routing and scheduling in multistage networks using genetic algorithms

Routing and Scheduling in Multistage Networks using Genetic AlgorithmsAdvisor: Dr. Yi PanChunyan Ji3/26/01

Presentation OutlineBackground and Motivation of this researchGenetic AlgorithmAnalysis of Testing ResultsSimulation Package in Java AppletConclusion and Future workDemo

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

Crosstalk in OMINTwo ways to produce undesired coupling in a Switching Element

Approaches to avoid crosstalk2N*2N regular OMIN to provide N*N connectionRouting traffic through an N*N OMIN to avoid coupling two signals within each Switching Element

Legal path in SW at a timePaths without crosstalk in SE:

Omega NetworkEach connection between stages is shuffle-exchanged000->000001->010010->100 111->111

Routing in Omega Network

Routing same ex. in 2 passes

The Window Method

Conflict Graph

Routing AlgorithmWhile (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 AlgorithmsSequential 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

ChromosomesBinary: 01011010Permutation encoding:21314231Index represents the node in the graph and the integer value represents the color of its corresponding node

Operators of GACrossoverMutationSelection

CrossoverSingle Crossover:Parent 1: 2311242212341Parent 2: 1232422311243After crossover,Offspring 1: 2311242311243Offspring 2: 1232422212341

Operators of GA(cont.)Double Crossover

Parent 1: 2311242212341Parent 2: 1232422311243After double crossover,Offspring 1: 2312422312341Offspring 2: 1231242211243

MutationOffspring from the crossover:Offspring 1: 2311242311243Offspring 2: 1232422212341Offspring after mutation:Offspring 1: 2312242311243Offspring 2: 1232322212311

SelectionFitness Function:number of colorsvalid solutionsBetting fitting offspring (less number of colors) gets to be the parent of next generation

Parameters of GACrossover ProbabilityMutation ProbabilityPopulation SizeNumber of Generations

Example

Sequential Algo. Coloring

Degree-descending Coloring

GA Coloring(MP=0.1,Gen=100)

Analysis of testing results

Sheet1

nodesRoundsGensMu ProbCrsOverPopuSeqAlgoDescendsmallestGeneticTimediff(S-G)diff(D-G)

