is applied for near to optimal flight route finding. The software tool developed during the study and complexity analysis proved the applicability and timed effectivity of the flight planning approach. Findings The sparse bidirectional graph with edges connecting only (geographically) closest neighbours can naturally model local airspace and weather phenomena. It can be naturally applied to effective near to optimal flight route planning. Research limitations/implications Practical results were acquired for one country airspace model. Practical implications More efficient and applicable flight planning methodology was introduced. Social implications Aircraft following the new routes will fly shorter trajectories, which positively influence on the natural environment, flight time and fuel consumption. Originality/value The airspace model proposed is based on standard mathematical backgrounds. However, it includes the original airspace and weather mapping idea, as well as it enables to shorten flight planning computations.

Time-Dependent Alternative Route Planning: Theory and Practice

We consider the problem of computing a set of meaningful alternative origin-to-destination routes, in real-world road network instances whose arcs are accompanied by travel-time functions rather than fixed costs. In this time-dependent alternative route scenario, we present a novel query algorithm, called Time-Dependent Alternative Graph (TDAG), that exploits the outcome of a time-consuming preprocessing phase to create a manageable amount of travel-time metadata, in order to provide answers for arbitrary alternative-routes queries, in only a few milliseconds for continental-size instances. The resulting set of alternative routes is aggregated in the form of a time-dependent alternative graph, which is characterized by the minimum route overlap, small stretch factor, small size, and low complexity. To our knowledge, this is the first work that deals with the time-dependent setting in the framework of alternative routes. The preprocessed metadata prescribe the minimum travel-time informations between a small set of “landmark” nodes and all other nodes in the graph. The TDAG query algorithm carries out the work in two distinct phases: initially, a collection phase constructs candidate alternative routes; consequently, a pruning phase cautiously discards uninteresting or low-quality routes from the candidate set. Our experimental evaluation on real-world, time-dependent road networks demonstrates that TDAG performed much better (by one or two orders of magnitude) than the existing baseline approaches.

A freight train dispatching approach for handling perturbations: a real case for the longest heavy-haul railway in China

Purpose This paper aims to reschedule the freight train timetable in case of disturbance to restore the train services as soon as possible. Design/methodology/approach Hence, an integer linear programming model for the real-time freight heavy-haul railway traffic management is developed in case of large primary delays caused by the delayed cargos loading. The proposed model based on the alternative graph at the microscopic level depicts the freight train movements in detail. Multiple dispatching measures such as re-timing and re-ordering are taken into account. Moreover, two objective functions, namely, the total final delays and the consecutive delays, are minimized in the freight trains dispatching problem. Findings Finally, a real-world computational experiment based on the Haolebaoji-Ji’an freight heavy-haul railway is implemented. The results of all disrupted cases are obtained within 10 s. The results give insight into that the consecutive delays are more than the total final delays when the same disrupted situation and the consecutive or total final delays increase as the primary delays increase. Originality/value An integer linear programming model based on the alternative graph for the real-time freight heavy-haul railway traffic management is developed in case of large primary delays caused by the delayed cargos loading. The method can be developed as the computer-aided tool for freight train dispatchers.

Graph-Based Image Matching for Indoor Localization

Graphs are a very useful framework for representing information. In general, these data structures are used in different application domains where data of interest are described in terms of local and spatial relations. In this context, the aim is to propose an alternative graph-based image representation. An image is encoded by a Region Adjacency Graph (RAG), based on Multicolored Neighborhood (MCN) clustering. This representation is integrated into a Content-Based Image Retrieval (CBIR) system, designed for the vision-based positioning task. The image matching phase, in the CBIR system, is managed with an approach of attributed graph matching, named the extended-VF algorithm. Evaluated in a context of indoor localization, the proposed system reports remarkable performance.

USEFULNESS OF DIRECTED ACYCLIC SUBWORD GRAPHS IN PROBLEMS RELATED TO STANDARD STURMIAN WORDS

The class of finite Sturmian words consists of words having particularly simple compressed representation, which is a generalization of the Fibonacci recurrence for Fibonacci words. The subword graphs of these words (especially their compacted versions) have a very special regular structure. In this paper we investigate this structure in more detail than in previous papers and show how several syntactical properties of Sturmian words follow from their graph properties. Consequently simple alternative graph-based proofs of several known facts are presented. The very special structure of subword graphs leads also to special easy algorithms computing some parameters of Sturmian words: the number of subwords, the critical factorization point, lexicographically maximal suffixes, occurrences of subwords of a fixed length, and right special factors. These algorithms work in linear time with respect to n, the size of the compressed representation of the standard word, though the words themselves can be of exponential size with respect to n. Some of the computed parameters can be also of exponential size, however we provide their linear size compressed representations. We introduce also a new concept related to standard words: Ostrowski automata.

Understanding Conic Sections Using Alternate Graph Paper

A description of two alternative coordinate systems and their use in graphing conic sections. This alternative graph paper helps students explore the idea of eccentricity using the definitions of the conic sections. Includes multiple examples of the uses of these alternative graphing sections, along with focus - directrix definitions of conic sections to be used with the new coordinate systems.