Energy-Optimal Routes for Electric Vehicles

Abstract. 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 [26, 31], we extend the Customizable Route Planning approach [8] 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 0.3ms on average. Additional evaluation on an artificial but realistic [22, 36] vehicle model with unlimited range demonstrates the excellent scalability of our algorithm: Even for long-range queries across Europe it achieves query times below 5ms 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.

Modeling and Engineering Constrained Shortest Path Algorithms for Battery Electric Vehicles

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

Optimal routes for electric vehicles facing uncertainty, congestion, and energy constraints

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 165-170).There are many benefits of owning a battery electric vehicle, including zero tailpipe emissions, potential independence from oil, lower fuel costs, and the option to recharge the battery at home. However, a significant concern about owning a battery electric vehicle is range anxiety: the fear that the battery will run out of charge before the driver reaches his or her destination. We address range anxiety by providing a robust optimization framework to give drivers confidence that they can reach their destinations in a reasonable amount of time with enough energy in the battery, even when there is uncertainty in travel time and energy consumption on the roads. The robust optimization appropriately incorporates uncertainty without significantly increasing the complexity of the problem. This thesis describes that optimization framework and how to use it on real-world examples to find appropriate routes, with a central part being the application of robust optimization to the problem. We develop an energy model, an optimization-based formulation using robust optimization, and algorithms to quickly find good routes for battery electric vehicles. The combination of using robust optimization, the A-Star algorithm to find shortest paths, and Lagrangian relaxation allows us to solve the problem in seconds or less. For one example start and destination, our algorithms required less than 2 seconds for each instance (energy consumption limit). In addition, for example trips, we compute a Pareto frontier to illustrate the time-energy tradeoff from driving different routes. We use Lagrangian relaxation to provide lower bounds and estimates that suggest that our algorithms produce near-optimal solutions. We apply our methodology to example trips in Massachusetts and Michigan to demonstrate its practicality and its potential for real-world use. Future work could continue to improve the modeling accuracy and include algorithmic enhancements to further improve running time, especially for larger networks.by Matthew William Fontana.Ph.D

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

Optimal Routing of Energy-aware Vehicles in Networks with Inhomogeneous Charging Nodes

We study the routing problem for vehicles with limited energy through a network of inhomogeneous charging nodes. This is substantially more complicated than the homogeneous node case studied in [1]. We seek to minimize the total elapsed time for vehicles to reach their destinations considering both traveling and recharging times at nodes when the vehicles do not have adequate energy for the entire journey. We study two versions of the problem. In the single vehicle routing problem, we formulate a mixed-integer nonlinear programming (MINLP) problem and show that it can be reduced to a lower dimensionality problem by exploiting properties of an optimal solution. We also obtain a Linear Programming (LP) formulation allowing us to decompose it into two simpler problems yielding near-optimal solutions. For a multi-vehicle problem, where traffic congestion effects are included, we use a similar approach by grouping vehicles into "subflows". We also provide an alternative flow optimization formulation leading to a computationally simpler problem solution with minimal loss in accuracy. Numerical results are included to illustrate these approaches.Comment: To appear in proceeding of 22nd Mediterranean Conference on Control and Automation, MED'1

Forecasting Recharging Demand to Integrate Electric Vehicle Fleets in Smart Grids

Electric vehicle fleets and smart grids are two growing technologies. These technologies provided new possibilities to reduce pollution and increase energy efficiency. In this sense, electric vehicles are used as mobile loads in the power grid. A distributed charging prioritization methodology is proposed in this paper. The solution is based on the concept of virtual power plants and the usage of evolutionary computation algorithms. Additionally, the comparison of several evolutionary algorithms, genetic algorithm, genetic algorithm with evolution control, particle swarm optimization, and hybrid solution are shown in order to evaluate the proposed architecture. The proposed solution is presented to prevent the overload of the power grid