8100100.5Single22.722.582.562.5600.02

10010000.5Single22.732.592.572.5700.02

820010000.5Single22.6652.512.4852.48!!0.0050.03

100100.001Single42.782.682.672.671 sec00.01

1001000.001Single42.772.652.632.638 sec00.02

10010000.001Single42.782.612.582.5874 sec00.03

20010000.001Single42.72.562.5252.525147 sec00.035

16100100.5Single23.753.493.423.4200.07

1001000.5Single23.663.523.463.45!!0.010.07

1001000.5While23.693.543.453.42!!0.030.12

00

(#4)100100.01While43.653.453.363.350.010.1

(#8)100100.001While43.73.533.433.410.020.12

(#9)100200.01While43.823.523.453.440.010.08

(#9)100200.001While43.73.593.513.50.010.09

(#4)100300.01While43.773.543.413.40.010.14

(#4)100300.001While43.733.533.453.440.010.09

(#7)100500.01While43.63.523.373.360.010.16

(#20)100500.001While43.633.533.383.370.010.16

(#9)100800.01While43.693.513.393.380.010.13

(#4)100800.001While43.783.553.53.490.010.06

(#5)1001000.01While43.673.473.383.370.010.1

(#2)1001000.001While43.723.523.433.420.010.1

(#4)1001000.001Double43.743.493.383.3722 sec0.010.12

(#1)100010000.001Double43.6983.5433.4323.4339m24s0.0020.113

(#1)100010000.001Single43.6943.5183.4163.41259m28s0.0040.106

321001000.5While24.524.354.274.2700.08

10010000.5While254.44.44.3>13hours0.10.1

20200.001While4No improvement whithin 100 times

(#38)20500.001While44.654.44.34.2519 sec0.050.15

(#11)201000.001While44.654.44.254.236 sec0.050.2

(#24)50100.001While44.464.264.124.110 sec0.020.16

(#23)50200.001While44.544.284.264.2420 sec0.020.04

(#12)50500.001While44.64.384.344.3247 sec0.020.06

(#15)501000.001While44.584.34.264.2495 sec0.020.06

(#5)10050.001While44.54.244.24.1910 sec0.010.05

(#2)100100.001While44.544.284.214.1919 sec0.020.09

(#1)100200.001While44.54.244.194.1837 sec0.010.06

(#6)100500.001While44.534.274.174.1691 sec0.010.11

(#3)1001000.001While44.474.264.194.18197 sec0.010.08

641001000.5While2more than 24 hours

(#4)100100.001While45.325.055.025.011m29s0.010.04

(#5)100200.001While45.295.044.994.982m57s0.010.06

(#10)100500.001While45.354.984.964.957m39s0.010.03

(#1)1001000.001While45.285.065.035.0214m27s0.010.04

1281001000.001While46.195.875.855.8461m38s0.010.03

nodesRoundsGensMu ProbCrsOverPopuSeqAlgoDescendsmallestGeneticTime

8100100.5Single22.722.582.562.56

810010000.5Single22.732.592.572.57

820010000.5Single22.6652.512.4852.488 hours

16100100.5Single23.753.493.423.42

161001000.5Single23.663.523.463.454 hours

321001000.5Single24.524.354.274.27

3210010000.5Single254.44.44.313hours

641001000.5Single2more than 24 hours, and less valid offspring


8100100.001Single42.782.682.672.671 sec

81001000.001Single42.772.652.632.638 sec

810010000.001Single42.782.612.582.5874 sec

820010000.001Single42.72.562.5252.525147 sec

161001000.001Single43.723.523.433.4238sec

16100010000.001Single43.6943.5183.4163.41259m28s

32501000.001Single44.584.34.264.2495 sec

321001000.001Single44.474.264.194.18197 sec

64100500.001Single45.354.984.964.957m39s

641001000.001Single45.285.065.035.0214m27s

1281001000.001Single46.195.875.855.8461m38s

Sheet2

Sheet3

Color-exchanging Mutation results

Sheet1


8100100.5Single22.722.582.562.5600.02

10010000.5Single22.732.592.572.5700.02

820010000.5Single22.6652.512.4852.48!!0.0050.03

100100.001Single42.782.682.672.671 sec00.01

1001000.001Single42.772.652.632.638 sec00.02

10010000.001Single42.782.612.582.5874 sec00.03

20010000.001Single42.72.562.5252.525147 sec00.035

16100100.5Single23.753.493.423.4200.07

1001000.5Single23.663.523.463.45!!0.010.07

1001000.5While23.693.543.453.42!!0.030.12

00

(#4)100100.01While43.653.453.363.350.010.1

(#8)100100.001While43.73.533.433.410.020.12

(#9)100200.01While43.823.523.453.440.010.08

(#9)100200.001While43.73.593.513.50.010.09

(#4)100300.01While43.773.543.413.40.010.14

(#4)100300.001While43.733.533.453.440.010.09

(#7)100500.01While43.63.523.373.360.010.16

(#20)100500.001While43.633.533.383.370.010.16

(#9)100800.01While43.693.513.393.380.010.13

(#4)100800.001While43.783.553.53.490.010.06

(#5)1001000.01While43.673.473.383.370.010.1

(#2)1001000.001While43.723.523.433.420.010.1

(#4)1001000.001Double43.743.493.383.3722 sec0.010.12

(#1)100010000.001Double43.6983.5433.4323.4339m24s0.0020.113

(#1)100010000.001Single43.6943.5183.4163.41259m28s0.0040.106

321001000.5While24.524.354.274.2700.08

10010000.5While254.44.44.3>13hours0.10.1

20200.001While4No improvement whithin 100 times

(#38)20500.001While44.654.44.34.2519 sec0.050.15

(#11)201000.001While44.654.44.254.236 sec0.050.2

(#24)50100.001While44.464.264.124.110 sec0.020.16

(#23)50200.001While44.544.284.264.2420 sec0.020.04

