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Técnicas Distribuidas para Problemas de Scheduling a Gran Escala

Técnicas Distribuidas para Problemas de Scheduling a Gran Escala. GTI-IA, DSIC. Miguel A. Salido, M. Abril, F. Barber, P. Tormos, A. Llova, L. Ingolotti. Univerisdad Politécnica de Valencia España. IV Workshop Planificación, Scheduling y Razonamiento Temporal

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Técnicas Distribuidas para Problemas de Scheduling a Gran Escala

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  1. Técnicas Distribuidas para Problemas de Scheduling a Gran Escala GTI-IA, DSIC Miguel A. Salido, M. Abril, F. Barber, P. Tormos, A. Llova, L. Ingolotti Univerisdad Politécnica de Valencia España IV Workshop Planificación, Scheduling y Razonamiento Temporal Santiago de Compostela, 15 de Noviembre de 2005

  2. Índice 1. Introducción 2. Modelo Distribuido 3. Ejemplo 4. Planificación de Rutas ferroviarias 5. Evaluación 6. Conclusiones y Trabajo Futuro Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  3. Railway Scheduling Problem • Variables: departure & arrival time at stations • Domain: Integers • Constraints: • Railway infrastructure • User Requirements • Traffic Rules • Graph Partitioning • Objective: Divide the graph into a set of regions: • Each region has roughly the same number of nodes • The sum of all edges connecting different regions is minimized. Definitions • CSP • Variables: x1, x2, ....., xn • Domains : xiDi:{ai, bi} : i=1..n • Constraints: {c1,c2,..,ck} Distributed CSP Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  4. Distributed CSP A distributed CSP is a CSP in which the variables and constraints are distributed among block agents and there are interagent constraints. • A block agent is a virtual entity that essentially has the following properties: autonomy, sociability, reactivity and pro-activity. • Each block agent has a semi-independent subproblem (variables and constraints) and attempts to determine the variable values. • these values must also satisfy the interagent constraints. Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  5. Distributed Model Preprocessing Agent Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  6. Preprocessing Agent • Preprocessing Agent carries out a partition of the original problem in semi-independent subproblems. • It uses a graph partitioning software called METIS*. • METIS solves the partition problem efficiently. 14.000 nodes 2 seconds 410.000 edges *www-users.cs.umn.edu/karypis/metis/index.html Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  7. Subproblem Constraints involved Agent Id. Block Agents Subproblem c1:2x1+x3+2x5 c2:x1-x3 c3:x3-2x5+x7 c4:2x3+x5-2x7 Var:x1,x3,x5,x7 c5:x1+4x2+2x5 c6:x1+x2+x3 c7:3x1-2x7+x8 c8:2x3+x5-2x7 c9:2x2+x3-2x8 Used Variables:x1,x3,x5,x7 x1 x3 x5 x7 x2 x4 x8 New Variables:x2,x4,x8 (3,-,1,-,2,-,3,-,...) (3,4,1,1,2,-,3,-2,...) Domains: x2,x4,x8 Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  8. (-,2,2) (-,2,3) (3,1,1) (1,2,2) Example Three variables: x1, x2, x3 Domains: d1:{1,2,3} d2:{1,2} d3:{1,2,3} Constraints: c1: x2 = x3 c2: x1 ≠ x2 (-,1,2) (-,2,1) (-,1,1) (2,2,2) (1,1,1) (2,1,1) (3,2,2) Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  9. Initial departure time Periodic Trains (frequency) or not One, two-way tracks Halts (only commercial stops) New Trains to be added Stations (crossing and overtaking) Railway Scheduling Problem TIME Over a set of previously scheduled trains The problem:To assist to railway managers in order to obtain a correct railway schedule. Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  10. Our Approach: CSP • The railway scheduling problem as a Constraint Satisfaction Problem: • Variables(departure & arrival time to stations): {Traini_Arrivalj, Traini_Departurej} • Interpretation domain: Integers • Constraints: • Infrastructure Constraints: • Travel time between stations. • Maintenance times • Number of tracks in stations and sections,… • Traffic constraints: • Crossing and Overtaking. • Reception-time, Expedition-time. • Succession time between two consecutive trains,… • User Requirements: • Initial departure of first train, frequency, maximum travel time. • Type and Number of trains. • Commercial Stops,… Exponential Search Space In typical and simple cases thousands and thousands of alternatives Distributed CSP Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  11. How distribute the problem? • The preprocessing agent carries out the partition by means of METIS • The preprocessing agent carries out the partition by means of METIS • It divides the running map into clusters composed by contiguos stations Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  12. How distribute the problem? • The preprocessing agent carries out the partition by type of train Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  13. Random Problems > < n,a,p > n: variables a: arity p: partition size < < < < < < < < < Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  14. Distributed Railway Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  15. Distributed Railway Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  16. Conclusions • A distributed model for solving large-scale CSPs was present • A preprocessing agent partitions the problem in semi-independent sub-CSPs • A set of block agents incrementally and concurrently built partial solutions until a global solution is found. • Each block agent may solve its subproblem with different algorithms • Large CSPs (Railway Scheduling Problems) could be solved more efficiently. Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  17. Future Works • The Railway Scheduling Problem can be partitioned by different ways. • We are working on techniques to partition the problem, depending on the problems objective. • Evaluate the ways in which Railway Scheduling Problem can be distributed. Santiago de Compostela, 15/11/2005 PSRT’05 Workshop sobre Planificación, Scheduling y Razonamiento Temporal

  18. Técnicas Distribuidas para Problemas de Scheduling a Gran Escala GTI-IA, DSIC Miguel A. Salido, M. Abril, F. Barber, P. Tormos, A. Llova, L. Ingolotti Univerisdad Politécnica de Valencia España IV Workshop Planificación, Scheduling y Razonamiento Temporal Santiago de Compostela, 15 de Noviembre de 2005

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