An energy-efficient reliable path finding algorithm for stochastic road networks with electric vehicles

Abstract In this paper, we develop a novel reliable path finding algorithm for a stochastic road network with uncertainty in travel times while both electric vehicle energy and efficiency are simultaneously taken into account. We first propose a bi-objective optimization model to maximize (1) the on-time arrival reliability and (2) energy-efficiency for battery electric vehicles (BEVs) in a path finding problem. The former objective requires finding the reliable shortest path (RSP), which is the path with the minimal effective travel time measured by the sum of the mean travel time and a travel time safety margin for any given origin-destination (OD) pair. Then, we refer to energy-efficiency as the minimum of the electric energy consumption. We discuss the non-additive property of the RSP problem since we also consider the link travel time correlations, whereas the latter objective satisfies the additive criterion. To this end, we illustrate the existence of non-dominated solutions that satisfy both of the two objectives. Furthermore, it is shown that the intersection of two candidate sets – one for the RSPs and the other for paths with minimal energy-consumption - actually contains the optimal solution for the bi-objective optimization problem. The upper and lower bounds of the effective travel time are mathematically deduced and can be used to generate the candidate path set of this bi-objective problem via the K-shortest algorithm. Our proposed algorithm overcomes the infeasibility of traditional path finding algorithms (e.g., the Dijkstra algorithm) for RSPs. Moreover, using two numerical examples, we verify the effectiveness and efficiency of the proposed algorithm. We numerically demonstrate promising potential applications of the proposed algorithm in real-life road traffic networks.

[1]  Yafeng Yin,et al.  Behaviorally stable vehicle platooning for energy savings , 2019, Transportation Research Part C: Emerging Technologies.

[2]  Yafeng Yin,et al.  Deploying public charging stations for electric vehicles on urban road networks , 2015 .

[3]  Hsu-Hao Yang,et al.  Finding K shortest looping paths with waiting time in a time–window network , 2006 .

[4]  Baozhen Yao,et al.  Production , Manufacturing and Logistics An improved ant colony optimization for vehicle routing problem , 2008 .

[5]  Rajan Batta,et al.  The Variance-Constrained Shortest Path Problem , 1994, Transp. Sci..

[6]  B. Schutter,et al.  Optimal trajectory planning for trains – A pseudospectral method and a mixed integer linear programming approach , 2013 .

[7]  Lixing Yang,et al.  Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem , 2014 .

[8]  Stephen D. Clark,et al.  Modelling network travel time reliability under stochastic demand , 2005 .

[9]  Hong Kam Lo,et al.  Adaptive Vehicle Routing for Risk-averse Travelers☆ , 2013 .

[10]  Yasuo Asakura,et al.  Road network reliability caused by daily fluctuation of traffic flow , 1991 .

[11]  Ping Hu,et al.  Transit network design based on travel time reliability , 2014 .

[12]  Fritz Busch,et al.  Optimal location of wireless charging facilities for electric vehicles: Flow-capturing location model with stochastic user equilibrium , 2015 .

[13]  H. Frank,et al.  Shortest Paths in Probabilistic Graphs , 1969, Oper. Res..

[14]  Jing Zhou,et al.  A Route Choice Model with Context-Dependent Value of Time , 2017, Transp. Sci..

[15]  Hesham Rakha,et al.  Trip Travel-Time Reliability: Issues and Proposed Solutions , 2010, J. Intell. Transp. Syst..

[16]  Guoyuan Wu,et al.  Deep reinforcement learning enabled self-learning control for energy efficient driving , 2019, Transportation Research Part C: Emerging Technologies.

[17]  Matthew Brand,et al.  Stochastic Shortest Paths Via Quasi-convex Maximization , 2006, ESA.

[18]  Samer Madanat,et al.  Optimal design of electric vehicle public charging system in an urban network for Greenhouse Gas Emission and cost minimization , 2017 .

[19]  Enjian Yao,et al.  Electric vehicles’ energy consumption estimation with real driving condition data , 2015 .

[20]  Huey-Kuo Chen,et al.  Heuristics for the stochastic/dynamic user-optimal route choice problem , 2000, Eur. J. Oper. Res..

