prsa for wdm
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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 !!