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Mixed-integer Programming Based Approaches for the Movement Planner Problem: Model , Heuristics and Decomposition B

Mixed-integer Programming Based Approaches for the Movement Planner Problem: Model , Heuristics and Decomposition Bamboo@Tsinghua. Chiwei Yan Department of Civil & Environmental Engineering Massachusetts Institute of Technology. Luyi Yang

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Mixed-integer Programming Based Approaches for the Movement Planner Problem: Model , Heuristics and Decomposition B

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  1. Mixed-integer Programming Based Approaches for the Movement Planner Problem: Model, Heuristics and DecompositionBamboo@Tsinghua ChiweiYan Department of Civil & Environmental EngineeringMassachusetts Institute of Technology LuyiYang The University of ChicagoBooth School of Business RAS Problem Solving Competition 2012

  2. Problem Formulation: Definition of Segments • Acollection of tracks (main tracks, sidings, switches, crossovers) between two adjacent nodes • A train must pass through everysegment between its origin and destination and travel on one specific track within a given segment.

  3. Notation entry (exit) time for train at segment

  4. Mixed-integer Linear Programming Model schedule deviance train delay TWT deviance unpreferred track time

  5. Mixed-integer Linear Programming Model

  6. Mixed-integer Linear Programming Model

  7. Solution Approaches • Combinatorially difficult to solve • Even the smallest test instance requires more than one hourin our implementation! • What we propose: • Formulation enhancement • Heuristic variable fixing procedure • Decomposition algorithm

  8. Solution Approaches: Formulation Enhancement • Dominance transitivity • No delays at intermediate nodes = • Fixing MOW-related variables • Fine-tuning big-M

  9. Solution Approaches: Heuristic Variable Fixing • Imposing dominance for “distant” trains If the lower bounds are too far apart, there is little chance for the later train to catch up … • Prohibiting unattractive overtakes • Entry time is no later • Type priority is no lower • Origin is no farther • Estimating what to be realized prior to the end of planning horizon

  10. Solution Approaches: Decomposition Algorithm End of Iteration 1 End of Iteration 2 End of Iteration 3 End of Planning Horizon Time Axis roll back ratio

  11. Computational Results • Implementation: C++ and ILOG CPLEX 12.1 • Platform: a PC with 2.40 GHz CPU and 4GB RAM • Maximum computational time: 1 hour

  12. Concluding Remarks • Successfully formulate the Movement Planner Problem as MILP • To solve the problem, we propose • Formulation enhancement • Heuristic variable fixing • Decomposition algorithm • Summary of computational results • Expedite the search for optimal solutions by a factor of 400 for Data Set 1 • Obtain satisficing solutions for larger instances Data Set 2: less than 30 seconds Data Set 3: less than 2.5 minutes

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