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

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

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

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

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

Omega Network Each connection between stages is shuffle-exchanged 000-> > >100 … 111->111

Routing in Omega Network

Routing same ex. in 2 passes

The Window Method

Conflict Graph

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.

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

Genetic Algorithm

Chromosomes Binary: Permutation encoding: Index represents the node in the graph and the integer value represents the color of its corresponding node

Operators of GA Crossover Mutation Selection

Crossover Single Crossover: Parent 1: Parent 2: After crossover, Offspring 1: Offspring 2:

Operators of GA(cont.) Double Crossover Parent 1: Parent 2: After double crossover, Offspring 1: Offspring 2:

Mutation Offspring from the crossover: Offspring 1 : Offspring 2 : Offspring after mutation: Offspring 1 : Offspring 2 :

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

Parameters of GA Crossover Probability Mutation Probability Population Size Number of Generations

Example

Sequential Algo. Coloring

Degree-descending Coloring

GA Coloring(MP=0.1,Gen=100)

Analysis of testing results

Color-exchanging Mutation results

Generations affects GA

Generations(MP=0.1)

Generations(MP=0.01)

Generations(MP=0.3)

Generations(MP=0.4)

Generations(MP=0.001)

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

Maximum passes reduced by GA in this research

Single vs. Double Crossover

Comparisons of 5 algorithms

Java Applet

Sequential Algo.(128*128)

Sequential Down Algo.

Degree-ascending Algo.

Degree-descending Algo.

Genetic Algorithm

Comparisons of 5 algorithms

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