PRSA For WDM

Md. Tanveer Anwar

University of Arkansas

PRSAPRSA = 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

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)

Physical Topology for WDM Network

Wavelength Interchanging Cross-connect (WIXC)

Wavelength Selective Cross-connect (WSXC)

S1

S2

S1

S2

D1

D2

D1

D2

Example of Wavelength AssignmentConstraint

Simple PRSA Problem

A

D

CB

6

12

5

3 4

S-D Pairs Cost Capacity

AB 2 5

AC 1 5

AD 5 5

BC 6 5

BD 3 5

CD 4 5

GRAPH TRAFFIC

INDEX S-D Pair

0 AB 1

1 AC 1

2 AD 1

3 BA 1

4 BC 1

5 BD 1

6 CA 1

7 CB 1

8 CD 1

9 DA 1

10 DB 1

11 DC 1

Simple PRSA Problem

A

D

CB

6

12

5

3 4

INDEX S-D Pair

0 AB 1

1 AC 1

…. …. ….

11 DC 1

0 1 2 3 4 5 6 7 8 9 10 11

K2 K0 K0 K1 K0 K2 K2 K2 K0 K0 K0 K2

K0 : Shortest

K1: 2nd Shortest

K2: 3rd Shortest

CHROMOSOME (12 Genomes)

K – Shortest PathsTRAFFIC

0 1 2 3 4 5 6 7 8 9 10 11

C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 Total Cost

4 Nodes : 312

25 Nodes : 3600

Combinatorial Problem

Optimal Solution (ILP)

Ample/Cplex Advantages

Optimal Solution

Fast

Disadvantages

The problem must be bounded

Requires High Memory (RAM)

PRSA Algorithm Preview

Parent A Parent A 1 0 1 1 11 0 1 1 1Parent B Parent B 1 1 0 1 01 1 0 1 0Child A Child A 1 0 0 1 01 0 0 1 0Child B Child B 1 1 1 1 11 1 1 1 1

Crossover Operation

Metropolis Criteria

Parent A Parent A 1 0 1 1 11 0 1 1 1Parent B Parent B 1 1 0 1 01 1 0 1 0Child A Child A 1 0 0 1 01 0 0 1 0Child B Child B 1 1 0 1 11 1 0 1 1

Mutation Operation

If Child wins, accept it.

If Parent wins, Accept the child with a probability:

EXP((fparent – fchild)/T)

Competition Between Parents and Children

Parent AParent A

Child AChild A

Parent BParent B

Child BChild B

Parent AParent A

Child BChild B

PRSA Algorithm

Initialize the Temperature (SA)

Initialize population with n chromosomes (GA)

Repeat for max generationsDo 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

Results

p = 50, m = 2 m = 2, c = 0.99 p = 50, c = 0.99

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 !!