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Register a new userJoint Routing and Charging Problem of Multiple Electric Vehicles: A Fast Optimization Algorithm
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Canqi Yao
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Logistics has gained great attentions with the prosperous development of commerce, which is often seen as the classic optimal vehicle routing problem. Meanwhile, electric vehicle (EV) has been widely used in logistic fleet to curb the emission of green house gases in recent years. Solving the optimization problem of joint routing and charging of multiple EVs is in a urgent need, whose objective function includes charging time, charging cost, EVs travel time, usage fees of EV and revenue from serving customers. This joint problem is formulated as a mixed integer programming (MIP) problem, which, however, is NP-hard due to integer restrictions and bilinear terms from the coupling between routing and charging decisions. The main contribution of this paper lies at proposing an efficient two stage algorithm that can decompose the original MIP problem into two linear programming (LP) problems, by exploiting the exactness of LP relaxation and eliminating the coupled term. This algorithm can achieve a nearoptimal solution in polynomial time. In addition, another variant algorithm is proposed based on the two stage one, to further improve the quality of solution.
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This paper aims to answer the research question as to optimal design of decision-making processes for autonomous vehicles (AVs), including dynamical selection of driving velocity and route choices on a transportation network. Dynamic traffic assignment (DTA) has been widely used to model travelerss route choice or/and departure-time choice and predict dynamic traffic flow evolution in the short term. However, the existing DTA models do not explicitly describe ones selection of driving velocity on a road link. Driving velocity choice may not be crucial for modeling the movement of human drivers but it is a must-have control to maneuver AVs. In this paper, we aim to develop a game-theoretic model to solve for AVss optimal driving strategies of velocity control in the interior of a road link and route choice at a junction node. To this end, we will first reinterpret the DTA problem as an N-car differential game and show that this game can be tackled with a general mean field game-theoretic framework. The developed mean field game is challenging to solve because of the forward and backward structure for velocity control and the complementarity conditions for route choice. An efficient algorithm is developed to address these challenges. The model and the algorithm are illustrated on the Braess network and the OW network with a single destination. On the Braess network, we first compare the LWR based DTA model with the proposed game and find that the driving and routing control navigates AVs with overall lower costs. We then compare the total travel cost without and with the middle link and find that the Braess paradox may still arise under certain conditions. We also test our proposed model and solution algorithm on the OW network.
With the advances in the Internet of Things technology, electric vehicles (EVs) have become easier to schedule in daily life, which is reshaping the electric load curve. It is important to design efficient charging algorithms to mitigate the negative impact of EV charging on the power grid. This paper investigates an EV charging scheduling problem to reduce the charging cost while shaving the peak charging load, under unknown future information about EVs, such as arrival time, departure time, and charging demand. First, we formulate an EV charging problem to minimize the electricity bill of the EV fleet and study the EV charging problem in an online setting without knowing future information. We develop an actor-critic learning-based smart charging algorithm (SCA) to schedule the EV charging against the uncertainties in EV charging behaviors. The SCA learns an optimal EV charging strategy with continuous charging actions instead of discrete approximation of charging. We further develop a more computationally efficient customized actor-critic learning charging algorithm (CALC) by reducing the state dimension and thus improving the computational efficiency. Finally, simulation results show that our proposed SCA can reduce EVs expected cost by 24.03%, 21.49%, 13.80%, compared with the Eagerly Charging Algorithm, Online Charging Algorithm, RL-based Adaptive Energy Management Algorithm, respectively. CALC is more computationally efficient, and its performance is close to that of SCA with only a gap of 5.56% in the cost.
Given the rise of electric vehicle (EV) adoption, supported by government policies and dropping technology prices, new challenges arise in the modeling and operation of electric transportation. In this paper, we present a model for solving the EV routing problem while accounting for real-life stochastic demand behavior. We present a mathematical formulation that minimizes travel time and energy costs of an EV fleet. The EV is represented by a battery energy consumption model. To adapt our formulation to real-life scenarios, customer pick-ups and drop-offs were modeled as stochastic parameters. A chance-constrained optimization model is proposed for addressing pick-ups and drop-offs uncertainties. Computational validation of the model is provided based on representative transportation scenarios. Results obtained showed a quick convergence of our model with verifiable solutions. Finally, the impact of electric vehicles charging is validated in Downtown Manhattan, New York by assessing the effect on the distribution grid.
We consider the scheduling of multiple tasks with pre-determined deadlines under random processing cost. This problem is motivated by the potential of large scale adoption of plug-in (hybrid) electric vehicles (PHEVs) in the near future. The charging requests of PHEVs usually have deadline constraints, and the electricity cost associated with PHEV charging is usually random due to the uncertainty in both system load and renewable generation. We seek to properly schedule the battery charging of multiple PHEVs so as to minimize the overall cost, which is derived from the total charging cost and the penalty for not completing charging before requested deadlines. Through a dynamic programming formulation, we establish the Less Laxity and Longer remaining Processing time (LLLP) principle that improves any charging policy on a sample-path basis, when the non-completion penalty is a convex function of the additional time needed to fulfill the uncompleted request. Specifically, the LLLP principle states that priority should be given to vehicles that have less laxity and longer remaining processing times. Numerical results demonstrate that heuristic policies that violate the LLLP principle, for example, the earliest deadline first (EDF) policy, can result in significant performance loss.
The number of electric vehicles (EVs) is expected to increase. As a consequence, more EVs will need charging, potentially causing not only congestion at charging stations, but also in the distribution grid. Our goal is to illustrate how this gives rise to resource allocation and performance problems that are of interest to the Sigmetrics community.
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