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Routing and Scheduling in Multistage Networks using Genetic Algorithms

Routing and Scheduling in Multistage Networks using Genetic Algorithms. Advisor: Dr. Yi Pan Chunyan Ji 3/26/01. Presentation Outline. Background and Motivation of this research Genetic Algorithm Analysis of Testing Results Simulation Package in Java Applet Conclusion and Future work Demo.

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Routing and Scheduling in Multistage Networks using Genetic Algorithms

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  1. Routing and Scheduling in Multistage Networks using Genetic Algorithms Advisor: Dr. Yi Pan Chunyan Ji 3/26/01

  2. Presentation Outline • Background and Motivation of this research • Genetic Algorithm • Analysis of Testing Results • Simulation Package in Java Applet • Conclusion and Future work • Demo

  3. Background and Motivation of this research • Multistage Interconnection Network • Network size N=2n (n is the number of stages) • N/2 switching elements in each stage

  4. Crosstalk in OMIN • Two ways to produce undesired coupling in a Switching Element

  5. Approaches to avoid crosstalk • 2N*2N regular OMIN to provide N*N connection • Routing traffic through an N*N OMIN to avoid coupling two signals within each Switching Element

  6. Legal path in SW at a time • Paths without crosstalk in SE:

  7. Omega Network • Each connection between stages is shuffle-exchanged • 000->000 • 001->010 • 010->100 • … • 111->111

  8. Routing in Omega Network

  9. Routing same ex. in 2 passes

  10. Routing same ex. in 2 passes

  11. The Window Method

  12. Conflict Graph

  13. Routing Algorithm • While (not end of messages list) • 1. Select one of the left messages; • 2. Schedule the message in a time slot with no conflict with other messages that have been already scheduled.

  14. Four Routing Algorithms • Sequential Algorithm: Choose a message in increasing order of the message source address. • Seq-Down Algorithm: Choose a message in decreasing order of the message source address. • Degree-ascending Algo: Choose a message in the order of the increasing degrees in conflict graph. • Degree-descending Algo: Choose a message in the order of the decreasing degrees in conflict graph

  15. Genetic Algorithm

  16. Chromosomes • Binary: 01011010 • Permutation encoding:21314231 • Index represents the node in the graph and the integer value represents the color of its corresponding node

  17. Operators of GA • Crossover • Mutation • Selection

  18. Crossover • Single Crossover: Parent 1: 2311242212341 Parent 2: 1232422311243 After crossover, Offspring 1: 2311242311243 Offspring 2: 1232422212341

  19. Operators of GA(cont.) • Double Crossover Parent 1: 2311242212341 Parent 2: 1232422311243 After double crossover, Offspring 1: 2312422312341 Offspring 2: 1231242211243

  20. Mutation • Offspring from the crossover: Offspring 1: 2311242311243 Offspring 2: 1232422212341 Offspring after mutation: Offspring 1: 2312242311243 Offspring 2: 1232322212311

  21. Selection • Fitness Function:number of colors • valid solutions • Betting fitting offspring (less number of colors) gets to be the parent of next generation

  22. Parameters of GA • Crossover Probability • Mutation Probability • Population Size • Number of Generations

  23. Example

  24. Sequential Algo. Coloring

  25. Degree-descending Coloring

  26. GA Coloring(MP=0.1,Gen=100)

  27. Analysis of testing results

  28. Color-exchanging Mutation results

  29. Generations affects GA

  30. Generations(MP=0.1)

  31. Generations(MP=0.01)

  32. Generations(MP=0.3)

  33. Generations(MP=0.4)

  34. Generations(MP=0.001)

  35. Analysis • Best Mutation Probability: 0.1---0.3 • Generations:100---300 • Population size:4--8 • Crossover Probability used: 100% • In this research, maximum colors reduced by GA: 2

  36. Maximum passes reduced by GA in this research

  37. Single vs. Double Crossover

  38. Comparisons of 5 algorithms

  39. Java Applet

  40. Sequential Algo.(128*128)

  41. Sequential Down Algo.

  42. Degree-ascending Algo.

  43. Degree-descending Algo.

  44. Genetic Algorithm

  45. Comparisons of 5 algorithms

  46. Conclusion and Future work • Genetic Algorithm can be used as a optimizing tool • Disadvantage:time consuming • Perform GA in parallel • Other complicated GA techniques to improve the results

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