[21]  Y. Nie,et al.  Shortest path problem considering on-time arrival probability , 2009 .

[22]  Konrad Reif,et al.  On the computation of the energy-optimal route dependent on the traffic load in Ingolstadt , 2013 .

[23]  Ayman Moawad,et al.  Vehicle energy consumption estimation using large scale simulations and machine learning methods , 2019, Transportation Research Part C: Emerging Technologies.

[24]  Agachai Sumalee,et al.  Network-wide on-line travel time estimation with inconsistent data from multiple sensor systems under network uncertainty , 2018 .

[25]  Xing Wu,et al.  Modeling Heterogeneous Risk-Taking Behavior in Route Choice: A Stochastic Dominance Approach , 2011 .

[26]  Xiang Li,et al.  An energy-efficient scheduling approach to improve the utilization of regenerative energy for metro systems , 2015 .

[27]  Thomas Engel,et al.  A novel eco-driving application to reduce energy consumption of electric vehicles , 2013, 2013 International Conference on Connected Vehicles and Expo (ICCVE).

[28]  A. Nazemi,et al.  An efficient dynamic model for solving the shortest path problem , 2013 .

[29]  Yafeng Yin,et al.  A prospect-based user equilibrium model with endogenous reference points and its application in congestion pricing , 2011 .

[30]  Xi Lin,et al.  Designing locations and capacities for charging stations to support intercity travel of electric vehicles: An expanded network approach , 2019 .

[31]  Hai-Jun Huang,et al.  An optimal charging station location model with the consideration of electric vehicle’s driving range , 2018 .

[32]  Enjian Yao,et al.  Modeling EV charging choice considering risk attitudes and attribute non-attendance , 2019, Transportation Research Part C: Emerging Technologies.

[33]  Hesham Rakha,et al.  Issues and Solutions to Macroscopic Traffic Dispersion Modeling , 2006 .

[34]  Mashrur Chowdhury,et al.  Utilizing real-time information transferring potentials to vehicles to improve the fast-charging process in electric vehicles , 2013 .

[35]  Zhaowang Ji,et al.  Path finding under uncertainty , 2005 .

[36]  Jie Sun,et al.  Stochastic Eco-routing in a Signalized Traffic Network , 2015 .

[37]  Jianhui Wang,et al.  Sustainability SI: Optimal Prices of Electricity at Public Charging Stations for Plug-in Electric Vehicles , 2016 .

[38]  Yafeng Yin,et al.  Network equilibrium models with battery electric vehicles , 2014 .

[39]  Yafeng Yin,et al.  A cost-competitiveness analysis of charging infrastructure for electric bus operations , 2018, Transportation Research Part C: Emerging Technologies.

[40]  Yafeng Yin,et al.  Optimal deployment of charging lanes for electric vehicles in transportation networks , 2016 .

[41]  Sebastien Blandin,et al.  A Tractable Class of Algorithms for Reliable Routing in Stochastic Networks , 2011 .

[42]  Xuesong Zhou,et al.  Finding the most reliable path with and without link travel time correlation: A Lagrangian substitution based approach , 2011 .

[43]  Qingquan Li,et al.  Reliable Shortest Path Problems in Stochastic Time-Dependent Networks , 2014, J. Intell. Transp. Syst..

[44]  Tetsuo Tezuka,et al.  Optimization of shared autonomous electric vehicles operations with charge scheduling and vehicle-to-grid , 2019, Transportation Research Part C: Emerging Technologies.

[45]  Michael W. Levin,et al.  Effect of Road Grade on Networkwide Vehicle Energy Consumption and Ecorouting , 2014 .

[46]  Z. Shen,et al.  Lagrangian relaxation for the reliable shortest path problem with correlated link travel times , 2017 .

[47]  John Smart,et al.  Energy impact evaluation for eco-routing and charging of autonomous electric vehicle fleet: Ambient temperature consideration , 2018 .

[48]  Ravi Seshadri,et al.  Finding most reliable paths on networks with correlated and shifted log–normal travel times , 2014 .

