Pareto Optimal Path Generation Algorithm in Stochastic Transportation Networks

Routing problems play a crucial part in urban transportation network operation and management. This study addresses the problem of finding a set of non-dominated shortest paths in stochastic transportation networks. Instead of the previous practice of assuming the travel time variability to be tracked by a known probability density function, it is extracted from the existing correlation between the traffic flow and the corresponding links’ time. The time horizon is divided into time intervals/slots in which the network is assumed to experience a static traffic equilibrium with different traffic conditions for each slot. Starting with Priori demand information, prior generated paths, and a chosen traffic assignment method, the proposed methodology conducts successive simulations to the network intervals. It manages to draw both links and paths probability distribution of their travel time considering the correlation among them. Then, multi-objective analysis is conducted on the generated paths to produce the Pareto-optimal set for each demand node pair in the network. Numerical studies are conducted to show the methodology efficiency and generality for any network. The expected travel time and the reliability could be drawn for each path in the network.

[1]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[2]  R Bellman,et al.  On the Theory of Dynamic Programming. , 1952, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Stephen D. Boyles,et al.  An outer approximation algorithm for the robust shortest path problem , 2013 .

[4]  George F. List,et al.  An Information-Theoretic Sensor Location Model for Traffic Origin-Destination Demand Estimation Applications , 2010, Transp. Sci..

[5]  Ziyou Gao,et al.  Finding Most Reliable Path With Extended Shifted Lognormal Distribution , 2018, IEEE Access.

[6]  Elise Miller-Hooks,et al.  Adaptive least-expected time paths in stochastic, time-varying transportation and data networks , 2001, Networks.

[7]  Martin W. P. Savelsbergh,et al.  Proactive route guidance to avoid congestion , 2016 .

[8]  Enrique F. Castillo,et al.  Traffic Estimation and Optimal Counting Location Without Path Enumeration Using Bayesian Networks , 2008, Comput. Aided Civ. Infrastructure Eng..

[9]  Hani S. Mahmassani,et al.  Dynamic origin-destination demand estimation using automatic vehicle identification data , 2006, IEEE Transactions on Intelligent Transportation Systems.

[10]  Hani S. Mahmassani,et al.  Simulation-Based Method for Finding Minimum Travel Time Budget Paths in Stochastic Networks with Correlated Link Times , 2014 .

[11]  Giuseppe Confessore,et al.  A Network Based Model for Traffic Sensor Location with Implications on O/D Matrix Estimates , 2001, Transp. Sci..

[12]  Mahmoud Owais,et al.  Issues Related to Transit Network Design Problem , 2015 .

[13]  Maria Grazia Speranza,et al.  Congestion avoiding heuristic path generation for the proactive route guidance , 2018, Comput. Oper. Res..

[14]  Ariel Orda,et al.  Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length , 1990, JACM.

[15]  Hani S. Mahmassani,et al.  Path Finding in Stochastic Time Varying Networks with Spatial and Temporal Correlations for Heterogeneous Travelers , 2016 .

[16]  Warrren B Powell,et al.  The Convergence of Equilibrium Algorithms with Predetermined Step Sizes , 1982 .

[17]  Mahmoud Owais,et al.  Complete hierarchical multi-objective genetic algorithm for transit network design problem , 2018, Expert Syst. Appl..

[18]  Enrique Castillo,et al.  Optimal traffic plate scanning location for OD trip matrix and route estimation in road networks , 2010 .

[19]  Song Gao,et al.  Optimal paths in dynamic networks with dependent random link travel times , 2012 .

[20]  Khaled F. Hussain,et al.  Sensor location model for O/D estimation: Multi-criteria meta-heuristics approach , 2019, Operations Research Perspectives.

[21]  Khaled F. Hussain,et al.  Robust Deep Learning Architecture for Traffic Flow Estimation from a Subset of Link Sensors , 2020 .

[22]  J. Y. Yen,et al.  Finding the K Shortest Loopless Paths in a Network , 2007 .

[23]  Chelsea C. White,et al.  Optimal vehicle routing with real-time traffic information , 2005, IEEE Transactions on Intelligent Transportation Systems.

[24]  Tao Ma,et al.  Dynamic factor model for network traffic state forecast , 2018, Transportation Research Part B: Methodological.

[25]  Mahmoud Owais,et al.  Location Strategy for Traffic Emission Remote Sensing Monitors to Capture the Violated Emissions , 2019, Journal of Advanced Transportation.

[26]  Khaled Abdelghany,et al.  An iterative learning approach for network contraction: Path finding problem in stochastic time‐varying networks , 2019, Comput. Aided Civ. Infrastructure Eng..

[27]  Liping Fu,et al.  An adaptive routing algorithm for in-vehicle route guidance system with real-time information , 2001 .

[28]  Zhaowang Ji,et al.  Finding multi-objective paths in stochastic networks: a simulation-based genetic algorithm approach , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[29]  John N. Tsitsiklis,et al.  Dynamic Shortest Paths in Acyclic Networks with Markovian Arc Costs , 1993, Oper. Res..

[30]  Otto Anker Nielsen,et al.  Stochastic user equilibrium with equilibrated choice sets: Part II – Solving the restricted SUE for the logit family , 2015 .

[31]  Chang Wook Ahn,et al.  Multi-objective path finding in stochastic time-dependent road networks using non-dominated sorting genetic algorithm , 2015, Expert Syst. Appl..

[32]  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..

[33]  Enrique Castillo,et al.  Trip matrix and path flow reconstruction and estimation based on plate scanning and link observations , 2008 .

[34]  Ning Wang,et al.  Model to Locate Sensors for Estimation of Static Origin–Destination Volumes Given Prior Flow Information , 2012 .

[35]  Shirish S. Joshi,et al.  A Mean-Variance Model for Route Guidance in Advanced Traveler Information Systems , 2001, Transp. Sci..

[36]  Yueyue Fan,et al.  Shortest paths in stochastic networks with correlated link costs , 2005 .

[37]  Marco Sciandrone,et al.  A computational study of path-based methods for optimal traffic assignment with both inelastic and elastic demand , 2019, Comput. Oper. Res..

[38]  Hani S. Mahmassani,et al.  Time dependent, shortest-path algorithm for real-time intelligent vehicle highway system applications , 1993 .

[39]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[40]  Randolph W. Hall,et al.  The Fastest Path through a Network with Random Time-Dependent Travel Times , 1986, Transp. Sci..

[41]  Hani S. Mahmassani,et al.  Least Expected Time Paths in Stochastic, Time-Varying Transportation Networks , 1999, Transp. Sci..

[42]  Enrique F. Castillo,et al.  The Observability Problem in Traffic Models: Algebraic and Topological Methods , 2008, IEEE Transactions on Intelligent Transportation Systems.

[43]  Xing Wu,et al.  Reliable a Priori Shortest Path Problem with Limited Spatial and Temporal Dependencies , 2009 .

[44]  Taher Hassan,et al.  Incorporating Dynamic Bus Stop Simulation into Static Transit Assignment Models , 2018 .