(#12)50500.001While44.64.384.344.3247 sec0.020.06

(#15)501000.001While44.584.34.264.2495 sec0.020.06

(#5)10050.001While44.54.244.24.1910 sec0.010.05

(#2)100100.001While44.544.284.214.1919 sec0.020.09

(#1)100200.001While44.54.244.194.1837 sec0.010.06

(#6)100500.001While44.534.274.174.1691 sec0.010.11

(#3)1001000.001While44.474.264.194.18197 sec0.010.08

641001000.5While2more than 24 hours

(#4)100100.001While45.325.055.025.011m29s0.010.04

(#5)100200.001While45.295.044.994.982m57s0.010.06

(#10)100500.001While45.354.984.964.957m39s0.010.03

(#1)1001000.001While45.285.065.035.0214m27s0.010.04

1281001000.001While46.195.875.855.8461m38s0.010.03


8100100.5Single22.722.582.562.56

810010000.5Single22.732.592.572.57

820010000.5Single22.6652.512.4852.488 hours

16100100.5Single23.753.493.423.42

161001000.5Single23.663.523.463.454 hours

321001000.5Single24.524.354.274.27

3210010000.5Single254.44.44.313hours



8100100.001Single42.782.682.672.671 sec

81001000.001Single42.772.652.632.638 sec

810010000.001Single42.782.612.582.5874 sec

820010000.001Single42.72.562.5252.525147 sec

161001000.001Single43.723.523.433.4238sec

16100010000.001Single43.6943.5183.4163.41259m28s

32501000.001Single44.584.34.264.2495 sec

321001000.001Single44.474.264.194.18197 sec

64100500.001Single45.354.984.964.957m39s

641001000.001Single45.285.065.035.0214m27s

1281001000.001Single46.195.875.855.8461m38s

Sheet2

Sheet3

Generations affects GA

Chart4

3.743.72

3.493.52

3.383.43

3.373.42

Double Crossover

Single Crossover

Seq->Des->Sma->Genetic

Average Passes

100Rounds,100Gens(16*16),MP=0.001

Chart5

2.772.652.632.63

3.723.523.433.415

4.474.264.194.175

5.285.065.035.01

Sequential Algorithm

Degree Descending Algorithm

Smallest of Four Algorithm

Genetic Algorithm

Number of Nodes(8,16,32,64...)

Average Passes

100 Rnds, 100 Gens, MP=0.001

Chart7

3.6953.684

3.5283.528

3.4053.42

3.4023.416

Double Crossover

Single Crossover


Average Passes

1000Rnds,1000Gens(16*16),MP=0.001

Sheet1

roundsgenerationsMut PorbSeq AlgoDeg-DescendSmallestGenetic

100100.013.653.453.363.35

100200.013.823.523.453.44

100300.013.773.543.413.4

100500.013.63.523.373.36

100800.013.693.613.393.38

1001000.013.673.473.383.37


100100.0013.73.533.433.41

100200.0013.73.593.513.5

100300.0013.733.533.453.44

100500.0013.633.533.383.37

100800.0013.783.553.53.49

1001000.0013.723.523.433.42


100100.13.663.453.383.36

100200.13.763.613.543.52

100300.13.813.573.53.48

100500.13.743.663.543.51

100800.13.723.533.463.43

1001000.13.823.583.463.43

roundsgenerationsMut PorbSeq AlgoDeg-DescendSmallestGeneticdiff:Sm-G

100100.13.733.53.393.360.03

100200.13.693.543.483.470.01

100300.13.73.53.413.350.06

100500.13.753.553.463.370.09

100800.13.783,63.523.470.05

1001000.13.733.563.493.460.03

3.6953.5283.4053.402

3.6843.5283.423.416

3.743.493.383.37

3.723.523.433.42

2.773.724.475.28

2.653.524.265.06

2.633.434.195.03

2.633.4154.1755.01

mp=0.282.842.752.72.652.84

163.773.613.493.453.77

324.514.194.164.144.51

64(0.1)5.295.075.055.045.29

RoundsMut ProbSeq AlgoDeg-DescendSmallest AlgoGeneticGenerations

10000.013.7033.553.4433.44150

10000.013.7033.553.4433.436100

10000.013.7033.553.4433.43150

10000.013.7033.553.4433.428200

10000.013.7033.553.4433.428250

10000.013.7033.553.4433.425300


10000.13.7183.5413.443.41450

10000.13.7183.5413.443.402100

10000.13.7183.5413.443.391150

10000.13.7183.5413.443.389200

10000.13.7183.5413.443.387250

10000.13.7183.5413.443.387300

Sheet2

Sheet2

3.663.763.813.743.723.82

3.453.613.573.663.533.58

3.383.543.53.543.463.46

3.363.523.483.513.433.43

10 generations

20 generations

30 generations

50 generations

80 generations

100 genreations

Sequential->Descending->Smallest->Genetic Algorithm

Average passes

100Rounds(16*16), MP=0.1

Sheet3

3.73.73.733.633.783.72

3.533.593.533.533.553.52

3.433.513.453.383.53.43

3.413.53.443.373.493.42

10 generations

20 generations

30 generations

50 generations

80 generations

100 generations


Average Passes

100 Rounds(16*16), MP=0.001

3.7033.553.4433.441

3.7033.553.4433.436

3.7033.553.4433.43

3.7033.553.4433.428

3.7033.553.4433.428

3.7033.553.4433.425


Degree-descending Algorithm

Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes

Comparisons of Various Generations(MP=0.1,Rnds=1000)

3.7183.5413.443.414

3.7183.5413.443.402

3.7183.5413.443.391

3.7183.5413.443.389

3.7183.5413.443.387

3.7183.5413.443.387



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes

Comparisons of various Generations(MP=0.1,Rnds=1000)

