18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, ATMOS 2018, August 23-24, 2018, Helsinki, Finland

This paper addresses the capacity planning problem of coordinating train services and network maintenance windows for a railway system. We present model reformulations, for a mixed integer linear optimization model, which give a mathematically stronger model and substantial improvements in solving performance – as demonstrated with computational experiments on a set of synthetic test instances. As a consequence, more instances can be solved to optimality within a given time limit and the optimality gap can be reduced quicker. 2012 ACM Subject Classification Applied computing → Transportation

[1]  Ding-Wei Huang,et al.  Lane-changing behavior on highways. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Gerd Wanielik,et al.  Situation Assessment for Automatic Lane-Change Maneuvers , 2010, IEEE Transactions on Intelligent Transportation Systems.

[3]  Roberto Roberti,et al.  An Exact Algorithm for the Two-Echelon Capacitated Vehicle Routing Problem , 2013, Oper. Res..

[4]  Joan Feigenbaum,et al.  On graph problems in a semi-streaming model , 2005, Theor. Comput. Sci..

[5]  Till Fluschnik,et al.  On the Computational Complexity of Length- and Neighborhood-Constrained Path Problems , 2020, Inf. Process. Lett..

[6]  Bruce Hoppe,et al.  Efficient Dynamic Network Flow Algorithms , 1995 .

[7]  José R. Correa,et al.  Dynamic Equilibria in Fluid Queueing Networks , 2014, Oper. Res..

[8]  Guido Perboli,et al.  New Families of Valid Inequalities for the Two-Echelon Vehicle Routing Problem , 2010, Electron. Notes Discret. Math..

[9]  José Eugenio Naranjo,et al.  Lane-Change Fuzzy Control in Autonomous Vehicles for the Overtaking Maneuver , 2008, IEEE Transactions on Intelligent Transportation Systems.

[10]  Michael R. Bussieck,et al.  Optimal Lines in Public Rail Transport , 1998 .

[11]  H. Fleischner Eulerian graphs and related topics , 1990 .

[12]  Russell Impagliazzo,et al.  Which Problems Have Strongly Exponential Complexity? , 2001, J. Comput. Syst. Sci..

[13]  Richard M. Wilson,et al.  Graph puzzles, homotopy, and the alternating group☆ , 1974 .

[14]  Rolf H. Möhring,et al.  The Modeling Power of the Periodic Event Scheduling Problem: Railway Timetables - and Beyond , 2004, ATMOS.

[15]  Gregory Gutin,et al.  Rural postman parameterized by the number of components of required edges , 2017, J. Comput. Syst. Sci..

[16]  Bin Ran,et al.  Modelling Dynamic Transportation Networks with Variational Inequalities , 2018 .

[17]  Maria Grazia Speranza,et al.  A survey on two-echelon routing problems , 2015, Comput. Oper. Res..

[18]  René van Bevern,et al.  The parameterized complexity of finding secluded solutions to some classical optimization problems on graphs , 2018, Discret. Optim..

[19]  老子,et al.  The simple way , 1913 .

[20]  Leo Kroon,et al.  A Cycle Based Optimization Model for the Cyclic Railway Timetabling Problem , 2001 .

[21]  A. Amditis,et al.  Towards Manoeuver Negotiation: AutoNet2030 Project from a Car Maker Perspective , 2016 .

[22]  Philip N. Klein,et al.  A subexponential parameterized algorithm for Subset TSP on planar graphs , 2014, SODA.

[23]  Anita Schöbel,et al.  A Matching Approach for Periodic Timetabling , 2016, ATMOS.

[24]  Lucas P. Veelenturf,et al.  Passenger oriented railway disruption management by adapting timetables and rolling stock schedules , 2017 .

[25]  D. R. Fulkerson,et al.  Constructing Maximal Dynamic Flows from Static Flows , 1958 .

[26]  Stefan Kratsch,et al.  Recent developments in kernelization: A survey , 2014, Bull. EATCS.

[27]  Christian Liebchen,et al.  Periodic Timetable Optimization in Public Transport , 2006, OR.

[28]  Martin Skutella,et al.  An Introduction to Network Flows over Time , 2008, Bonn Workshop of Combinatorial Optimization.

