1. Introduction to Genetic Algorithm and Some Experience Sharing
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2. Genetic Algorithm (GA) Evolutionary Procedure
Outline
Introduction
Genetic Algorithm (GA) Evolutionary Procedure
Some Experience Discussion
Conclusion
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3. Introduction
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4. Introduction Presented by John Holland in 1975
Mimicking the Natural Selection and Natural Genetics
A Numerical Optimization Method of Global Search
Suited to Large Scale and Complicated System Riddle with Some Local Minimum
Exploitation and exploration
Near-optimal Solution
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5. Introduction
y=x2 × o
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6. Introduction GA’s Form: Binary Genetic Algorithm
Continuous Parameter Genetic Algorithm
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7. GA Evolutionary Procedure
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8. The flow chart of genetic algorithm
Define chromosome formation
and fitness function
Create initial population
Evaluate fitness value
Select
Crossover
Mutate
Stop
Test stopping criterion
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9. Define chromosome formation and fitness functionP1 Q1
system, experiment, equation,... P2 Q2 P3 ： ： QM PN
chromosome=[P1, P2, P3, ...,PN]
P1, P2, P3, ...,PN: gene
fitness function or
cost function
Chromosome formation and fitness choice are depending on problem
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10. Define chromosome formation
and fitness function
fitness function: Represent pros and cons of a chromosome.
fitness function=-cost function or
fitness function=1/cost function
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11. Define chromosome formation and fitness function
binary GA:
quantization and encode
| | …|
P1, P2, P3, ...,PN
real number
chromosome=[ | |…| ] P1 P2 PN
continuous parameter GA:
chromosome=[P1, P2, P3, ...,PN]
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12. Define chromosome formation
and fitness function
EX:
chromosome formation
continuous parameter GA:
chromosome=[x, y]
binary GA:
chromosome=[ | ]
cost function C
C=-h or C=1/h
fitness function f
f=-C or 1/C h y x
x, y: space coordinate input
h: height output
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13. Create Initial Population
Generate chromosomes of first generation.
Determine the number of chromosome K at every generation.
Random generated
Methods:
Generate K initial chromosomes to evolve directly.
Generate L initial chromosomes, in which L>K. Choose best K to evolve.
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14. Select Determine parents chromosomes to mate.
Select procedure: Rank according to fitness Select appropriate members into mating pool Select appropriate parents from mating pool  Send to mate.
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15. Select n<=K Rank mating pool n K :: Select n better chromosomes
Generated by initialization or mate 1 2 3 n
mating pool
n<=K
Select n better chromosomes
Select parents to mate
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16. Select Mechanism A method selecting parents from the mating pool.
Method 1: Paring from top to bottom ::
Rank 1 2 3 K
mating pool
pair
To mate
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17. Select Mechanism Method 2: Random Paring
Random generate two parents from the mating pool to mate. The selected probability for each chromosome is the same. The procedure does not stop until K/2 pairs parents are generated.
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18. Method 3: Weighted Random Paring
Select Mechanism
Method 3: Weighted Random Paring
(a). Rank weighting: The selected probability is determined according to their rank.
Ex. n=6
Selected probability
rank i
cost Pi 1
-13778
0.2857 2
-13360
0.2381
0.5238 3
-13338
0.1905
0.7143 4
-13255
0.1429
0.8572 5
-13166
0.0952
0.9524 6
-13164
0.0476
1.0000
n: the number of chromosome
in the mating pool
i : rank
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19. Select Mechanism Method 3: Weighted Random Paring
(b). Cost weighting: The selected probability is calculated from the cost of the chromosome.
Ex. n=6
Selected probability Pi
rank i
cost Ci Pi 1
-13778
-699
0.4401 2
-13360
-281
0.1772
0.6174 3
-13338
-259
0.1632
0.7805 4
-13255
-176
0.1109
0.8915 5
-13166
-87
0.0547
0.9461 6
-13164
-85
0.0539
1.0000 7
-13079 ×
i : rank
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20. Method 4: Tournament selection
Select Mechanism
Method 4: Tournament selection
Two chromosomes are selected randomly. The chromosome which fitness is better selected as parent.
Ex. n=6
selected chromosomes
parent
paring
2,1 1
1,5
5,5 5
6,3 3
3,4
4,5 4
1,1
1,4
Hint: numerical represents the rank of the chromosome
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21. Crossover (Mating)
A GA operation creating one or more temporary offspring from the parents selected in the mating pool.