Generations(MP=0.1)

Chart2

3.7183.5413.443.414

3.7183.5413.443.402

3.7183.5413.443.391

3.7183.5413.443.389

3.7183.5413.443.387

3.7183.5413.443.387



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


Chart4

3.743.72

3.493.52

3.383.43

3.373.42

Double Crossover

Single Crossover


Average Passes

100Rounds,100Gens(16*16),MP=0.001

Chart5

2.772.652.632.63

3.723.523.433.415

4.474.264.194.175

5.285.065.035.01




Genetic Algorithm


Average Passes

100 Rnds, 100 Gens, MP=0.001

Chart7

3.6953.684

3.5283.528

3.4053.42

3.4023.416

Double Crossover

Single Crossover


Average Passes

1000Rnds,1000Gens(16*16),MP=0.001

Sheet1


100100.013.653.453.363.35

100200.013.823.523.453.44

100300.013.773.543.413.4

100500.013.63.523.373.36

100800.013.693.613.393.38

1001000.013.673.473.383.37


100100.0013.73.533.433.41

100200.0013.73.593.513.5

100300.0013.733.533.453.44

100500.0013.633.533.383.37

100800.0013.783.553.53.49

1001000.0013.723.523.433.42


100100.13.663.453.383.36

100200.13.763.613.543.52

100300.13.813.573.53.48

100500.13.743.663.543.51

100800.13.723.533.463.43

1001000.13.823.583.463.43


100100.13.733.53.393.360.03

100200.13.693.543.483.470.01

100300.13.73.53.413.350.06

100500.13.753.553.463.370.09

100800.13.783,63.523.470.05

1001000.13.733.563.493.460.03

3.6953.5283.4053.402

3.6843.5283.423.416

3.743.493.383.37

3.723.523.433.42

2.773.724.475.28

2.653.524.265.06

2.633.434.195.03

2.633.4154.1755.01

mp=0.282.842.752.72.652.84

163.773.613.493.453.77

324.514.194.164.144.51

64(0.1)5.295.075.055.045.29

seqdessmallGenetic

3.7033.553.4433.441

3.7033.553.4433.436

3.7033.553.4433.43

3.7033.553.4433.428

3.7033.553.4433.428

3.7033.553.4433.425

seqdessmallGenetic

3.7183.5413.443.414

3.7183.5413.443.402

3.7183.5413.443.391

3.7183.5413.443.389

3.7183.5413.443.387

3.7183.5413.443.387

Sheet2

Sheet2

3.663.763.813.743.723.82

3.453.613.573.663.533.58

3.383.543.53.543.463.46

3.363.523.483.513.433.43

10 generations

20 generations

30 generations

50 generations

80 generations

100 genreations


Average passes

100Rounds(16*16), MP=0.1

Sheet3

3.73.73.733.633.783.72

3.533.593.533.533.553.52

3.433.513.453.383.53.43

3.413.53.443.373.493.42

10 generations

20 generations

30 generations

50 generations

80 generations

100 generations


Average Passes

100 Rounds(16*16), MP=0.001

3.7033.553.4433.441

3.7033.553.4433.436

3.7033.553.4433.43

3.7033.553.4433.428

3.7033.553.4433.428

3.7033.553.4433.425



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7183.5413.443.414

3.7183.5413.443.402

3.7183.5413.443.391

3.7183.5413.443.389

3.7183.5413.443.387

3.7183.5413.443.387



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


Generations(MP=0.01)

Chart1

3.7033.553.4433.441

3.7033.553.4433.436

3.7033.553.4433.43

3.7033.553.4433.428

3.7033.553.4433.428

3.7033.553.4433.425



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


Chart4

3.743.72

3.493.52

3.383.43

3.373.42

Double Crossover

Single Crossover


Average Passes

100Rounds,100Gens(16*16),MP=0.001

Chart5

2.772.652.632.63

3.723.523.433.415

4.474.264.194.175

5.285.065.035.01




Genetic Algorithm


Average Passes

100 Rnds, 100 Gens, MP=0.001

Chart7

3.6953.684

3.5283.528

3.4053.42

3.4023.416

Double Crossover

Single Crossover


Average Passes

1000Rnds,1000Gens(16*16),MP=0.001

Sheet1


100100.013.653.453.363.35

100200.013.823.523.453.44

100300.013.773.543.413.4

100500.013.63.523.373.36

100800.013.693.613.393.38

1001000.013.673.473.383.37


100100.0013.73.533.433.41

100200.0013.73.593.513.5

100300.0013.733.533.453.44

100500.0013.633.533.383.37

100800.0013.783.553.53.49

1001000.0013.723.523.433.42


100100.13.663.453.383.36

100200.13.763.613.543.52

100300.13.813.573.53.48

100500.13.743.663.543.51

100800.13.723.533.463.43

1001000.13.823.583.463.43


100100.13.733.53.393.360.03

100200.13.693.543.483.470.01

100300.13.73.53.413.350.06

100500.13.753.553.463.370.09

100800.13.783,63.523.470.05

1001000.13.733.563.493.460.03

3.6953.5283.4053.402

3.6843.5283.423.416

3.743.493.383.37

3.723.523.433.42

2.773.724.475.28

2.653.524.265.06

2.633.434.195.03

2.633.4154.1755.01

mp=0.282.842.752.72.652.84

163.773.613.493.453.77

324.514.194.164.144.51

64(0.1)5.295.075.055.045.29

seqdessmallGenetic

3.7033.553.4433.441

3.7033.553.4433.436

3.7033.553.4433.43

3.7033.553.4433.428

3.7033.553.4433.428

3.7033.553.4433.425

Sheet2

Sheet2

3.663.763.813.743.723.82

3.453.613.573.663.533.58

3.383.543.53.543.463.46

3.363.523.483.513.433.43

10 generations

20 generations

30 generations

50 generations

80 generations

100 genreations


Average passes

100Rounds(16*16), MP=0.1

Sheet3

3.73.73.733.633.783.72

3.533.593.533.533.553.52

3.433.513.453.383.53.43

3.413.53.443.373.493.42

10 generations

20 generations

30 generations

50 generations

80 generations

100 generations


Average Passes

100 Rounds(16*16), MP=0.001

3.7033.553.4433.441

3.7033.553.4433.436

3.7033.553.4433.43

3.7033.553.4433.428

3.7033.553.4433.428

3.7033.553.4433.425



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


Generations(MP=0.3)

