Engineering Time-Dependent Many-to-Many Shortest Paths Computation

Computing distance tables is important for many logistics problems like the vehicle routing problem (VRP). While shortest distances from all source nodes in S to all target nodes in T are time-independent, travel times are not. We present the first efficient algorithms to compute time-dependent travel time tables in large time-dependent road networks. Our algorithms are based on time-dependent contraction hierarchies (TCH), currently the fastest time-dependent speed-up technique. The computation of a table is inherently in Theta(|S|*|T|), and therefore inefficient for large tables. We provide one particular algorithm using only Theta(|S|+|T|) time and space, being able to answer queries two orders of magnitude faster than the basic TCH implementation. If small errors are acceptable, approximate versions of our algorithms are further orders of magnitude faster

Engineering Time-dependent One-To-All Computation

Abstract Very recently a new algorithm to the nonnegative single-source shortest path problem on road networks has been discovered. It is very cacheefficient, but only on static road networks. We show how to augment it to the time-dependent scenario. The advantage if the new approach is that it settles nodes, even for a profile query, by scanning all downward edges. We improve the scanning of the downward edges with techniques developed for time-dependent many-to-many computations

Route Planning in Transportation Networks

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

Building Blocks for Mapping Services

Mapping services are ubiquitous on the Internet. These services enjoy a considerable user base. But it is often overlooked that providing a service on a global scale with virtually millions of users has been the playground of an oligopoly of a select few service providers are able to do so. Unfortunately, the literature on these solutions is more than scarce. This thesis adds a number of building blocks to the literature that explain how to design and implement a number of features

Advanced Route Planning in Transportation Networks

We present fast and efficient algorithms for routing in road and public transit networks. An algorithm for public transit can handle very large and poorly structured networks in a fully realistic scenario. Algorithms to answer flexible shortest path queries consider additional query parameters, such as edge weight or restrictions. Finally, specialized algorithms compute sets of related shortest path distances for time-dependent distance table computation, ride sharing and closest POI location

Scheduling and Routing of Truck Drivers Considering Regulations on Drivers’ Working Hours

In many countries, truck drivers are obliged by law to take a break or a rest regularly. In the European Union, for example, this is governed by Regulation (EC) No. 561/2006. It states that, after 4.5 hours of driving a truck, it is prohibited to continue driving until a 45-minute break is taken. After accumulating a driving time of 9 hours, a rest of 11 hours is mandatory. These are only two rules of a considerably longer list of break rules set out in this regulation, and it is only one of many regulations there are worldwide. Such breaks and rests have to be planned into the work schedules of the drivers. In general, the task of a dispatcher is to find routes and schedules for the truck drivers such that every customer is served in time. With the regulations on drivers’ working hours, both the routing and the scheduling parts of the task become more challenging. In this thesis, we study several optimization problems that arise in the context of drivers’ working hours. One is known as the truck driver scheduling problem. Here, a sequence of customers is given, and the task is to find a schedule for a driver such that every customer is visited within one of the customer’s time windows and the applicable break rules are complied with. Depending on the regarded break rules, we get different variants of the truck driver scheduling problem. Little is known about the complexity of the individual problem variants. One of the two focal points of this thesis is to present polynomial-time algorithms for different variants of the problem, for which polynomial-time algorithms are not yet known. With this, we can falsify the NP-hardness conjecture of Xu et al. (2003) for an important special case of their considered problem variant. But this thesis is not only about scheduling, it is also about routing. This constitutes the second focal point of this thesis. We present an integrated approach for the vehicle routing and truck driver scheduling problem. Here, a route refers to the order in which the customers are visited. However, the meaning of route is twofold. In another studied problem, the truck driver scheduling and routing problem, it means the sequence of road segments that the driver takes to drive from one customer to the other. In this problem, we take into account that, before taking a break, truck drivers need to head for a rest area or at least a spot where their vehicle can be parked. We even consider the time-dependent scenario in which driving times on road segments vary over the day due to rush hours. Both an exact approach and a heuristic for this problem are presented, and both are evaluated on a recent road network instance of Germany. It turns out that the heuristic is at least two orders of magnitude faster but still hardly worse than the exact approach. Our main motivation is the application in practice. It is our aim – and this is especially true for the second focal point – to provide helpful algorithms that may find their way into software products for dispatchers, like the described approach for the vehicle routing and truck driver scheduling problem is already integrated into the vehicle route planning tools of a commercial provider of logistics optimization software

Time-Dependent Route Planning with Contraction Hierarchies

Design and experimental evaluation of route planning algorithms for time-dependent road networks, which model regular effects like congestions. By generalizing contraction hierarchies, we achieve fast and space efficient computation of minimum travel time routes and profiles. We also consider additional constant costs (e.g., to penalize detours and motorway tolls), which makes route planning NP-hard. Then, routes become heuristic, but we get quite near to the optimum as experiments show