The vehicle scheduling problem, arising in public transport bus companies, addresses the task of assigning buses to cover a given set of timetabled trips with consideration of practical requirements such as multiple depots and vehicle types as well as further extensions. An optimal schedule is characterized by minimal fleet size and/or minimal operational costs. Various publications were released as a result of extensive research in the last decades on this topic. Several modeling approaches as well as specialized solution strategies were presented for the problem and its extensions. This paper discusses the modeling approaches for different kinds of vehicle scheduling problems and gives an up-to-date and comprehensive overview on the basis of a general problem definition. Although we concentrate on the presentation of modeling approaches, also the basic ideas of solution approaches are given.
This paper discusses the integrated vehicle- and crew-scheduling problem in public transit with multiple depots. It is well known that the integration of both planning steps discloses additional flexibility that can lead to gains in efficiency, compared to sequential planning. We present a new modeling approach that is based on a time-space network representation of the underlying vehicle-scheduling problem. The integrated problem is solved with column generation in combination with Lagrangian relaxation. The column generation subproblem is modeled as a resource-constrained shortest-path problem based on a novel time-space network formulation. Feasible solutions are generated by a heuristic branch-and-price method that involves fixing service trips to depots. Numerical results show that our approach outperforms other methods from the literature for well-known test problems.
Diagnosing autism spectrum disorders (ASD) is a complicated, time-consuming process which is particularly challenging in older individuals. one of the most widely used behavioral diagnostic tools is the Autism Diagnostic observation Schedule (ADoS). previous work using machine learning techniques suggested that ASD detection in children can be achieved with substantially fewer items than the original ADOS. Here, we expand on this work with a specific focus on adolescents and adults as assessed with the ADOS Module 4. We used a machine learning algorithm (support vector machine) to examine whether ASD detection can be improved by identifying a subset of behavioral features from the ADOS Module 4 in a routine clinical sample of N = 673 high-functioning adolescents and adults with ASD (n = 385) and individuals with suspected ASD but other best-estimate or no psychiatric diagnoses (n = 288). We identified reduced subsets of 5 behavioral features for the whole sample as well as age subgroups (adolescents vs. adults) that showed good specificity and sensitivity and reached performance close to that of the existing ADOS algorithm and the full ADOS, with no significant differences in overall performance. These results may help to improve the complicated diagnostic process of ASD by encouraging future efforts to develop novel diagnostic instruments for ASD detection based on the identified constructs as well as aiding clinicians in the difficult question of differential diagnosis. Autism Spectrum Disorders (ASD) comprise a range of pervasive neurodevelopmental disorders with a population prevalence of approximately 1% 1. They are characterized by early-onset persistent impairments in social communication and interaction as well as the presence of restricted, repetitive behaviors or interests 2,3. Diagnosing ASD is a complicated, lengthy and time-consuming process, which requires outstanding and specific clinical expertise 4,5. Although research makes constant progress in understanding the underlying genetic and neurobiological factors associated with ASD, there are currently no reliable biological markers for ASD and the diagnosis remains based on behavioral symptoms 1,6,7. The current so-called "gold standard" of ASD diagnosis comprises the use of various standardized diagnostic instruments that assist clinicians in reaching a best-estimate clinical diagnosis 7-9. Two of the most widely used diagnostic instruments are the Autism Diagnostic Observation Schedule (ADOS respectively ADOS-2 for the revised second edition) 10,11 and the Autism Diagnostic Interview
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