Karl Nachtigall

Solving periodic event scheduling problems with SAT

In this paper, periodic event scheduling problems (PESP) are encoded as satisfiability problems (SAT) and solved by a state-of-the-art SAT solver. Two encodings, based on direct and order encoded domains, are presented. An experimental evaluation suggests that the SAT-based approach using order encoding outperforms constraint-based PESP solvers, which until now were considered to be the best solvers for PESP. This opens the possibility to model significantly larger real-world problems.

Energy-Optimized Routing of Electric Vehicles in Urban Delivery Systems

Battery electric vehicles seem to offer great opportunities in context with ecological compatibility of urban transport systems. Along with the technical innovations appropriate operating models are required. In this contribution we propose an extension of the Vehicle Routing Problem, which adapts most of the needs for operating electric vehicles. This includes an objective function that considers energy consumption depending on driving resistances and loading weight, as well as additional restrictions to handle the maximum range depending on battery capacity and recharging options. To illustrate the problem a set of test instances is solved. For this purpose we present an adapted tabu search heuristics. The results are analyzed in respect of changes compared to distance-based optimization and the influence of battery capacity.

On the Modeling of Recharging Stops in Context of Vehicle Routing Problems

Caused by regulations regarding to climate protection, battery electric vehicles (BEVs) offer great opportunities in context of ecological compatibility of urban transport systems. Therefore, operating models in context of vehicle routing are required. Because of the BEVs more restrictive driving range in comparison to vehicles with an internal combustion engine (ICE) and due to the fact of a less-developed network of service stations, model formulations have to include the possibility of recharging at dedicated locations. So additional restrictions in formulations are needed to handle the maximum range depending on battery capacity. There were published only a small number of articles addressed to energy consumption, battery range and possible recharging stops in mixed-integer programming (MIP) formulations in the underlying practice relevant Vehicle Routing Problem with Time Windows (VRPTW) over the past few years. So we describe different MIP-formulations for an enhanced VRPTW, considering capacity restrictions concerning to cargo and energy, customer time windows and the capability of charging stops. Effects of these formulations are shown for small-sized problems, while a column generation approach is presented for more realistic problem instances.

Modelling and Solving a Train Path Assignment Model

We introduce a binary linear model for solving the train path assignment problem. For each train request a train path has to be constructed from a set of predefined path parts within a time-space network. For each possible path we use a binary decision variable to indicate, whether the path is used by the train request. Track and halting capacity constraints are taken into account. We discuss different objective functions, like maximizing revenue or maximizing total train path quality. The problem is solved by using column generation within a branch and price approach. This paper gives some modeling and implementation details and presents computational results from real world instances.

A Modulo Network Simplex Method for Solving Periodic Timetable Optimisation Problems

In the last 15 years periodic timetable problems had been found much interest in combinatorial optimization. The results presented in [5, 9, 2, 3, 6, 7, 1] are based on a periodic event scheduling model published by Serafini and Ukovich [10].

Applying Bidirectional Long Short-Term Memories (BLSTM) to Performance Data in Air Traffic Management for System Identification

The performance analysis of complex systems like Air Traffic Management (ATM) is a challenging task. To overcome statistical complexities through analyzing non-linear time series we approach the problem with machine learning methods. Therefore we understand ATM (and its identified system model) as a system of coupled and interdependent sub-systems working in time-continuous processes, measurable through time-discrete time series.

Modelling and Solving a Train Path Assignment Model with Traffic Day Restriction

The German Railway Company (DB Netz) schedules freight trains by connecting pre-constructed slots to a full train path. We consider this problem with special attention to traffic day restrictions and model it by a binary linear decision model. For each train request a train path has to be constructed from a set of pre-defined path parts within a time-space network. Those train requests should be realized only at certain days of the week. Each customer request has a specific traffic day pattern, which is a difficult challenge for the allocation process. Infrastructure capacity managers intend to achieve an efficient utilization of the capacity, whereas customers are interested in homogeneous train paths, i.e. they want the same traffic path connection for all requested traffic days. We discuss those partly contradictory requirements within the context of our binary linear decision model. The problem is solved by using column generation within a branch and price approach. We give some modeling and implementation details and present computational results from real world instances.

A Novel Approach to Strategic Planning of Rail Freight Transport

Railway traffic now and in future faces ever-growing challenges. On the one hand, infrastructure measures must be planned and in the medium respectively long term corresponding operating programs have to be generated. On the other hand, in the short term economical and political reasons exert increasing influence on the requirements of timetabling as well. Consequently, it exists the need for highly optimized, automated algorithms and its corresponding intelligent conjunction. A state-of-the-art realization is reflected in the software system TAKT. The implementation offers a complete new approach to solve the problems like computing conflict-free, optimized time tables or searching, optimizing and maximizing rail freight transport train paths based on an existing operating program.

Tourenplanung für den Einsatz von Elektrofahrzeugen in städtischen Liefersystemen

Lieferverkehre in Ballungsgebieten, insbesondere Sammel- und Verteilverkehre, erfordern teils schwierige Dispositionsentscheidungen. Hierunter zahlen die Zuordnung der Sendungen zu Touren, deren Bedienungsreihenfolge und die Gewahrleistung der Einhaltung von Zeitfenstern und Kapazitatsanforderungen. Fur die Entscheidungsunterstutzung arbeiten die Disponenten mit den etablierten Modellvarianten des Vehicle Routing Problems (VRP) und entsprechenden Losungsalgorithmen, welche visualisiert und erweitert um den notwendigen Bedienungskomfort in mittlerweile ausgereiften Softwareanwendungen zur Verfugung stehen.