Moritz Baum

Energy-optimal routes for electric vehicles

We study the problem of electric vehicle route planning, where an important aspect is computing paths that minimize energy consumption. Thereby, any method must cope with specific properties, such as recuperation, battery constraints (over- and under-charging), and frequently changing cost functions (e. g., due to weather conditions). This work presents a practical algorithm that quickly computes energy-optimal routes for networks of continental scale. Exploiting multi-level overlay graphs [25, 30], we extend the Customizable Route Planning approach [7] to our scenario in a sound manner. This includes the efficient computation of profile queries and the adaption of bidirectional search to battery constraints. Our experimental study uses detailed consumption data measured from a production vehicle (Peugeot iOn). It reveals for the network of Europe that a new cost function can be incorporated in about five seconds, after which we answer random queries within 0.3 ms on average. Additional evaluation on an artificial but realistic [21, 35] vehicle model with unlimited range demonstrates the excellent scalability of our algorithm: Even for long-range queries across Europe it achieves query times below 5 ms on average---fast enough for interactive applications. Altogether, our algorithm exhibits faster query times than previous approaches, while improving (metric-dependent) preprocessing time by three orders of magnitude.

Speed-Consumption Tradeoff for Electric Vehicle Route Planning

We study the problem of computing routes for electric vehicles (EVs) in road networks. Since their battery capacity is limited, and consumed energy per distance increases with velocity, driving the fastest route is often not desirable and may even be infeasible. On the other hand, the energy-optimal route may be too conservative in that it contains unnecessary detours or simply takes too long. In this work, we propose to use multicriteria optimization to obtain Pareto sets of routes that trade energy consumption for speed. In particular, we exploit the fact that the same road segment can be driven at dierent speeds within reasonable intervals. As a result, we are able to provide routes with low energy consumption that still follow major roads, such as freeways. Unfortunately, the size of the resulting Pareto sets can be too large to be practical. We therefore also propose several nontrivial techniques that can be applied on-line at query time in order to speed up computation and filter insignificant solutions from the Pareto sets. Our extensive experimental study, which uses a real-world energy consumption model, reveals that we are able to compute diverse sets of alternative routes on continental networks that closely resemble the exact Pareto set in just under a second—several orders of magnitude faster than the exhaustive algorithm. 1998 ACM Subject Classification G.2.2 Graph Theory, G.2.3 Applications

Shortest feasible paths with charging stops for battery electric vehicles

We study the problem of minimizing overall trip time for battery electric vehicles (EVs) in road networks. As battery capacity is limited, stops at charging stations may be inevitable. Careful route planning is crucial, since charging stations are scarce and recharging is time-consuming. We extend the Constrained Shortest Path (CSP) problem for EVs with realistic models of charging stops, including varying charging power and battery swapping stations. While the resulting problem is NP-hard, we propose a combination of algorithmic techniques to achieve good performance in practice. Extensive experimental evaluation shows that our approach (CHArge) enables computation of optimal solutions on realistic inputs, even of continental scale. Finally, we investigate heuristic variants of CHArge that derive high-quality routes in well below a second on sensible instances.

Dynamic Time-Dependent Route Planning in Road Networks with User Preferences

Algorithms for computing driving directions on road networks often presume constant costs on each arc. In practice, the current traffic situation significantly influences the travel time. One can distinguish traffic congestion that can be predicted using historical traffic data, and congestion due to unpredictable events, e.i¾źg., accidents. We study the dynamic and time-dependent route planning problem, which takes both live traffic and long-term prediction into account. We propose a practical algorithm that, while robust to user preferences, is able to integrate global changes of the time-dependent metric faster than previous approaches and allows queries in the order of milliseconds.

Towards route planning algorithms for electric vehicles with realistic constraints

Route planning applications designed for electric vehicles have to consider a number of additional constraints. With the limited range and comparatively long charging times, it is of utmost importance to consider energy consumption in routing applications. However, recently published algorithmic approaches for electric vehicle routing focus solely on specific aspects of this problem, such as optimizing energy consumption as single criterion. In this work, we present first steps towards a holistic framework for computing shortest paths for electric vehicles with limited range. This includes the possibility of driving instructions, such as driving speed adjustments to save energy, realistic modeling of battery charging procedures, and the integration of turn costs.

