Electric Vehicle routing is often modeled as a Shortest Feasible Path Problem (SFPP), which minimizes total travel time while maintaining a non-zero State of Charge (SoC) along the route. However, the problem assumes perfect information about energy consumption and charging stations, which are difficult to even estimate in practice. Further, drivers might have varying risk tolerances for different trips. To overcome these limitations, we propose two generalizations to the SFPP; they compute the shortest feasible path for any initial SoC and, respectively, for every possible minimum SoC threshold. We present algorithmic solutions for each problem, and provide two constructs: Starting Charge Maps and Buffer Maps, which represent the tradeoffs between robustness of feasible routes and their travel times. The two constructs are useful in many ways, including presenting alternate routes or providing charging prompts to users. We evaluate the performance of our algorithms on realistic input instances.

We study the one-to-many journey planning problem in multi-modal transportation networks consisting of a public transit network and an additional, non-schedule-based mode of transport. Given a departure time and a single source vertex, we aim to compute optimal journeys to all vertices in a set of targets, optimizing both travel time and the number of transfers used. Solving this problem yields a crucial component in many other problems, such as efficient point-of-interest queries, computation of isochrones, or multi-modal traffic assignments. While many algorithms for multi-modal journey planning exist, none of them are applicable to one-to-many scenarios. Our solution is based on the combination of two state-of-the-art approaches: ULTRA, which enables efficient journey planning in multi-modal networks, but only for one-to-one queries, and (R)PHAST, which enables efficient one-to-many queries, but only in time-independent networks. Similarly to ULTRA, our new approach can be combined with any existing public transit algorithm that allows a search to all stops, which we demonstrate for CSA and RAPTOR. For small to moderately sized target sets, the resulting algorithms are nearly as fast as the pure public transit algorithms they are based on. For large target sets, we achieve a speedup of up to 7 compared to a naive one-to-many extension of a state-of-the-art multi-modal approach.

We study a bi-modal journey planning scenario consisting of a public transit network and a transfer graph representing a secondary transportation mode (e.g., walking or cycling). Given a pair of source and target locations, the objective is to find a Pareto set of journeys optimizing arrival time and the number of required transfers. For public transit networks with a restricted, transitively closed transfer graph, one of the fastest known algorithms solving this bi-criteria problem is Trip-Based Routing [Witt, 2015]. However, this algorithm cannot be trivially extended to unrestricted transfer graphs. In this work, we combine Trip-Based Routing with ULTRA [Baum et al., 2019], a preprocessing technique that allows any public transit algorithm that requires transitive transfers to handle an unrestricted transfer graph. Since both ULTRA and Trip-Based Routing precompute transfer shortcuts in a preprocessing phase, a naive combination of the two leads to a three-phase algorithm that performs redundant work and produces superfluous shortcuts. We therefore propose a new, integrated preprocessing phase that combines the advantages of both and reduces the number of computed shortcuts by up to a factor of 9 compared to a naive combination. The resulting query algorithm, ULTRA-Trip-Based is the fastest known algorithm for the considered problem setting, achieving a speedup of up to 4 compared to the fastest previously known approach, ULTRA-RAPTOR.

We study multi-modal route planning in a network comprised of schedule-based public transportation, unrestricted walking, and cycling with bikes available from bike sharing stations. So far this problem has only been considered for scenarios with at most one bike sharing operator, for which MCR is the best known algorithm [Delling et al., 2013]. However, for practical applications, algorithms should be able to distinguish between bike sharing stations of multiple competing bike sharing operators. Furthermore, MCR has recently been outperformed by ULTRA for multi-modal route planning scenarios without bike sharing [Baum et al., 2019]. In this paper, we present two approaches for modeling multi-modal transportation networks with multiple bike sharing operators: The operator-dependent model requires explicit handling of bike sharing stations within the algorithm, which we demonstrate with an adapted version of MCR. In the operator-expanded model, all relevant information is encoded within an expanded network. This allows for applying any multi-modal public transit algorithm without modification, which we show for ULTRA. We proceed by describing an additional preprocessing step called operator pruning, which can be used to accelerate both approaches. We conclude our work with an extensive experimental evaluation on the networks of London, Switzerland, and Germany. Our experiments show that the new preprocessing technique accelerates both approaches significantly, with the fastest algorithm (ULTRA-RAPTOR with operator pruning) being more than an order of magnitude faster than the basic MCR approach. Moreover, the ULTRA preprocessing step also benefits from operator pruning, as its running time is reduced by a factor of 14 to 20.

