Pareto-Optimal Sustainable Transportation Network Design under Spatial Queuing

Abstract This paper presents a multi-objective network design problem with environmental considerations for urban networks with queues. A spatial queuing link model is introduced to take account of the spatial effect of queuing. With this more realistic link performance function capturing spatial queuing, the network equilibrium flow patterns can be more accurately identified. Furthermore, to better estimate vehicle emissions, this paper proposes a refined emission estimation model, which distinguishes between travel speeds in free-running state and queue-forming state over a link. A multi-objective bi-level programming is then developed, in which the upper-level problem optimizes the investment decisions, whereas the lower-level problem characterizes the user equilibrium with spatial queuing delays. The metaheuristic of non-dominated sorting genetic algorithm II (NSGA-II) is adopted to solve the multi-objective network design problem. Numerical tests on the Sioux Falls network and the Barcelona network confirm the effectiveness of our proposed model and algorithm in identifying queuing equilibrium flows and Pareto optimal solutions. The refined models and valuable information about trade-offs among objectives are particularly helpful for environmentally sustainable transport network planning.

[1]  Shuai Li,et al.  Multi-objective optimal control formulations for bus service reliability with traffic signals , 2017 .

[2]  Hai Yang,et al.  An equivalent continuously differentiable model and a locally convergent algorithm for the continuous network design problem , 2001 .

[3]  Michiel C.J. Bliemer,et al.  Quasi-dynamic traffic assignment with residual point queues incorporating a first order node model , 2014 .

[4]  M. Bell.  STOCHASTIC USER EQUILIBRIUM ASSIGNMENT IN NETWORKS WITH QUEUES , 1995 .

[5]  Mike Smith,et al.  A link-based elastic demand equilibrium model with capacity constraints and queueing delays , 2013 .

[6]  Suh-Wen Chiou,et al.  Bilevel programming for the continuous transport network design problem , 2005 .

[7]  Yafeng Yin,et al.  Robust signal timing optimization with environmental concerns , 2013 .

[8]  Yasuo Asakura,et al.  Accuracy of Optimum Road Pricing considering Local Emissions of Road Traffic Network , 2009, CTS 2009.

[9]  Elena López,et al.  Integration of Sustainability Issues in Strategic Transportation Planning: A Multi-criteria Model for the Assessment of Transport Infrastructure Plans , 2010, Comput. Aided Civ. Infrastructure Eng..

[10]  W. Y. Szeto,et al.  The Chemical Reaction Optimization Approach to Solving the Environmentally Sustainable Network Design Problem , 2014, Comput. Aided Civ. Infrastructure Eng..

[11]  Mike Smith,et al.  The existence, uniqueness and stability of traffic equilibria , 1979 .

[12]  W. Y. Szeto,et al.  Reliability-based stochastic transit assignment with capacity constraints: Formulation and solution method , 2013 .

[13]  Hai Yang,et al.  Managing congestion and emissions in road networks with tolls and rebates , 2012 .

[14]  S. Lawphongpanich,et al.  Internalizing Emission Externality on Road Networks , 2006 .

[15]  Stef Proost,et al.  Optimizing Traffic System Performance with Environmental Constraints: Tolls and/or Additional Delays , 2020 .

[16]  Chao Yang,et al.  A review of sustainable network design for road networks , 2016 .

[17]  Yehuda Gur,et al.  Traffic Assignment which Considers Queue Formation , 1997 .

[18]  Nilay Noyan,et al.  Bi-level multi-objective traffic network optimisation with sustainability perspective , 2018, Expert Syst. Appl..

[19]  Stephen G. Ritchie,et al.  Surrogate-based optimization for the design of area charging schemes under environmental constraints , 2019, Transportation Research Part D: Transport and Environment.

[20]  P G Boulter,et al.  A review of instantaneous emission models for road vehicles , 2007 .

[21]  Francesco Viti,et al.  Repeated anticipatory network traffic control using iterative optimization accounting for model bias correction. , 2016 .

[22]  W. Y. Szeto,et al.  Review on Urban Transportation Network Design Problems , 2013 .

[23]  Larry J. LeBlanc,et al.  An Algorithm for the Discrete Network Design Problem , 1975 .

[24]  Shing Chung Josh Wong,et al.  Road Network Equilibrium Approaches to Environmental Sustainability , 2012 .

[25]  S. Wong,et al.  Environmentally Sustainable Toll Design for Congested Road Networks with Uncertain Demand , 2012 .

[26]  Antonino Vitetta,et al.  Signal setting with demand assignment: global optimization with day‐to‐day dynamic stability constraints , 2012 .

[27]  William H. K. Lam,et al.  CAPACITY-CONSTRAINED TRAFFIC ASSIGNMENT IN NETWORKS WITH RESIDUAL QUEUES , 2000 .

[28]  Sushant Sharma,et al.  Continuous Network Design with Emission Pricing as a Bi-Level Optimization Problem , 2006 .