Chart8

3.6943.5513.4333.403

3.6943.5513.4333.389

3.6943.5513.4333.384

3.6943.5513.4333.382

3.6943.5513.4333.38

3.6943.5513.4333.38



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


Chart4

3.743.72

3.493.52

3.383.43

3.373.42

Double Crossover

Single Crossover


Average Passes

100Rounds,100Gens(16*16),MP=0.001

Chart5

2.772.652.632.63

3.723.523.433.415

4.474.264.194.175

5.285.065.035.01




Genetic Algorithm


Average Passes

100 Rnds, 100 Gens, MP=0.001

Chart7

3.6953.684

3.5283.528

3.4053.42

3.4023.416

Double Crossover

Single Crossover


Average Passes

1000Rnds,1000Gens(16*16),MP=0.001

Sheet1


100100.013.653.453.363.35

100200.013.823.523.453.44

100300.013.773.543.413.4

100500.013.63.523.373.36

100800.013.693.613.393.38

1001000.013.673.473.383.37


100100.0013.73.533.433.41

100200.0013.73.593.513.5

100300.0013.733.533.453.44

100500.0013.633.533.383.37

100800.0013.783.553.53.49

1001000.0013.723.523.433.42


100100.13.663.453.383.36

100200.13.763.613.543.52

100300.13.813.573.53.48

100500.13.743.663.543.51

100800.13.723.533.463.43

1001000.13.823.583.463.43


100100.13.733.53.393.360.03

100200.13.693.543.483.470.01

100300.13.73.53.413.350.06

100500.13.753.553.463.370.09

100800.13.783,63.523.470.05

1001000.13.733.563.493.460.03

3.6953.5283.4053.402

3.6843.5283.423.416

3.743.493.383.37

3.723.523.433.42

2.773.724.475.28

2.653.524.265.06

2.633.434.195.03

2.633.4154.1755.01

mp=0.282.842.752.72.652.84

163.773.613.493.453.77

324.514.194.164.144.51

64(0.1)5.295.075.055.045.29


10000.013.7033.553.4433.44150

10000.013.7033.553.4433.436100

10000.013.7033.553.4433.43150

10000.013.7033.553.4433.428200

10000.013.7033.553.4433.428250

10000.013.7033.553.4433.425300


10000.13.7183.5413.443.41450

10000.13.7183.5413.443.402100

10000.13.7183.5413.443.391150

10000.13.7183.5413.443.389200

10000.13.7183.5413.443.387250

10000.13.7183.5413.443.387300


10000.0013.7093.5373.4443.444

10000.0013.7093.5373.4443.444

10000.0013.7093.5373.4443.443

10000.0013.7093.5373.4443.443

10000.0013.7093.5373.4443.443

10000.0013.7093.5373.4443.442


0.13.7123.5423.4443.406

3.7123.5423.4443.396

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392


10000.23.7343.5693.4553.415

10000.23.7343.5693.4553.401

10000.23.7343.5693.4553.395

10000.23.7343.5693.4553.394

10000.23.7343.5693.4553.394

10000.23.7343.5693.4553.394


10000.33.6943.5513.4333.403

10000.33.6943.5513.4333.389

10000.33.6943.5513.4333.384

10000.33.6943.5513.4333.382

10000.33.6943.5513.4333.38

10000.33.6943.5513.4333.38


10000.43.7163.5573.4453.445

10000.43.7163.5573.4453.444

10000.43.7163.5573.4453.444

10000.43.7163.5573.4453.444

10000.43.7163.5573.4453.444

10000.43.7163.5573.4453.444

Sheet2

Sheet2

3.663.763.813.743.723.82

3.453.613.573.663.533.58

3.383.543.53.543.463.46

3.363.523.483.513.433.43

10 generations

20 generations

30 generations

50 generations

80 generations

100 genreations


Average passes

100Rounds(16*16), MP=0.1

Sheet3

3.73.73.733.633.783.72

3.533.593.533.533.553.52

3.433.513.453.383.53.43

3.413.53.443.373.493.42

10 generations

20 generations

30 generations

50 generations

80 generations

100 generations


Average Passes

100 Rounds(16*16), MP=0.001

3.7033.553.4433.441

3.7033.553.4433.436

3.7033.553.4433.43

3.7033.553.4433.428

3.7033.553.4433.428

3.7033.553.4433.425



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7093.5373.4443.444

3.7093.5373.4443.444

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.442

3.7183.5413.443.414

3.7183.5413.443.402

3.7183.5413.443.391

3.7183.5413.443.389

3.7183.5413.443.387

3.7183.5413.443.387



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7123.5423.4443.406

3.7123.5423.4443.396

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7093.5373.4443.444

3.7093.5373.4443.444

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.442



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes

Comprisons of various Generations(MP=0.001,Rnds=1000)

3.6943.5513.4333.403

3.6943.5513.4333.389

3.6943.5513.4333.384

3.6943.5513.4333.382

3.6943.5513.4333.38

3.6943.5513.4333.38



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


Generations(MP=0.4)

