A modified Physarum-inspired model for the user equilibrium traffic assignment problem

Abstract The user equilibrium traffic assignment principle is very important in the traffic assignment problem. Mathematical programming models are designed to solve the user equilibrium problem in traditional algorithms. Recently, the Physarum shows the ability to address the user equilibrium and system optimization traffic assignment problems. However, the Physarum model are not efficient in real traffic networks with two-way traffic characteristics and multiple origin–destination pairs. In this article, a modified Physarum -inspired model for the user equilibrium problem is proposed. By decomposing traffic flux based on origin nodes, the traffic flux from different origin–destination pairs can be distinguished in the proposed model. The Physarum can obtain the equilibrium traffic flux when no shorter path can be discovered between each origin–destination pair. Finally, numerical examples demonstrate the rationality and convergence properties of the proposed model.

[1]  Michael Florian,et al.  A New Look at Projected Gradient Method for Equilibrium Assignment , 2009 .

[2]  A. Tero,et al.  A mathematical model for adaptive transport network in path finding by true slime mold. , 2007, Journal of theoretical biology.

[3]  Sankaran Mahadevan,et al.  A Biologically Inspired Network Design Model , 2015, Scientific Reports.

[4]  Wei Wang,et al.  Alternative Quasi-Newton Methods for Capacitated User Equilibrium Assignment , 2003 .

[5]  Keechoo Choi,et al.  A modified gradient projection algorithm for solving the elastic demand traffic assignment problem , 2014, Comput. Oper. Res..

[6]  Suh-Wen Chiou,et al.  An efficient algorithm for computing traffic equilibria using TRANSYT model , 2010 .

[7]  Matteo Matteucci,et al.  An ant colony system for transportation user equilibrium analysis in congested networks , 2013, Swarm Intelligence.

[8]  Yong Deng,et al.  A Bio-Inspired Method for the Constrained Shortest Path Problem , 2014, TheScientificWorldJournal.

[9]  Gary L. Miller,et al.  Approaching Optimality for Solving SDD Linear Systems , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[10]  Andrew Adamatzky,et al.  Physarum in silicon: the Greek motorways study , 2014, Natural Computing.

[11]  John E. Warnock,et al.  Dynamic modeling , 1977, SIGGRAPH.

[12]  Javier J. Sánchez Medina,et al.  User Equilibrium Study of AETROS Travel Route Optimization System , 2011, EUROCAST.

[13]  T. Koopmans,et al.  Studies in the Economics of Transportation. , 1956 .

[14]  Hillel Bar-Gera,et al.  Convergence of Traffic Assignments: How Much Is Enough? 1 , 2004 .

[15]  Mariano Gallo,et al.  An Ant Colony Optimisation algorithm for solving the asymmetric traffic assignment problem , 2012, Eur. J. Oper. Res..

[16]  Andrew Schumann,et al.  Logical Modelling of Physarum Polycephalum , 2011, ArXiv.

[17]  Yu Luo,et al.  An improved method to rank generalized fuzzy numbers with different left heights and right heights , 2015, J. Intell. Fuzzy Syst..

[18]  Hillel Bar-Gera,et al.  Origin-based Algorithms for Transportation Network Modelling , 1999 .

[19]  Hillel Bar-Gera,et al.  Origin-Based Algorithm for the Traffic Assignment Problem , 2002, Transp. Sci..

[20]  Andrew Adamatzky,et al.  Physarum machines: encapsulating reaction–diffusion to compute spanning tree , 2007, Naturwissenschaften.

[21]  Kurt Mehlhorn,et al.  Physarum can compute shortest paths , 2011, SODA.

[22]  Eduardo Reck Miranda,et al.  Music with Unconventional Computing: Towards a Step Sequencer from Plasmodium of Physarum Polycephalum , 2015, EvoMUSART.

[23]  Per Olov Lindberg,et al.  The Stiff Is Moving - Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment , 2013, Transp. Sci..

[24]  Andrew Adamatzky,et al.  Bioevaluation of World Transport Networks , 2012 .

[25]  Suh-Wen Chiou.  An efficient algorithm for optimal design of area traffic control with network flows , 2009 .

[26]  Athanasios K. Ziliaskopoulos,et al.  A Linear Programming Model for the Single Destination System Optimum Dynamic Traffic Assignment Problem , 2000, Transp. Sci..

[27]  Andrew Adamatzky,et al.  Slime Mold Solves Maze in One Pass, Assisted by Gradient of Chemo-Attractants , 2011, IEEE Transactions on NanoBioscience.

