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PRSA For WDM

PRSA For WDM. Md. Tanveer Anwar University of Arkansas. PRSA. PRSA = GA + SA (parallel) Genetic Algorithms Heuristic optimization technique Approximates global solution Inherently parallel Simulated Annealing Heuristic optimization technique Global Optimum solution

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PRSA For WDM

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  1. PRSA For WDM Md. Tanveer Anwar University of Arkansas

  2. PRSA PRSA = GA + SA (parallel) • Genetic Algorithms • Heuristic optimization technique • Approximates global solution • Inherently parallel • Simulated Annealing • Heuristic optimization technique • Global Optimum solution • Not Inherently parallel • Parallel Recombinative Simulated Annealing

  3. Wavelength-Division Multiplexing • Coarse WDM • - Channel spacing of 20 nanometers (nm) • - Avoid temperature control problems • - Less expensive • Dense WDM • - Channel spacing < 1 nm • - 160 channels possible in 2001 • Ultra Dense WDM • - 1,022 channels (Bell Labs)

  4. Physical Topology for WDM Network

  5. Wavelength Selective Cross-connect (WSXC) S1 D1 S2 D2 Wavelength Interchanging Cross-connect (WIXC) S1 D1 S2 D2

  6. Example of Wavelength Assignment Constraint

  7. Simple PRSA Problem 6 GRAPH TRAFFIC A 2 1 B C 5 4 3 D

  8. Simple PRSA Problem 6 TRAFFIC K – Shortest Paths A K0 : Shortest K1: 2nd Shortest K2: 3rd Shortest 2 1 B C 5 CHROMOSOME (12 Genomes) 4 3 D Total Cost 4 Nodes : 312 25 Nodes : 3600 Combinatorial Problem

  9. Optimal Solution (ILP) Ample/Cplex Advantages Optimal Solution Fast Disadvantages The problem must be bounded Requires High Memory (RAM)

  10. Parent A Parent A Child A Parent B Child B Child B PRSA Algorithm Preview Crossover Operation Mutation Operation Parent A 1 0 1 1 1 Parent B 1 1 0 1 0 Child A 1 0 0 1 0 Child B 1 1 1 1 1 Parent A 1 0 1 1 1 Parent B 1 1 0 1 0 Child A 1 0 0 1 0 Child B 1 1 0 1 1 Competition Between Parents and Children Metropolis Criteria If Child wins, accept it. If Parent wins, Accept the child with a probability: EXP((fparent – fchild)/T)

  11. PRSA Algorithm Initialize the Temperature (SA) Initialize population with n chromosomes (GA) Repeat for max generations Do n/2 times • Select 2 parent chromosomes at random (GA) • Generate 2 children using crossover and mutation (GA) • Hold competitions using the Metropolis criterion between children and parents (SA) • Overwrite parents with trial winner Lower the Temperature (GA) Send/Receive migrants to/from other processors

  12. Results p = 50, m = 2 m = 2, c = 0.99 p = 50, c = 0.99

  13. Conclusion • Another Method to solve Combinatorial Problems • Like S.A, a smaller cooling coefficient that causes a faster decrease in temperature increases convergence rate at the expense of the final solution • A large population size is preferable but not too large • Keep the # of migrants to a minimum. Thank You !!

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