Chart9

3.7163.5573.4453.445

3.7163.5573.4453.444

3.7163.5573.4453.444

3.7163.5573.4453.444

3.7163.5573.4453.444

3.7163.5573.4453.444



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


Chart4

3.743.72

3.493.52

3.383.43

3.373.42

Double Crossover

Single Crossover


Average Passes

100Rounds,100Gens(16*16),MP=0.001

Chart5

2.772.652.632.63

3.723.523.433.415

4.474.264.194.175

5.285.065.035.01




Genetic Algorithm


Average Passes

100 Rnds, 100 Gens, MP=0.001

Chart7

3.6953.684

3.5283.528

3.4053.42

3.4023.416

Double Crossover

Single Crossover


Average Passes

1000Rnds,1000Gens(16*16),MP=0.001

Sheet1


100100.013.653.453.363.35

100200.013.823.523.453.44

100300.013.773.543.413.4

100500.013.63.523.373.36

100800.013.693.613.393.38

1001000.013.673.473.383.37


100100.0013.73.533.433.41

100200.0013.73.593.513.5

100300.0013.733.533.453.44

100500.0013.633.533.383.37

100800.0013.783.553.53.49

1001000.0013.723.523.433.42


100100.13.663.453.383.36

100200.13.763.613.543.52

100300.13.813.573.53.48

100500.13.743.663.543.51

100800.13.723.533.463.43

1001000.13.823.583.463.43


100100.13.733.53.393.360.03

100200.13.693.543.483.470.01

100300.13.73.53.413.350.06

100500.13.753.553.463.370.09

100800.13.783,63.523.470.05

1001000.13.733.563.493.460.03

3.6953.5283.4053.402

3.6843.5283.423.416

3.743.493.383.37

3.723.523.433.42

2.773.724.475.28

2.653.524.265.06

2.633.434.195.03

2.633.4154.1755.01

mp=0.282.842.752.72.652.84

163.773.613.493.453.77

324.514.194.164.144.51

64(0.1)5.295.075.055.045.29


10000.013.7033.553.4433.44150

10000.013.7033.553.4433.436100

10000.013.7033.553.4433.43150

10000.013.7033.553.4433.428200

10000.013.7033.553.4433.428250

10000.013.7033.553.4433.425300


10000.13.7183.5413.443.41450

10000.13.7183.5413.443.402100

10000.13.7183.5413.443.391150

10000.13.7183.5413.443.389200

10000.13.7183.5413.443.387250

10000.13.7183.5413.443.387300


10000.0013.7093.5373.4443.444

10000.0013.7093.5373.4443.444

10000.0013.7093.5373.4443.443

10000.0013.7093.5373.4443.443

10000.0013.7093.5373.4443.443

10000.0013.7093.5373.4443.442


0.13.7123.5423.4443.406

3.7123.5423.4443.396

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392


10000.23.7343.5693.4553.415

10000.23.7343.5693.4553.401

10000.23.7343.5693.4553.395

10000.23.7343.5693.4553.394

10000.23.7343.5693.4553.394

10000.23.7343.5693.4553.394


10000.33.6943.5513.4333.40350

10000.33.6943.5513.4333.389100

10000.33.6943.5513.4333.384150

10000.33.6943.5513.4333.382200

10000.33.6943.5513.4333.38250

10000.33.6943.5513.4333.38300


10000.43.7163.5573.4453.44550

10000.43.7163.5573.4453.444100

10000.43.7163.5573.4453.444150

10000.43.7163.5573.4453.444200

10000.43.7163.5573.4453.444250

10000.43.7163.5573.4453.444300

Sheet2

Sheet2

3.663.763.813.743.723.82

3.453.613.573.663.533.58

3.383.543.53.543.463.46

3.363.523.483.513.433.43

10 generations

20 generations

30 generations

50 generations

80 generations

100 genreations


Average passes

100Rounds(16*16), MP=0.1

Sheet3

3.73.73.733.633.783.72

3.533.593.533.533.553.52

3.433.513.453.383.53.43

3.413.53.443.373.493.42

10 generations

20 generations

30 generations

50 generations

80 generations

100 generations


Average Passes

100 Rounds(16*16), MP=0.001

3.7033.553.4433.441

3.7033.553.4433.436

3.7033.553.4433.43

3.7033.553.4433.428

3.7033.553.4433.428

3.7033.553.4433.425



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7093.5373.4443.444

3.7093.5373.4443.444

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.442

3.7183.5413.443.414

3.7183.5413.443.402

3.7183.5413.443.391

3.7183.5413.443.389

3.7183.5413.443.387

3.7183.5413.443.387



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7123.5423.4443.406

3.7123.5423.4443.396

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7093.5373.4443.444

3.7093.5373.4443.444

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.442



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.6943.5513.4333.403

3.6943.5513.4333.389

3.6943.5513.4333.384

3.6943.5513.4333.382

3.6943.5513.4333.38

3.6943.5513.4333.38



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7163.5573.4453.445

3.7163.5573.4453.444

3.7163.5573.4453.444

3.7163.5573.4453.444

3.7163.5573.4453.444

3.7163.5573.4453.444



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


Generations(MP=0.001)

Chart6

3.7093.5373.4443.444

3.7093.5373.4443.444

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.442



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


Chart4

3.743.72

3.493.52

3.383.43

3.373.42

Double Crossover

Single Crossover


Average Passes

100Rounds,100Gens(16*16),MP=0.001

Chart5

2.772.652.632.63

3.723.523.433.415

4.474.264.194.175

5.285.065.035.01




Genetic Algorithm


Average Passes

100 Rnds, 100 Gens, MP=0.001

Chart7

3.6953.684

3.5283.528

3.4053.42

3.4023.416

Double Crossover

Single Crossover


Average Passes

1000Rnds,1000Gens(16*16),MP=0.001

Sheet1


100100.013.653.453.363.35

100200.013.823.523.453.44

100300.013.773.543.413.4

100500.013.63.523.373.36

100800.013.693.613.393.38

1001000.013.673.473.383.37


100100.0013.73.533.433.41

100200.0013.73.593.513.5

100300.0013.733.533.453.44

100500.0013.633.533.383.37

100800.0013.783.553.53.49

1001000.0013.723.523.433.42


100100.13.663.453.383.36

100200.13.763.613.543.52

100300.13.813.573.53.48

100500.13.743.663.543.51

100800.13.723.533.463.43

1001000.13.823.583.463.43


100100.13.733.53.393.360.03

100200.13.693.543.483.470.01

100300.13.73.53.413.350.06

100500.13.753.553.463.370.09

100800.13.783,63.523.470.05

1001000.13.733.563.493.460.03

3.6953.5283.4053.402

3.6843.5283.423.416

3.743.493.383.37

3.723.523.433.42

2.773.724.475.28

2.653.524.265.06

2.633.434.195.03

2.633.4154.1755.01

mp=0.282.842.752.72.652.84

163.773.613.493.453.77

324.514.194.164.144.51

64(0.1)5.295.075.055.045.29


10000.013.7033.553.4433.44150

10000.013.7033.553.4433.436100

10000.013.7033.553.4433.43150

10000.013.7033.553.4433.428200

10000.013.7033.553.4433.428250

10000.013.7033.553.4433.425300


10000.13.7183.5413.443.41450

10000.13.7183.5413.443.402100

10000.13.7183.5413.443.391150

10000.13.7183.5413.443.389200

10000.13.7183.5413.443.387250

10000.13.7183.5413.443.387300


10000.0013.7093.5373.4443.444

10000.0013.7093.5373.4443.444

10000.0013.7093.5373.4443.443

10000.0013.7093.5373.4443.443

10000.0013.7093.5373.4443.443

10000.0013.7093.5373.4443.442


0.13.7123.5423.4443.406

3.7123.5423.4443.396

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392


10000.23.7343.5693.4553.415

10000.23.7343.5693.4553.401

10000.23.7343.5693.4553.395

10000.23.7343.5693.4553.394

10000.23.7343.5693.4553.394

10000.23.7343.5693.4553.394


10000.33.6943.5513.4333.403

10000.33.6943.5513.4333.389

10000.33.6943.5513.4333.384

10000.33.6943.5513.4333.382

10000.33.6943.5513.4333.38

10000.33.6943.5513.4333.38


10000.43.7163.5573.4453.445

10000.43.7163.5573.4453.444

10000.43.7163.5573.4453.444

10000.43.7163.5573.4453.444

10000.43.7163.5573.4453.444

10000.43.7163.5573.4453.444

Sheet2

Sheet2

3.663.763.813.743.723.82

3.453.613.573.663.533.58

3.383.543.53.543.463.46

3.363.523.483.513.433.43

10 generations

20 generations

30 generations

50 generations

80 generations

100 genreations


Average passes

100Rounds(16*16), MP=0.1

Sheet3

3.73.73.733.633.783.72

3.533.593.533.533.553.52

3.433.513.453.383.53.43

3.413.53.443.373.493.42

10 generations

20 generations

30 generations

50 generations

80 generations

100 generations


Average Passes

100 Rounds(16*16), MP=0.001

3.7033.553.4433.441

3.7033.553.4433.436

3.7033.553.4433.43

3.7033.553.4433.428

3.7033.553.4433.428

3.7033.553.4433.425



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7093.5373.4443.444

3.7093.5373.4443.444

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.442

3.7183.5413.443.414

3.7183.5413.443.402

3.7183.5413.443.391

3.7183.5413.443.389

3.7183.5413.443.387

3.7183.5413.443.387



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7123.5423.4443.406

3.7123.5423.4443.396

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7093.5373.4443.444

3.7093.5373.4443.444

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.442



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


AnalysisBest Mutation Probability: 0.1---0.3 Generations:100---300Population size:4--8Crossover Probability used: 100%In this research, maximum colors reduced by GA: 2