[29]  Ronald Koch,et al.  Nash Equilibria and the Price of Anarchy for Flows over Time , 2011, Theory of Computing Systems.

[30]  Daniele Vigo,et al.  The Two-Echelon Capacitated Vehicle Routing Problem: Models and Math-Based Heuristics , 2011, Transp. Sci..

[31]  Umit Ozguner,et al.  On optimal design of a lane change controller , 1995, Proceedings of the Intelligent Vehicles '95. Symposium.

[32]  Martin Skutella,et al.  Fast and Memory-Efficient Algorithms for Evacuation Problems , 2017, SODA.

[33]  Teodor Gabriel Crainic,et al.  Bounds for the Two-EchelonVehicle Routing Problem , 2008 .

[34]  Yves Rochat,et al.  Probabilistic diversification and intensification in local search for vehicle routing , 1995, J. Heuristics.

[35]  Gregory Gutin,et al.  Parameterized complexity of the k-arc Chinese Postman Problem , 2017, J. Comput. Syst. Sci..

[36]  Marc E. Pfetsch,et al.  The Line Connectivity Problem , 2009 .

[37]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[38]  Bojan Mohar,et al.  The Minor Crossing Number , 2006, SIAM J. Discret. Math..

[39]  Leon W P Peeters,et al.  Cyclic Railway Timetable Optimization , 2003 .

[40]  Ralf Borndörfer,et al.  Passenger routing for periodic timetable optimization , 2017, Public Transp..

[41]  Marie Schmidt,et al.  Timetabling with passenger routing , 2015, OR Spectr..

[42]  David Peleg,et al.  Secluded Connectivity Problems , 2013, ESA.

[43]  Stephen T. Hedetniemi,et al.  Independence and Irredundance in k-Regular Graphs , 1998, Ars Comb..

[44]  Gregory Gutin,et al.  The Mixed Chinese Postman Problem Parameterized by Pathwidth and Treedepth , 2016, SIAM J. Discret. Math..

[45]  Rolf Niedermeier,et al.  Efficient Algorithms for Eulerian Extension , 2010, WG.

[46]  José R. Correa,et al.  Long Term Behavior of Dynamic Equilibria in Fluid Queuing Networks , 2017, IPCO.

[47]  Teodor Gabriel Crainic,et al.  An adaptive large neighborhood search heuristic for Two-Echelon Vehicle Routing Problems arising in city logistics , 2012, Comput. Oper. Res..

[48]  Stefan Kratsch,et al.  Compression via Matroids: A Randomized Polynomial Kernel for Odd Cycle Transversal , 2011, TALG.

[49]  T. Crainic,et al.  GRASP with Path Relinking for the Two-Echelon Vehicle Routing Problem , 2013 .

[50]  Fahad Panolan,et al.  Lossy kernelization , 2016, STOC.

[51]  Walter Ukovich,et al.  A Mathematical Model for Periodic Scheduling Problems , 1989, SIAM J. Discret. Math..

[52]  Gregory Gutin,et al.  Parameterized complexity of k-Chinese Postman Problem , 2013, Theor. Comput. Sci..

[53]  Kangzhou Wang,et al.  Matheuristic for a two-echelon capacitated vehicle routing problem with environmental considerations in city logistics service , 2017 .

[54]  Anita Schöbel,et al.  Line planning in public transportation: models and methods , 2012, OR Spectr..

[55]  Martin Skutella,et al.  Multicommodity flows over time: Efficient algorithms and complexity , 2003, Theor. Comput. Sci..

[56]  Manfred K. Warmuth,et al.  NxN Puzzle and Related Relocation Problem , 1990, J. Symb. Comput..

[57]  Manfred K. Warmuth,et al.  Finding a Shortest Solution for the N × N Extension of the 15-PUZZLE Is Intractable , 1986, AAAI.

[58]  Éva Tardos,et al.  “The quickest transshipment problem” , 1995, SODA '95.

[59]  Petr A. Golovach,et al.  Finding Connected Secluded Subgraphs , 2017, IPEC.

[60]  Stefan Kratsch,et al.  Kernelization Lower Bounds by Cross-Composition , 2012, SIAM J. Discret. Math..