On the Complexity of Partitioning Graphs for Arc-Flags

Precomputation of auxiliary data in an additional off-line step is a common approach towards improving the performance of shortest-path queries in large-scale networks. One such technique is the arc-flags algorithm, where the preprocessing involves computing a partition of the input graph. The quality of this partition significantly affects the speed-up observed in the query phase. It is evaluated by considering the search-space size of subsequent shortest-path queries, in particular its maximum or its average over all queries. In this paper, we substantially strengthen existing hardness results of Bauer et al. and show that optimally filling this degree of freedom is NP-hard for trees with unit-length edges, even if we bound the height or the degree. On the other hand, we show that optimal partitions for paths can be computed efficiently and give approximation algorithms for cycles and trees.

Fast Exact Computation of Isochrones in Road Networks

We study the problem of computing isochrones in static and dynamic road networks, where the objective is to identify the boundary of the region in range from a given source within a certain amount of time. While there is a wide range of practical applications for this problemi¾źe.i¾źg., urban planning, geomarketing, visualizing the cruising range of a vehicle, there has been little research on fast algorithms for large, realistic inputs, and existing approaches tend to compute more information than necessary. Our contribution is twofold: 1 We propose a more compact but sufficient definition of isochrones, based on which, 2 we provide several easy-to-parallelize, scalable algorithmic approaches for faster computation. By extensive experimental analysis, we demonstrate that our techniques enable fast isochrone computation within milliseconds even on continental networks, significantly faster than the state-of-the-art.

Scalable exact visualization of isocontours in road networks via minimum-link paths

Isocontours in road networks represent the area that is reachable from a source within a given resource limit. We study the problem of computing accurate isocontours in realistic, large-scale networks. We propose isocontours represented by polygons with minimum number of segments that separate reachable and unreachable components of the network. Since the resulting problem is not known to be solvable in polynomial time, we introduce several heuristics that run in (almost) linear time and are simple enough to be implemented in practice. A key ingredient is a new practical linear-time algorithm for minimum-link paths in simple polygons. Experiments in a challenging realistic setting show excellent performance of our algorithms in practice, computing near-optimal solutions in a few milliseconds on average, even for long ranges.

Consumption profiles in route planning for electric vehicles : Theory and applications

In route planning for electric vehicles (EVs), consumption profiles are a functional representation of optimal energy consumption between two locations, subject to initial state of charge. Efficient computation of profiles is a relevant problem on its own, but also a fundamental ingredient to many route planning approaches for EVs. In this work, we show that the complexity of a profile is at most linear in the graph size. Based on this insight, we derive a polynomial-time algorithm for the problem of finding an energy-optimal path between two locations that allows stops at charging stations. Exploiting efficient profile search, our approach also allows partial recharging at charging stations to save energy. In a sense, our results close the gap between efficient techniques for energy-optimal routes (based on simpler models) and NP-hard time-constrained problems involving charging stops for EVs. We propose a practical implementation, which we carefully integrate with Contraction Hierarchies and A* search. Even though the practical variant formally drops correctness, a comprehensive experimental study on a realistic, large-scale road network reveals that it always finds the optimal solution in our tests and computes even long-distance routes with charging stops in less than 300 ms.

Time-Dependent Route Planning for Truck Drivers

We study the problem of computing time-dependent shortest routes for truck drivers. In contrast to conventional route planning, truck drivers have to obey government regulations that impose limits on non-stop driving times. Therefore, route planners must plan break periods in advance and select suitable parking lots. To ensure that maximum driving times are not exceeded, predictable congestion due to, e. g., peak hours should also be taken into account. Therefore, we introduce the truck driver routing problem in time-dependent road networks. It turns out that the combination of time-dependent driving times with constraints imposed by drivers’ working hours requires computation of multiple time-dependent profiles for optimal solutions. Although conceptually simple, profile search is expensive. We greatly reduce (empirical) running times by calculating bounds on arrival and departure times during additional search phases to only query partial profiles and only to a fraction of the parking lots. Carefully integrating this approach with a one-to-many extension of time-dependent contraction hierarchies makes our approach practical. For even faster queries, we also propose a heuristic variant that works very well in practice. Excellent performance of our algorithms is demonstrated on a recent real-world instance of Germany that is much harder than time-dependent instances considered in previous works.