Maximum passes reduced by GA in this research

Sheet1


8100100.5Single22.722.582.562.5600.020.16

10010000.5Single22.732.592.572.5700.020.16

820010000.5Single22.6652.512.4852.48!!0.0050.030.185

0

100100.001Single42.782.682.672.671 sec00.010.11

1001000.001Single42.772.652.632.638 sec00.020.14

10010000.001Single42.782.612.582.5874 sec00.030.2

20010000.001Single42.72.562.5252.525147 sec00.0350.175

0

0

16100100.5Single23.753.493.423.4200.070.33

1001000.5Single23.663.523.463.45!!0.010.070.21

1001000.5While23.693.543.453.42!!0.030.120.27

000

(#4)100100.01While43.653.453.363.350.010.10.3

(#8)100100.001While43.73.533.433.410.020.120.29

(#9)100200.01While43.823.523.453.440.010.080.38

(#9)100200.001While43.73.593.513.50.010.090.2

(#4)100300.01While43.773.543.413.40.010.140.37

(#4)100300.001While43.733.533.453.440.010.090.29

(#7)100500.01While43.63.523.373.360.010.160.24

(#20)100500.001While43.633.533.383.370.010.160.26

(#9)100800.01While43.693.513.393.380.010.130.31

(#4)100800.001While43.783.553.53.490.010.060.29

(#5)1001000.01While43.673.473.383.370.010.10.3

(#2)1001000.001While43.723.523.433.420.010.10.3

(#4)1001000.001Double43.743.493.383.3722 sec0.010.120.37

(#1)100010000.001Double43.6983.5433.4323.4339m24s0.0020.1130.268

(#1)100010000.001Single43.6943.5183.4163.41259m28s0.0040.1060.282

0

321001000.5While24.524.354.274.2700.080.25

10010000.5While254.44.44.3>13hours0.10.10.7

0

20200.001While4No improvement whithin 100 times0

(#38)20500.001While44.654.44.34.2519 sec0.050.150.4

(#11)201000.001While44.654.44.254.236 sec0.050.20.45

(#24)50100.001While44.464.264.124.110 sec0.020.160.36

(#23)50200.001While44.544.284.264.2420 sec0.020.040.3

(#12)50500.001While44.64.384.344.3247 sec0.020.060.28

(#15)501000.001While44.584.34.264.2495 sec0.020.060.34

(#5)10050.001While44.54.244.24.1910 sec0.010.050.31

(#2)100100.001While44.544.284.214.1919 sec0.020.090.35

(#1)100200.001While44.54.244.194.1837 sec0.010.060.32

(#6)100500.001While44.534.274.174.1691 sec0.010.110.37

(#3)1001000.001While44.474.264.194.18197 sec0.010.080.29

0

641001000.5While2more than 24 hours0

0

(#4)100100.001While45.325.055.025.011m29s0.010.040.31

(#5)100200.001While45.295.044.994.982m57s0.010.060.31

(#10)100500.001While45.354.984.964.957m39s0.010.030.4

(#1)1001000.001While45.285.065.035.0214m27s0.010.040.26

0

1281001000.001While46.195.875.855.8461m38s0.010.030.35


8100100.5Single22.722.582.562.56

810010000.5Single22.732.592.572.57

820010000.5Single22.6652.512.4852.488 hours

16100100.5Single23.753.493.423.42

161001000.5Single23.663.523.463.454 hours

321001000.5Single24.524.354.274.27

3210010000.5Single254.44.44.313hours



8100100.001Single42.782.682.672.671 sec

81001000.001Single42.772.652.632.638 sec

810010000.001Single42.782.612.582.5874 sec

820010000.001Single42.72.562.5252.525147 sec

161001000.001Single43.723.523.433.4238sec

16100010000.001Single43.6943.5183.4163.41259m28s

32501000.001Single44.584.34.264.2495 sec

321001000.001Single44.474.264.194.18197 sec

64100500.001Single45.354.984.964.957m39s

641001000.001Single45.285.065.035.0214m27s

1281001000.001Single46.195.875.855.8461m38s

nodesSequential - GeneticDegree descending - GeneticSmallest - Genetic

8222

16222

32221

64211

128211

256211

Sheet2

Sheet3

Single vs. Double Crossover

Chart3

3.6953.684

3.5283.528

3.4053.42

3.4023.416

Double Crossover

Single Crossover

Seq->Des->Smallest->Genetic

Average Passes

1000 Rounds,1000 Gens, MP=0.001(16*16 Network)

Chart4

3.743.72

3.493.52

3.383.43

3.373.42

Double Crossover

Single Crossover


Average Passes

100Rounds,100Gens(16*16),MP=0.001

Chart5

2.772.652.632.63

3.723.523.433.415

4.474.264.194.175

5.285.065.035.01




Genetic Algorithm


Average Passes

100 Rnds, 100 Gens, MP=0.001

Chart7

3.6953.684

3.5283.528

3.4053.42

3.4023.416

Double Crossover

Single Crossover


Average Passes

1000Rnds,1000Gens(16*16),MP=0.001

Sheet1


100100.013.653.453.363.35

100200.013.823.523.453.44

100300.013.773.543.413.4

100500.013.63.523.373.36

100800.013.693.613.393.38

1001000.013.673.473.383.37


100100.0013.73.533.433.41

100200.0013.73.593.513.5

100300.0013.733.533.453.44

100500.0013.633.533.383.37

100800.0013.783.553.53.49

1001000.0013.723.523.433.42


100100.13.663.453.383.36

100200.13.763.613.543.52

100300.13.813.573.53.48

100500.13.743.663.543.51

100800.13.723.533.463.43

1001000.13.823.583.463.43


100100.13.733.53.393.360.03

100200.13.693.543.483.470.01

100300.13.73.53.413.350.06

100500.13.753.553.463.370.09

100800.13.783,63.523.470.05

1001000.13.733.563.493.460.03

3.6953.5283.4053.402

3.6843.5283.423.416

3.743.493.383.37

3.723.523.433.42

2.773.724.475.28

2.653.524.265.06

2.633.434.195.03

2.633.4154.1755.01

mp=0.282.842.752.72.652.84

163.773.613.493.453.77

324.514.194.164.144.51

64(0.1)5.295.075.055.045.29


10000.013.7033.553.4433.44150

10000.013.7033.553.4433.436100

10000.013.7033.553.4433.43150

10000.013.7033.553.4433.428200

10000.013.7033.553.4433.428250

10000.013.7033.553.4433.425300


10000.13.7183.5413.443.41450

10000.13.7183.5413.443.402100

10000.13.7183.5413.443.391150

10000.13.7183.5413.443.389200

10000.13.7183.5413.443.387250

10000.13.7183.5413.443.387300


10000.0013.7093.5373.4443.44450

10000.0013.7093.5373.4443.444100

10000.0013.7093.5373.4443.443150

10000.0013.7093.5373.4443.443200

10000.0013.7093.5373.4443.443250

10000.0013.7093.5373.4443.442300


0.13.7123.5423.4443.406

3.7123.5423.4443.396

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392


10000.23.7343.5693.4553.41550

10000.23.7343.5693.4553.401100

10000.23.7343.5693.4553.395150

10000.23.7343.5693.4553.394200

10000.23.7343.5693.4553.394250

10000.23.7343.5693.4553.394300


10000.33.6943.5513.4333.40350

10000.33.6943.5513.4333.389100

10000.33.6943.5513.4333.384150

10000.33.6943.5513.4333.382200

10000.33.6943.5513.4333.38250

10000.33.6943.5513.4333.38300


10000.43.7163.5573.4453.44550

10000.43.7163.5573.4453.444100

10000.43.7163.5573.4453.444150

10000.43.7163.5573.4453.444200

10000.43.7163.5573.4453.444250

10000.43.7163.5573.4453.444300

RoundsMPGensNetwork sizeSeqDescendSmallestGeneticGens

10000.110082.7342.5932.5732.562

163.7013.5483.4363.394

324.4934.2534.24.179

645.3435.0575.0335.023

Sheet1

Double Crossover

Single Crossover

Seq->Des-Smallest->Genetic

Average Passes

100 Rounds, 100 Generations, MP=0.001(16*16 Network)

Sheet2

Double Crossover

Single Crossover


Average Passes


Sheet3

Sheet3

3.7033.553.4433.441

3.7033.553.4433.436

3.7033.553.4433.43

3.7033.553.4433.428

3.7033.553.4433.428

3.7033.553.4433.425



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7093.5373.4443.444

3.7093.5373.4443.444

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.442

3.7183.5413.443.414

3.7183.5413.443.402

3.7183.5413.443.391

3.7183.5413.443.389

3.7183.5413.443.387

3.7183.5413.443.387



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7123.5423.4443.406

3.7123.5423.4443.396

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7093.5373.4443.444

3.7093.5373.4443.444

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.442



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.6943.5513.4333.403

3.6943.5513.4333.389

3.6943.5513.4333.384

3.6943.5513.4333.382

3.6943.5513.4333.38

3.6943.5513.4333.38



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7163.5573.4453.445

3.7163.5573.4453.444

3.7163.5573.4453.444

3.7163.5573.4453.444

3.7163.5573.4453.444

3.7163.5573.4453.444



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


Comparisons of 5 algorithms

Chart3

2.712.822.932.652.58

3.743.713.833.553.44

4.464.544.644.224.15

5.375.395.7955.05

6.176.126.715.875.74


Sequetial down Algorithm

Degree-ascending Algorithm


Genetic Algorithm

Number of stages of OMIN

Average Passes

Performances of 5 algorithms(MP=0.1,Gens=100)

Sheet1

2.712.822.932.652.58

3.743.713.833.553.44

4.464.544.644.224.15

5.375.395.7955.05

6.176.126.715.875.74

Sheet1


Sequetial down Algorithm

Degree-ascending Algorithm


Genetic Algorithm

Number of stages of OMIN

Average Passes

Performances of 5 algorithms(MP=0.1,Gens=100)