[61]  Xi Wu,et al.  A Completeness Theory for Polynomial (Turing) Kernelization , 2013, Algorithmica.

[62]  K. Wagner Über eine Eigenschaft der ebenen Komplexe , 1937 .

[63]  Trevor Wilson,et al.  Driving strategies in overtaking , 1982 .

[64]  Kay W. Axhausen,et al.  The Multi-Agent Transport Simulation , 2016 .

[65]  András Frank,et al.  An application of simultaneous diophantine approximation in combinatorial optimization , 1987, Comb..

[66]  Leo G. Kroon,et al.  On solving multi-type railway line planning problems , 2006, Eur. J. Oper. Res..

[67]  Simon Spoorendonk,et al.  A Branch-and-Cut Algorithm for the Symmetric Two-Echelon Capacitated Vehicle Routing Problem , 2013, Transp. Sci..

[68]  Kai Nagel,et al.  Two-lane traffic rules for cellular automata: A systematic approach , 1997, cond-mat/9712196.

[69]  D. R. Fulkerson,et al.  Flows in Networks. , 1964 .

[70]  Leo G. Kroon,et al.  A Variable Trip Time Model for Cyclic Railway Timetabling , 2003, Transp. Sci..

[71]  K. Nachtigall Periodic network optimizationi and fixed interval timetables , 1999 .

[72]  Carlos F. Daganzo,et al.  Lane-changing in traffic streams , 2006 .

[73]  Anita Schöbel,et al.  Evaluating line concepts using travel times and robustness , 2013, Public Transp..

[74]  János Pach,et al.  Improving the Crossing Lemma by Finding More Crossings in Sparse Graphs , 2006, Discret. Comput. Geom..

[75]  Ece Guran Schmidt,et al.  Lane Change Scheduling for Autonomous Vehicles , 2016 .

[76]  Rolf Niedermeier,et al.  Invitation to data reduction and problem kernelization , 2007, SIGA.

[77]  H. Rademacher Über partielle und totale differenzierbarkeit von Funktionen mehrerer Variabeln und über die Transformation der Doppelintegrale , 1919 .

[78]  Thibaut Vidal,et al.  A large neighbourhood based heuristic for two-echelon routing problems , 2015, Comput. Oper. Res..

[79]  Kai Nagel,et al.  High-speed microsimulations of traffic flow , 1995 .

[80]  Petr A. Golovach,et al.  Parameterized Complexity of Secluded Connectivity Problems , 2015, Theory of Computing Systems.

[81]  Philine Schiewe,et al.  Look-Ahead Approaches for Integrated Planning in Public Transportation , 2017, ATMOS.

[82]  Gregory Gutin,et al.  Parameterized Traveling Salesman Problem: Beating the Average , 2016, SIAM J. Discret. Math..

[83]  Karl Nachtigall,et al.  Solving Periodic Timetable Optimisation Problems by Modulo Simplex Calculations , 2008, ATMOS.

[84]  Li Gao,et al.  Research on Information Processing of Intelligent Lane-Changing Behaviors for Unmanned Ground Vehicles , 2016, 2016 9th International Symposium on Computational Intelligence and Design (ISCID).

[85]  Michel Gendreau,et al.  An adaptive large neighborhood search for the two-echelon multiple-trip vehicle routing problem with satellite synchronization , 2016, Eur. J. Oper. Res..

[86]  Anita Schöbel,et al.  An eigenmodel for iterative line planning, timetabling and vehicle scheduling in public transportation , 2017 .

[87]  Teodor Gabriel Crainic,et al.  Multi-start Heuristics for the Two-Echelon Vehicle Routing Problem , 2011, EvoCOP.

[88]  José R. Correa,et al.  Existence and Uniqueness of Equilibria for Flows over Time , 2011, ICALP.

[89]  Anita Schöbel,et al.  Improving the modulo simplex algorithm for large-scale periodic timetabling , 2013, Comput. Oper. Res..

[90]  Tim Roughgarden,et al.  Selfish routing and the price of anarchy , 2005 .

[91]  Masayoshi Tomizuka,et al.  Vehicle Lane Change Maneuver In Automated Highway Systems , 1994 .