[49]  Ziyou Gao,et al.  The constrained shortest path problem with stochastic correlated link travel times , 2016, Eur. J. Oper. Res..

[50]  Daniela Giordano,et al.  Algorithms to find shortest and alternative paths in free flow and congested traffic regimes , 2016 .

[51]  Yafeng Yin,et al.  Assessing Performance Reliability of Road Networks Under Nonrecurrent Congestion , 2001 .

[52]  Moshe Ben-Akiva,et al.  Adaptive route choices in risky traffic networks: A prospect theory approach , 2010 .

[53]  Peter C. Nelson,et al.  Reliable route guidance: A case study from Chicago , 2012 .

[54]  Pitu B. Mirchandani,et al.  Shortest distance and reliability of probabilistic networks , 1976, Comput. Oper. Res..

[55]  B. Yu,et al.  A parallel improved ant colony optimization for multi-depot vehicle routing problem , 2011, J. Oper. Res. Soc..

[56]  Yuchuan Du,et al.  Optimal design of autonomous vehicle zones in transportation networks , 2017 .

[57]  Hai-Jun Huang,et al.  Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues , 2002 .

[58]  Randolph W. Hall,et al.  TRAVEL OUTCOME AND PERFORMANCE: THE EFFECT OF UNCERTAINTY ON ACCESSIBILITY , 1983 .

[59]  Wei Liu,et al.  Deployment of stationary and dynamic charging infrastructure for electric vehicles along traffic corridors , 2017 .

[60]  Konstantinos G. Zografos,et al.  An integrated modelling approach for the bicriterion vehicle routing and scheduling problem with environmental considerations , 2017 .

[61]  Tom Van Woensel,et al.  The dynamic shortest path problem with time-dependent stochastic disruptions , 2018, Transportation Research Part C: Emerging Technologies.

[62]  William H. K. Lam,et al.  A traffic flow simulator for short‐term travel time forecasting , 2002 .

[63]  Bin Yu,et al.  Transit route network design-maximizing direct and transfer demand density , 2012 .

[64]  Satish V. Ukkusuri,et al.  Dynamic system optimal model for multi-OD traffic networks with an advanced spatial queuing model , 2015 .

[65]  Hong Kam Lo,et al.  Modeling the impacts of speed limits on uncertain road networks , 2018 .

[66]  Qingquan Li,et al.  Shortest Path Finding Problem in Stochastic Time-Dependent Road Networks With Stochastic First-In-First-Out Property , 2013, IEEE Transactions on Intelligent Transportation Systems.

[67]  David P. Watling,et al.  User equilibrium traffic network assignment with stochastic travel times and late arrival penalty , 2006, Eur. J. Oper. Res..

[68]  William H. K. Lam,et al.  A model for assessing the effects of dynamic travel time information via variable message signs , 2001 .

[69]  Tie-Qiao Tang,et al.  Electric vehicle’s electricity consumption on a road with different slope , 2014 .

[70]  Jing Zhou,et al.  A decision-making rule for modeling travelers' route choice behavior based on cumulative prospect theory , 2011 .

[71]  Zhaowang Ji,et al.  Multi-objective alpha-reliable path finding in stochastic networks with correlated link costs: A simulation-based multi-objective genetic algorithm approach (SMOGA) , 2011, Expert Syst. Appl..

[72]  Emanuel Melachrinoudis,et al.  Facility Location and Reliable Route Planning in Hazardous Material Transportation , 1997, Transp. Sci..

[73]  Bin Yu,et al.  Bus arrival time prediction at bus stop with multiple routes , 2011 .

[74]  William H. K. Lam,et al.  A Reliability-Based Stochastic Traffic Assignment Model for Network with Multiple User Classes under Uncertainty in Demand , 2006 .

[75]  Qingquan Li,et al.  Finding Reliable Shortest Paths in Road Networks Under Uncertainty , 2013 .

[76]  Bi Yu Chen,et al.  Reliable shortest path finding in stochastic networks with spatial correlated link travel times , 2012, Int. J. Geogr. Inf. Sci..