Sheet2

Sheet3

MBD001D29B4.xls

Chart3

3.6953.684

3.5283.528

3.4053.42

3.4023.416

Double Crossover

Single Crossover


Average Passes


Chart4

3.743.72

3.493.52

3.383.43

3.373.42

Double Crossover

Single Crossover


Average Passes

100Rounds,100Gens(16*16),MP=0.001

Chart5

2.772.652.632.63

3.723.523.433.415

4.474.264.194.175

5.285.065.035.01




Genetic Algorithm


Average Passes

100 Rnds, 100 Gens, MP=0.001

Chart7

3.6953.684

3.5283.528

3.4053.42

3.4023.416

Double Crossover

Single Crossover


Average Passes

1000Rnds,1000Gens(16*16),MP=0.001

Sheet1


100100.013.653.453.363.35

100200.013.823.523.453.44

100300.013.773.543.413.4

100500.013.63.523.373.36

100800.013.693.613.393.38

1001000.013.673.473.383.37


100100.0013.73.533.433.41

100200.0013.73.593.513.5

100300.0013.733.533.453.44

100500.0013.633.533.383.37

100800.0013.783.553.53.49

1001000.0013.723.523.433.42


100100.13.663.453.383.36

100200.13.763.613.543.52

100300.13.813.573.53.48

100500.13.743.663.543.51

100800.13.723.533.463.43

1001000.13.823.583.463.43


100100.13.733.53.393.360.03

100200.13.693.543.483.470.01

100300.13.73.53.413.350.06

100500.13.753.553.463.370.09

100800.13.783,63.523.470.05

1001000.13.733.563.493.460.03

3.6953.5283.4053.402

3.6843.5283.423.416

3.743.493.383.37

3.723.523.433.42

2.773.724.475.28

2.653.524.265.06

2.633.434.195.03

2.633.4154.1755.01

mp=0.282.842.752.72.652.84

163.773.613.493.453.77

324.514.194.164.144.51

64(0.1)5.295.075.055.045.29


10000.013.7033.553.4433.44150

10000.013.7033.553.4433.436100

10000.013.7033.553.4433.43150

10000.013.7033.553.4433.428200

10000.013.7033.553.4433.428250

10000.013.7033.553.4433.425300


10000.13.7183.5413.443.41450

10000.13.7183.5413.443.402100

10000.13.7183.5413.443.391150

10000.13.7183.5413.443.389200

10000.13.7183.5413.443.387250

10000.13.7183.5413.443.387300


10000.0013.7093.5373.4443.44450

10000.0013.7093.5373.4443.444100

10000.0013.7093.5373.4443.443150

10000.0013.7093.5373.4443.443200

10000.0013.7093.5373.4443.443250

10000.0013.7093.5373.4443.442300


0.13.7123.5423.4443.406

3.7123.5423.4443.396

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392


10000.23.7343.5693.4553.41550

10000.23.7343.5693.4553.401100

10000.23.7343.5693.4553.395150

10000.23.7343.5693.4553.394200

10000.23.7343.5693.4553.394250

10000.23.7343.5693.4553.394300


10000.33.6943.5513.4333.40350

10000.33.6943.5513.4333.389100

10000.33.6943.5513.4333.384150

10000.33.6943.5513.4333.382200

10000.33.6943.5513.4333.38250

10000.33.6943.5513.4333.38300


10000.43.7163.5573.4453.44550

10000.43.7163.5573.4453.444100

10000.43.7163.5573.4453.444150

10000.43.7163.5573.4453.444200

10000.43.7163.5573.4453.444250

10000.43.7163.5573.4453.444300


10000.110082.7342.5932.5732.562

163.7013.5483.4363.394

324.4934.2534.24.179

645.3435.0575.0335.023

Sheet1

Double Crossover

Single Crossover


Average Passes


Sheet2

Double Crossover

Single Crossover


Average Passes


Sheet3

Sheet3

3.7033.553.4433.441

3.7033.553.4433.436

3.7033.553.4433.43

3.7033.553.4433.428

3.7033.553.4433.428

3.7033.553.4433.425



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7093.5373.4443.444

3.7093.5373.4443.444

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.442

3.7183.5413.443.414

3.7183.5413.443.402

3.7183.5413.443.391

3.7183.5413.443.389

3.7183.5413.443.387

3.7183.5413.443.387



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7123.5423.4443.406

3.7123.5423.4443.396

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7093.5373.4443.444

3.7093.5373.4443.444

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.442



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.6943.5513.4333.403

3.6943.5513.4333.389

3.6943.5513.4333.384

3.6943.5513.4333.382

3.6943.5513.4333.38

3.6943.5513.4333.38



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7163.5573.4453.445

3.7163.5573.4453.444

3.7163.5573.4453.444

3.7163.5573.4453.444

3.7163.5573.4453.444

3.7163.5573.4453.444



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


MBD001D304B.xls

Chart1

3.743.72

3.493.52

3.383.43

3.373.42

Double Crossover

Single Crossover


Average Passes


Chart4

3.743.72

3.493.52

3.383.43

3.373.42

Double Crossover

Single Crossover


Average Passes

100Rounds,100Gens(16*16),MP=0.001

Chart5

2.772.652.632.63

3.723.523.433.415

4.474.264.194.175

5.285.065.035.01




Genetic Algorithm


Average Passes

100 Rnds, 100 Gens, MP=0.001

Chart7

3.6953.684

3.5283.528

3.4053.42

3.4023.416

Double Crossover

Single Crossover


Average Passes

1000Rnds,1000Gens(16*16),MP=0.001

Sheet1


100100.013.653.453.363.35

100200.013.823.523.453.44

100300.013.773.543.413.4

100500.013.63.523.373.36

100800.013.693.613.393.38

1001000.013.673.473.383.37


100100.0013.73.533.433.41

100200.0013.73.593.513.5

100300.0013.733.533.453.44

100500.0013.633.533.383.37

100800.0013.783.553.53.49

1001000.0013.723.523.433.42


100100.13.663.453.383.36

100200.13.763.613.543.52

100300.13.813.573.53.48

100500.13.743.663.543.51

100800.13.723.533.463.43

1001000.13.823.583.463.43


100100.13.733.53.393.360.03

100200.13.693.543.483.470.01

100300.13.73.53.413.350.06

100500.13.753.553.463.370.09

100800.13.783,63.523.470.05

1001000.13.733.563.493.460.03

3.6953.5283.4053.402

3.6843.5283.423.416

3.743.493.383.37

3.723.523.433.42

2.773.724.475.28

2.653.524.265.06

2.633.434.195.03

2.633.4154.1755.01

mp=0.282.842.752.72.652.84

163.773.613.493.453.77

324.514.194.164.144.51

64(0.1)5.295.075.055.045.29


10000.013.7033.553.4433.44150

10000.013.7033.553.4433.436100

10000.013.7033.553.4433.43150

10000.013.7033.553.4433.428200

10000.013.7033.553.4433.428250

10000.013.7033.553.4433.425300


10000.13.7183.5413.443.41450

10000.13.7183.5413.443.402100

10000.13.7183.5413.443.391150

10000.13.7183.5413.443.389200

10000.13.7183.5413.443.387250

10000.13.7183.5413.443.387300


10000.0013.7093.5373.4443.44450

10000.0013.7093.5373.4443.444100

10000.0013.7093.5373.4443.443150

10000.0013.7093.5373.4443.443200

10000.0013.7093.5373.4443.443250

10000.0013.7093.5373.4443.442300


0.13.7123.5423.4443.406

3.7123.5423.4443.396

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392


10000.23.7343.5693.4553.41550

10000.23.7343.5693.4553.401100

10000.23.7343.5693.4553.395150

10000.23.7343.5693.4553.394200

10000.23.7343.5693.4553.394250

10000.23.7343.5693.4553.394300


10000.33.6943.5513.4333.40350

10000.33.6943.5513.4333.389100

10000.33.6943.5513.4333.384150

10000.33.6943.5513.4333.382200

10000.33.6943.5513.4333.38250

10000.33.6943.5513.4333.38300


10000.43.7163.5573.4453.44550

10000.43.7163.5573.4453.444100

10000.43.7163.5573.4453.444150

10000.43.7163.5573.4453.444200

10000.43.7163.5573.4453.444250

10000.43.7163.5573.4453.444300


10000.110082.7342.5932.5732.562

163.7013.5483.4363.394

324.4934.2534.24.179

645.3435.0575.0335.023

Sheet1

Double Crossover

Single Crossover


Average Passes


Sheet2

Sheet2

3.7033.553.4433.441

3.7033.553.4433.436

3.7033.553.4433.43

3.7033.553.4433.428

3.7033.553.4433.428

3.7033.553.4433.425



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


Sheet3

3.7093.5373.4443.444

3.7093.5373.4443.444

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.442

3.7183.5413.443.414

3.7183.5413.443.402

3.7183.5413.443.391

3.7183.5413.443.389

3.7183.5413.443.387

3.7183.5413.443.387



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7123.5423.4443.406

3.7123.5423.4443.396

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392

3.7123.5423.4443.392



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7093.5373.4443.444

3.7093.5373.4443.444

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.443

3.7093.5373.4443.442



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.6943.5513.4333.403

3.6943.5513.4333.389

3.6943.5513.4333.384

3.6943.5513.4333.382

3.6943.5513.4333.38

3.6943.5513.4333.38



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


3.7163.5573.4453.445

3.7163.5573.4453.444

3.7163.5573.4453.444

3.7163.5573.4453.444

3.7163.5573.4453.444

3.7163.5573.4453.444



Smallest Algorithm

Genetic Algorithm

N*50 Generations

Average Passes


Java Applet

Sequential Algo.(128*128)

Sequential Down Algo.

Degree-ascending Algo.

Degree-descending Algo.

Genetic Algorithm

Comparisons of 5 algorithms

Conclusion and Future workGenetic Algorithm can be used as a optimizing toolDisadvantage:time consumingPerform GA in parallelOther complicated GA techniques to improve the results

routing and scheduling in multistage networks using genetic algorithms

Documents