[29]  N. Rouphail,et al.  Estimation of delays at traffic signals for variable demand conditions , 1993 .

[30]  Won-Kyu Kim,et al.  An equilibrium network design model with a social cost function for multimodal networks , 2006 .

[31]  Tschangho John Kim,et al.  Solving nonlinear bilevel programming models of the equilibrium network design problem: A comparative review , 1992, Ann. Oper. Res..

[32]  H. M. Zhang,et al.  Models and algorithms for the traffic assignment problem with link capacity constraints , 2004 .

[33]  W. Y. Szeto,et al.  Link-based system optimum dynamic traffic assignment problems with environmental objectives , 2016 .

[34]  Hong Kam Lo,et al.  Global Optimum of the Linearized Network Design Problem with Equilibrium Flows , 2010 .

[35]  W. Y. Szeto,et al.  A Sustainable Road Network Design Problem with Land Use Transportation Interaction over Time , 2015 .

[36]  Luc J. J. Wismans,et al.  Acceleration of Solving the Dynamic Multi-Objective Network Design Problem Using Response Surface Methods , 2014, J. Intell. Transp. Syst..

[37]  D. Bertsekas.  On the Goldstein-Levitin-Polyak gradient projection method , 1974, CDC 1974.

[38]  A. Nagurney.  Congested urban transportation networks and emission paradoxes , 2000 .

[39]  Shlomo Bekhor,et al.  An Alternative Approach for Solving the Environmentally-Oriented Discrete Network Design Problem , 2017 .

[40]  Tao Feng,et al.  Trade-offs between mobility and equity maximization under environmental capacity constraints: A case study of an integrated multi-objective model , 2014 .

[41]  Terry L. Friesz,et al.  A Simulated Annealing Approach to the Network Design Problem with Variational Inequality Constraints , 1992, Transp. Sci..

[42]  Michiel C.J. Bliemer,et al.  The multi-objective network design problem using minimizing externalities as objectives: comparison of a genetic algorithm and simulated annealing framework , 2018 .

[43]  Hai Yang,et al.  Traffic assignment and signal control in saturated road networks , 1995 .

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

[45]  Michiel C. J. Bliemer,et al.  Genetics of traffic assignment models for strategic transport planning , 2015 .

[46]  S. Travis Waller,et al.  Comparing Delay Minimization and Emissions Minimization in the Network Design Problem , 2012, Comput. Aided Civ. Infrastructure Eng..

[47]  Qiang Meng,et al.  General stochastic user equilibrium traffic assignment problem with link capacity constraints , 2008 .

[49]  Shing Chung Josh Wong,et al.  Reserve capacity of a signal-controlled road network , 1997 .

[50]  David E. Boyce,et al.  A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows , 1986 .

[51]  W. Y. Szeto,et al.  Multiobjective Environmentally Sustainable Road Network Design Using Pareto Optimization , 2017, Comput. Aided Civ. Infrastructure Eng..

[52]  M J Smith.  TRAFFIC CONTROL AND TRAFFIC ASSIGNMENT IN A SIGNAL-CONTROLLED NETWORK WITH QUEUEING , 1987 .

[53]  Hai Yang,et al.  Models and algorithms for road network design: a review and some new developments , 1998 .

[54]  W. Y. Szeto,et al.  Dynamic traffic assignment: A review of the methodological advances for environmentally sustainable road transportation applications , 2018 .

[55]  Qiang Meng,et al.  A Pareto-optimization approach for a fair ramp metering , 2010 .

[56]  Laurence R. Rilett,et al.  Traffic assignment under environmental and equity objectives , 1994 .

[57]  Mike J. Smith,et al.  Equilibrium in Capacitated Network Models with Queueing Delays, Queue-storage, Blocking Back and Control☆ , 2013 .

[58]  Francesco Viti,et al.  The Cost of Environmental Constraints in Traffic Networks: Assessing the Loss of Optimality , 2016 .

[59]  William H. K. Lam,et al.  Sustainable Transportation Network Design with Stochastic Demands and Chance Constraints , 2015 .

[60]  Thomas L. Magnanti,et al.  Network Design and Transportation Planning: Models and Algorithms , 1984, Transp. Sci..

[61]  Michael A Penic,et al.  TRANSYT-7F: ENHANCEMENT FOR FUEL CONSUMPTION, POLLUTION EMISSIONS, AND USER COSTS , 1992 .

[62]  Hirokazu Kato,et al.  Road Network Optimization Model with Consideration of Dynamic Changes in Long Term Evaluation for Developing Cities , 2009 .

[63]  Sushant Sharma,et al.  Multiobjective Network Design for Emission and Travel-Time Trade-off for a Sustainable Large Urban Transportation Network , 2011 .

[64]  Patrice Marcotte,et al.  Hyperpath Formulations of Traffic Assignment Problems , 1998 .

[65]  J. Wardrop.  ROAD PAPER. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH. , 1952 .