We study a multi-modal route planning scenario consisting of a public transit network and a transfer graph representing a secondary transportation mode (e.g., walking or taxis). The objective is to compute all journeys that are Pareto-optimal with respect to arrival time and the number of required transfers. While various existing algorithms can efficiently compute optimal journeys in either a pure public transit network or a pure transfer graph, combining the two increases running times significantly. As a result, even walking between stops is typically limited by a maximal duration or distance, or by requiring the transfer graph to be transitively closed. To overcome these shortcomings, we propose a novel preprocessing technique called ULTRA (UnLimited TRAnsfers): Given a complete transfer graph (without any limitations, representing an arbitrary non-schedule-based mode of transportation), we compute a small number of transfer shortcuts that are provably sufficient for computing all Pareto-optimal journeys. We demonstrate the practicality of our approach by showing that these transfer shortcuts can be integrated into a variety of state-of-the-art public transit algorithms, establishing the ULTRA-Query algorithm family. Our extensive experimental evaluation shows that ULTRA is able to improve these algorithms from limited to unlimited transfers without sacrificing query speed, yielding the fastest known algorithms for multi-modal routing. This is true not just for walking, but also for other transfer modes such as cycling or driving.

We study the problem of computing public transit traffic assignments in a multi-modal setting: Given a public transit timetable, an additional unrestricted transfer mode (e.g., walking), and a set of origin-destination pairs, we aim to compute the utilization of all vehicles. While it has been shown that unrestricted walking can significantly improve journeys, computing such journeys efficiently remains algorithmically challenging. Since traffic assignments require the computation of millions of shortest paths, using a multi-modal network has previously not been feasible. In this work we combine the novel ULTRA [2] approach, which enables UnLimited TRAnsfers at the cost of a short preprocessing phase, with a state-of-the-art assignment algorithm, making multi-modal assignments practical. Careful algorithm engineering results in an efficient assignment algorithm, which even outperforms the algorithm it is based on, while enabling unlimited walking for the first time. Finally, we evaluate our algorithm on real worl data, where it computes over 15 million journeys in less than 17 seconds, showing its efficiency.

We present a preprocessing-based acceleration technique for computing bi-criteria Pareto-optimal journeys in public transit networks, based on the well-known RAPTOR algorithm [Delling et al 2015]. Our key idea is to first partition a hypergraph into cells, in which vertices correspond to routes (e.g., bus lines) and hyperedges to stops, and to then mark routes sufficient for optimal travel across cells. The query can then be restricted to marked routes and those in the source and target cells. This results in a practical approach, suitable for networks that are too large to be efficiently handled by the basic RAPTOR algorithm.

We study the problem of answering profile queries in public transportation networks that allow unrestricted walking. That is, finding all Pareto-optimal journeys regarding travel time and number of transfers in a given time interval. We introduce a novel algorithm that, unlike most state-of-the-art algorithms, can compute profiles efficiently in a setting that allows arbitrary walking. Using our algorithm, we show in an extensive experimental study that allowing unrestricted walking, significantly reduces travel times, compared to settings where walking is restricted. Beyond that, we publish the transportation networks of Switzerland that we used in our study, in order to encourage further research on this topic.

We study the problem of computing constrained shortest paths for battery electric vehicles. Since battery capacities are limited, fastest routes are often infeasible. Instead, users are interested in fast routes where the energy consumption does not exceed the battery capacity. For that, drivers can deliberately reduce speed to save energy. Hence, route planning should provide both path and speed recommendations. To tackle the resulting NP-hard optimization problem, previous work trades correctness or accuracy of the underlying model for practical running times. In this work, we present a novel framework to compute optimal constrained shortest paths for electric vehicles that uses more realistic physical models, while taking speed adaptation into account. Careful algorithm engineering makes the approach practical even on large, realistic road networks: We compute optimal solutions in less than a second for typical battery capacities, matching performance of previous inexact methods. For even faster performance, the approach can easily be extended with heuristics that provide high quality solutions within milliseconds.

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.

We study the problem of computing traffic assignments for public transit networks: Given a public transit network and a demand (i.e. a list of passengers, each with associated origin, destination, and departure time), the objective is to compute the utilization of every vehicle. Efficient assignment algorithms are a core component of many urban traffic planning tools. In this work, we present a novel algorithm for computing public transit assignments. Our approach is based upon a microscopic Monte Carlo simulation of individual passengers. In order to model realistic passenger behavior, we base all routing decisions on travel time, number of transfers, time spent walking or waiting, and delay robustness. We show how several passengers can be processed during a single scan of the network, based on the Connection Scan Algorithm [Dibbelt et al., LNCS Springer 2013], resulting in a highly efficient algorithm. We conclude with an experimental study, showing that our assignments are comparable in terms of quality to the state-of-the-art. Using the parallelized version of our algorithm, we are able to compute a traffic assignment for more than ten million passengers in well below a minute, which outperforms previous works by more than an order of magnitude.

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.