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

2. PRSA = GA + SA (parallel)
Genetic Algorithms
Heuristic optimization technique
Approximates global solution
Inherently parallel
Simulated Annealing
Global Optimum solution
Not Inherently parallel
Parallel Recombinative Simulated Annealing
PRSA = GA + SA (parallel using MPI)
GA is a heuristic optimization technique for approximating the global solution to a complex problem space. GA is good at coarsely exploring the search space but is poor at precisely finding the local minima in the region that it finally selects. Therefore, the combination of a simple local search algorithm with GA is common.
In theory, SA with a logarithmic cooling schedule converges with probability one to the global optimum solution, but requires an infinite number of iterations.

3. Wavelength-Division Multiplexing
Coarse WDM
- Channel spacing of 20 nanometers (nm)
- Avoid temperature control problems
- Less expensive
Dense WDM
- Channel spacing < 1 nm
channels possible in 2001
Ultra Dense WDM
- 1,022 channels (Bell Labs)
WDM is the technology that enables multiple optical signals over a single fiber by carrying signals on separate wavelengths.

4. Physical Topology for WDM Network
We are provided with a physical topology composed 25 Nodes.
Each node has some traffic to every other node in the topology.
At each node there are WDM cross-connects. There are two general categories of WDM cross-connects.
Wavelength Selective Cross-Connects (WSXC)
Wavelength Interchanging Cross-Connects (WIXC)

5. Wavelength Selective Cross-connect (WSXC)D1 S2 D2
Wavelength Interchanging Cross-connect (WIXC)
WDM
Wavelength Selective Cross-connect (WSXC)
The wavelength on the input port is switched to an output port and the wavelength remains unchanged
Wavelength Interchanging Cross-connect (WIXC)
The cross-connect switches wavelengths from an input port to an output port and may change the input wavelength to a different output wavelength S1 D1 S2 D2

6. Example of Wavelength Assignment
Constraint
Routing and Wavelenght Assignment

7. Simple PRSA Problem GRAPH TRAFFIC 6 A 2 1 B C 5 4 3 D S-D Pairs Cost
Capacity AB 2 5 AC 1 AD BC 6 BD 3 CD 4
INDEX
S-D Pair l AB 1 AC 2 AD 3 BA 4 BC 5 BD 6 CA 7 CB 8 CD 9 DA 10 DB 11 DC A 2 1 B C 5 4 3 D

8. Simple PRSA Problem Combinatorial Problem 6 TRAFFIC K – Shortest Paths
INDEX
S-D Pair l AB 1 AC …. 11 DC A
K0 : Shortest
K1: 2nd Shortest
K2: 3rd Shortest 2 1 B C 5
CHROMOSOME (12 Genomes) 1 2 3 4 5 6 7 8 9 10 11 K2 K0 K1 4 3 D 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

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

10. PRSA Algorithm Preview
Crossover Operation
Mutation Operation
Parent A
Parent B
Child A
Child B
Parent A
Parent B
Child A
Child B
Competition Between Parents and Children
Parent A
Child A
Parent B
Child B
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
Simulate Annealing
Initialize the Temperature
Initialize the Current Solution
Evaluate the Solution
While Temperature > 0
Modify the current solution (Mutation)
Evaluate the new solution
Use Metropolis Selection Criteria to determine whether we should accept/reject the new solution
Lower the Temperature
Genetic Algorithm
Initialize population with n chromosomes
Evaluate fitness of each chromosome
Save best chromosome
Repeat for max generations
Select chromosomes for next generation
Pick two chromosomes with probability pC and exchange genetic material with a crossover operator
Mutate genes with probability pM
Use elitist strategy

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

13. Conclusion Thank You !! 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 !!