B.Sc thesis

1. EVOLUTIONARYALGORITHMFORGRAPHCOLORINGPROBLEM
Presented by
RobiulIslam
2009-2-60-004
And
Arup Kumar Pramanik
2009-2-60-008
East West University
Date : 28 April, 2013
1

2. SUPERVISOR
Professor Dr.MozammelHuqAzad Khan
Dept. of Computer Science & Engineering
East West University
2

3. KEYTERM
Evolutionary Algorithm
Binary Encoding
Mutation
Adding new population
Deterministic process
3

4. GRAPHCOLORINGPROBLEM
Acoloringofsimplegraphistheassignmentofacolortoeachvertexofthegraphsothatnotwoadjacentverticesareassignedthesamecolor.Thechromaticnumberofagraphistheleastnumberofcolorsneededforacoloringofthisgraph.
* Well-Known NP-hard Problem
* Two adjacency nodes does not contain
same colour
* Uses minimum number of colours
* Also known as vertex colouring problem
4

5. EVOLUTIONARYALGORITHM
Evolutionaryalgorithms(EA)aresearchalgorithmbasedonthemechanicsofnaturalselectionandnaturalgenetics
Ineverygeneration,anewsetofartificialcreatures(chromosome)iscreatedusingbitsandpiecesofthefittestoftheold,anoccasionalnewpartistriedforgoodmeasure.
5

6. DETAILSOFMYCIEL3.COL GRAPH
Node = 11
Edge = 20
Initialization Color = Maximum Out degree +1, which is upper bound of chromatic number
Represent binary matrix with Initialization Color*Node
Here number of row = 6
Number of column = 11
Row represent Color
Column represent Node
6

7. ENCODINGTECHNIQUE
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
Vertices
1
2
3
4
5
6
Colors
1 2 3 4 5 6 7 8 9 10 11
7

8. ALGORITHMDESCRIPTION: FITNESS
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
Vertices
1
2
3
4
5
6
Colors
1 2 3 4 5 6 7 8 9 10 11
Invalid Color
Valid Color
Unused Color
8

9. ALGORITHMDESCRIPTION: FITNESS(CONTINUE)
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
Invalid Row : 3
Valid Row : 2
Unused Row :1
Fitness = Invalid Row * (maximum out degree+1) + Valid Row
Here myciel3.col data file
Fitness Value = 3*6+2
= 20
1 2 3 4 5 6 7 8 9 10 11
1
2
3
4
5
6
Two edges share same ages those
colors are not valid
9

10. ALGORITHMDESCRIPTION: CORRECTION
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1 2 3 4 5 6 7 8 9 10 11
1
2
3
4
5
6
Invalid Row : 2
Valid Row : 4
Fitness Value = 2*6+4
= 16 10

11. ALGORITHMDESCRIPTION: CORRECTION(CONTINUE)
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
Invalid Row : 1
Valid Row : 5
Fitness Value = 1*6+5
= 11
1 2 3 4 5 6 7 8 9 10 11
1
2
3
4
5
6
11

12. ALGORITHMDESCRIPTION: CORRECTION(CONTINUE)
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
Invalid Row : 0
Valid Row : 6
Fitness Value = 0*6+6
= 6
1 2 3 4 5 6 7 8 9 10 11
1
2
3
4
5
6
12

13. ALGORITHMDESCRIPTION
Remove duplicate chromosome
Copying total number of population to a temporary population 13

14. ALGORITHMDESCRIPTION: MUTATION
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1 2 3 4 5 6 7 8 9 1011
1
2
3
4
5
6
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1 2 3 4 5 6 7 8 9 1011
1
2
3
4
5
6
Basic Chromosome
Mutated Chromosome
Randomly select one bit in a row with low probability
If it’s zero convert into one
If it’s one convert into zero 14

15. ALGORITHMDESCRIPTION: REPAPERINGPOPULATION
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1 2 3 4 5 6 7 8 9 1011
1
2
3
4
5
6
Mutated Chromosome
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
3
4
5
6
1 2 3 4 5 6 7 8 9 1011
After Reaper Chromosome
15

16. ALGORITHMDESCRIPTION
Calculate fitness of mutated population
Corrected mutation population
Remove duplicate chromosome of mutated population
16

17. MERGINGTEMPORARYPOPULATIONTOINITIALPOPULATIONACCORDINGTOMINIMUMFITNESSVALUEANDADDING
Adding new population of initial population replace worst population
6
5
6
5
6
5
6
4
4
5
6
5
Fitness Value of
Population
Fitness Value of
Mutated Population
4
5
4
5
5
5
Fitness Value after
Merge
17

18. DETERMINISTICPROCESS
Before
After
Valid Color 6
Valid Color 4
18

19. EXPERIMENTALRESULT
Data File (퐺)
Node
Edge
휒(퐺)
EAGCP
[1]
[2]
[3]
myciel3.col
11
20
4
4
4
4
4
myciel4.col
23
71
5
5
5
5
5
queen5_5.col
25
160
5
5
5
5
5
queen6_6.col
36
290
7
8
7
7
7
myciel5.col
47
236
6
6
6
6
6
huck.col
74
301
11
11
11
11
11
jean.col
80
254
10
10
10
10
10
anna.col
138
493
11
12
11
11
11
david.col
87
406
11
12
11
11
11
19

20. EXPERIMENTALRESULT
Data File :myciel3.col
Node: 11
Edge: 20
Generation: 51
Chi (G): 4
EAGCP: 4
Population Size: 50
Maximum Color: 6
Mutation Probability: 10%
Additional Probability: 10%
20

21. EXPERIMENTALRESULT(CONTINUE)
Date File : myciel4.col
Node: 23
Edge: 71
Generation: 163
Chi (G): 5
EAGCP: 5
Population Size: 50
Maximum Color: 12
Mutation Probability: 10%
Additional Probability: 10%
21

22. EXPERIMENTALRESULT(CONTINUE)
Date File : myciel5.col
Node: 47
Edge: 236
Generation: 765
Chi (G): 6
EAGCP: 6
Population Size: 150
Maximum Color: 24
Mutation Probability: 10%
Additional Probability: 10%
22

23. EXPERIMENTALRESULT(CONTINUE)
Data File: queen5_5.col
Node: 25
Edge: 160
Generation: 845
Chi (G): 5
EAGCP: 5
Population Size: 200
Maximum Color: 17
Mutation Probability: 15%
Additional Probability: 10%
23

24. EXPERIMENTALRESULT(CONTINUE)
Date File : huck.col
Node: 71
Edge: 301
Generation: 1897
Chi (G): 11
EAGCP: 11
Population Size: 500
Maximum Color: 54
Mutation Probability: 10%
Additional Probability: 10%
24

25. CONCLUSION
In this thesis work we have focused on a better minimize chromatic number with proper EA step for GCP
It helps mutation, evaluate, immune system and also reduce colour dynamically
Our best result of large dataset is huck.colwhich has 71 node and 301 edge and find expected color in this graph 25

26. FUTUREWORK
Used our algorithm in different stranded data set
Optimal result of large data set
Reducing the time complexity
26

27. THANKYOU
27