[28]  R. Jayakrishnan,et al.  A FASTER PATH-BASED ALGORITHM FOR TRAFFIC ASSIGNMENT , 1994 .

[29]  T. Koopmans,et al.  Studies in the Economics of Transportation. , 1956 .

[30]  Peter M. A. Sloot,et al.  Bio-Development of Motorway Network in the Netherlands: a slime mould Approach , 2013, Adv. Complex Syst..

[31]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[32]  David E. Boyce,et al.  Comparison of Disaggregate Simplicial Decomposition and Frank-Wolfe Algorithms for User-Optimal Route Choice , 1998 .

[33]  Eduardo Reck Miranda,et al.  Harnessing the Intelligence of Physarum Polycephalum for Unconventional Computing-Aided Musical Composition , 2014, Int. J. Unconv. Comput..

[34]  Dung-Ying Lin,et al.  An N-path user equilibrium for transportation networks , 2014 .

[35]  D. Bertsekas,et al.  Projection methods for variational inequalities with application to the traffic assignment problem , 1982 .

[36]  Robert B. Dial,et al.  A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration , 2006 .

[37]  A. Tero,et al.  Rules for Biologically Inspired Adaptive Network Design , 2010, Science.

[38]  Zili Zhang,et al.  A biologically inspired solution for fuzzy shortest path problems , 2013, Appl. Soft Comput..

[39]  Jeff Jones,et al.  Programmable reconfiguration of Physarum machines , 2009, Natural Computing.

[40]  Andrew Adamatzky,et al.  Towards Physarum Robots: Computing and Manipulating on Water Surface , 2008, ArXiv.

[41]  W. G. Hansen.  How Accessibility Shapes Land Use , 1959 .

[42]  Markos Papageorgiou,et al.  Dynamic modeling, assignment, and route guidance in traffic networks , 1990 .

[43]  S. Stephenson,et al.  Myxomycetes: A Handbook of Slime Molds , 1994 .

[44]  J G Wardrop,et al.  CORRESPONDENCE. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH. , 1952 .

[45]  Qing Wang,et al.  A Biologically Inspired Optimization Algorithm for Solving Fuzzy Shortest Path Problems with Mixed Fuzzy Arc Lengths , 2014, J. Optim. Theory Appl..

[46]  Torbjörn Larsson,et al.  Simplicial Decomposition with Disaggregated Representation for the Traffic Assignment Problem , 1992, Transp. Sci..

[47]  Xiaoge Zhang,et al.  An improved bio-inspired algorithm for the directed shortest path problem. , 2014, Bioinspiration & biomimetics.

[48]  Andrew Schumann,et al.  PHYSARUM SPATIAL LOGIC , 2011 .

[49]  Qing Wang,et al.  An anticipation mechanism for the shortest path problem based on Physarum polycephalum , 2015, Int. J. Gen. Syst..

[50]  J. A. Ventura,et al.  Finiteness in restricted simplicial decomposition , 1985 .

[51]  Jonathan M. Bunker,et al.  Transit Users’ Route‐Choice Modelling in Transit Assignment: A Review , 2010 .

[52]  Carlos Sun,et al.  COMPUTATIONAL STUDY OF A PATH-BASED ALGORITHM AND ITS VARIANTS FOR STATIC TRAFFIC ASSIGNMENT , 1996 .

[53]  Jeff Jones,et al.  On using compressibility to detect when slime mould completed computation , 2016, Complex..

[54]  Andrew Adamatzky,et al.  Slime mould imitates development of Roman roads in the Balkans , 2015 .

[55]  Ziyou Gao,et al.  An improved origin-based algorithm for solving the combined distribution and assignment problem , 2008, Eur. J. Oper. Res..

[56]  Moises Diaz-Cabrera,et al.  User equilibrium study of AETROS travel route optimization system , 2011, EUROCAST 2011.

[57]  T. Nakagaki,et al.  Intelligence: Maze-solving by an amoeboid organism , 2000, Nature.

[58]  Eduardo Reck Miranda,et al.  Music with Unconventional Computing: A System for Physarum Polycephalum Sound Synthesis , 2013, CMMR.

[59]  Larry J. LeBlanc,et al.  AN EFFICIENT APPROACH TO SOLVING THE ROAD NETWORK EQUILIBRIUM TRAFFIC ASSIGNMENT PROBLEM. IN: THE AUTOMOBILE , 1975 .

[60]  Chen Zhao,et al.  Analysis of the Chinese Airline Network as multi-layer networks , 2016 .

[61]  Xiaoge Zhang.  An Efficient Physarum Algorithm for Solving the Bicriteria Traffic Assignment Problem , 2015, Int. J. Unconv. Comput..