60 research outputs found

    Consumption Profiles in Route Planning for Electric Vehicles: Theory and Applications

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    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

    Robustness Generalizations of the Shortest Feasible Path Problem for Electric Vehicles

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    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

    Towards a more realistic, cost effective and greener ground movement through active routing: a multi-objective shortest path approach

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    Based on the multi-objective optimal speed profile generation framework for unimpeded taxiing aircraft presented in the precursor paper, this paper deals with how to seamlessly integrate such optimal speed profiles into a holistic decision making framework. The availability of a set of non-dominated unimpeded speed profiles for each taxiway segment with respect to conflicting objectives can significantly change the current airport ground movement research. More specifically, the routing and scheduling function that was previously based on distance, emphasizing time efficiency, could now be based on richer information embedded within speed profiles, such as the taxiing times along segments, the corresponding fuel consumption, and the associated economic implications. The economic implications are exploited over a day of operation to take into account cost differences between busier and quieter times of the airport. Therefore, the most cost-effective and tailored decision can be made, respecting the environmental impact. Preliminary results based on the proposed approach are promising and show a 9%–50% reduction in time and fuel respectively for two international airports, viz. Zurich and Manchester Airports. The study also suggests that, if the average power setting during the acceleration phase could be lifted from the level suggested by the International Civil Aviation Organization (ICAO), ground operations may achieve the best of both worlds, simultaneously improving both time and fuel efficiency. Now might be the time to move away from the conventional distance based routing and scheduling to a more comprehensive framework, capturing the multi-facetted needs of all stakeholders involved in airport ground operations

    Route Planning in Transportation Networks

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    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

    Modeling and Engineering Constrained Shortest Path Algorithms for Battery Electric Vehicles

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    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

    An Efficient Algorithm for Placing Electric Vehicle Charging Stations

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    Motivated by the increasing popularity of electric vehicles (EV) and a lack of charging stations in the road network, we study the shortest path hitting set (SPHS) problem. Roughly speaking, given an input graph G, the goal is to compute a small-size subset H of vertices of G such that by placing charging stations at vertices in H, every shortest path in G becomes EV-feasible, i.e., an EV can travel between any two vertices of G through the shortest path with a full charge. In this paper, we propose a bi-criteria approximation algorithm with running time near-linear in the size of G that has a logarithmic approximation on |H| and may require the EV to slightly deviate from the shortest path. We also present a data structure for computing an EV-feasible path between two query vertices of G

    Vehicle Routing Problem with Time Window Constrain using KMeans Clustering to Obtain the Closest Customer

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    In this paper, the problem statement is solving the Vehicle Routing Problem (VRP) with Time Window constraint using the Ant Colony Algorithm with K-Means Clustering. In this problem, the vehicles must start at a common depot, pickup from various ware houses, deliver to the respective nodes within the time window provided by the customer and returns to depot. The objectives defined are to reduction in usage of number of vehicles, the total logistics cost and to reduce carbon emissions. The mathematical model described in this paper has considered multiple pickup and multiple delivery points. The proposed solution of this paper aims to provide better and more efficient solution while minimizing areas of conflict so as to provide the best output on a large scale in Vehicle Routing Problem, K-Means Clustering, Time Window constraint, Ant Colony Algorithm
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