Exploitation and exploration
Crossover type:
single-point crossover
two-point crossover
uniform crossover
blending crossover (continuous parameter GA)
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22. Crossover (Mating)-binary GA
single-point crossover:
parent
parent
crossover point
offspring
offspring
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23. Crossover (Mating)-binary GA
two-point crossover:
parent
parent
crossover point
offspring
offspring
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24. Crossover (Mating)-binary GA
uniform crossover:
parent
parent
offspring
offspring
mask
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25. Crossover-continuous parameter GA
single-point crossover:
parent1 = [Pm1,Pm2,Pm3,Pm4,Pm5,Pm6, …, PmN]
crossover point
parent2 = [Pd1,Pd2,Pd3, Pd4,Pd5,Pd6, …,PdN]
offspring2 = [Pd1,Pd2,Pd3, Pm4,Pm5,Pm6, …, PmN]
offspring1 = [Pm1,Pm2,Pm3, Pd4,Pd5,Pd6, …,PdN]
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26. Crossover-continuous parameter GA
two-point crossover:
parent1 = [Pm1,Pm2, Pm3,Pm4, Pm5,Pm6, …, PmN]
crossover point
parent2 = [Pd1,Pd2, Pd3, Pd4, Pd5,Pd6, …,PdN]
offspring2 = [Pd1,Pd2, Pm3,Pm4, Pd5,Pd6, …, PdN]
offspring1 = [Pm1,Pm2, Pd3,Pd4, Pm5,Pm6, …,PmN]
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27. Crossover-continuous parameter GA
uniform crossover:
parent1 = [Pm1,Pm2, Pm3,Pm4, Pm5,Pm6, …, PmN]
parent2 = [Pd1,Pd2, Pd3, Pd4, Pd5,Pd6, …,PdN]
offspring2 = [Pm1,Pd2, Pm3,Pm4, Pd5,Pd6, …, PmN]
offspring1 = [Pd1,Pm2, Pd3,Pd4, Pm5,Pm6, …,PdN]
mask= [ … 1]
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28. Crossover-continuous parameter GA
blending crossover:
parent1 = [Pm1,Pm2,Pm3,Pm4,Pm5,Pm6, …, PmN]
parent2 = [Pd1, Pd2, Pd3, Pd4, Pd5, Pd6, …, PdN]
offspring = [Pnew1,Pnew2, Pnew3,Pnew4, Pnew5,Pnew6, …,PnewN]
=random number on interval [0, 1] for i-th gene in the offspring
Pmi=the i-th gene in the mother chromosome
Pdi=the i-th gene in the father chromosome
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29. Mutation Operation on temporary offspring from crossover
Escape from the local minimum and explore other zone.
Avoid pre-maturity
Low mutation rate (typically 1%～20%)
For binary GA, the mutated bit will be flip. (10, 01)
For continuous parameter GA, the mutated gene will be replaced by an arbitrary value.
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30. generated by crossover
Mutation-binary GA
chromosome
cost
-13778
-11956
-13338
-13553
-13289
-12164
-13372
-13642
-13036
-10586
-12587
-13652
chromosome
temporary offspring
generated by crossover
mutation rate=5%
12×14× 0.05≒8
mutation
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31. Mutation-continuous parameter GA
0<=x<=10
Chromosome=[x,y]
temporary offspring
generated by crossover
0<=y<=10
chromosome x y 1
9.0465
8.3128 2
9.0469
8.7384 ︰ 10
9.3469
7.9025 11
1.5034
9.0860 21
0.6056
5.1942 22
4.1539
4.7773 23
8.6750
2.7271 24
4.1208
3.1754
mutation rate=4%
24×2× 0.04≒2
chromosome10=[9.3469, ]
chromosome10=[3.5746, ]
chromosome23=[8.6750, ]
chromosome23=[8.6750, ]
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32. Stopping Criterion (a) A pre-set number of iterations.
(b) The same best chromosome is selected repeated for successive iterations.
(c) A acceptable solution is obtained.
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33. Elitism Permit some better chromosomes surviving into next generation.
Rank 1 2 3 K n :
sent to next generation directly
K-n
present generation
next generation
generated by GA operation
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34. Elitism Advantage: Fast convergence Better solution
Lower computation load
Drawback:
Pre-maturity (Easy sink into the local minimum)
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35. Some Experience Discussion
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36. Elitism or non-Elitism?
Comparison of GA with elitism and GA without elitism
Ex. Find F(x,y)=xsin(4x)+1.1ysin(2y) minimum value, 0<=x, y<=10
Binary GA
Chromosome=[x,y]
x,y: encode by 10bits
Population size=40
Ngood=20
Crossover rate=0.6
Mutation rate=0.1
Iteration number=100
Run number=30
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37. Size of population More chromosomes: Less chromosomes: Advantage
Better solution
Drawback
Larger computation load
Less chromosomes:
Advantage
Lighter computation load
Drawback
Worse solution
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38. Ex. Find F(x,y)=xsin(4x)+1.1ysin(2y) minimum value, 0<=x, y<=10
Size of population
Ex. Find F(x,y)=xsin(4x)+1.1ysin(2y) minimum value, 0<=x, y<=10
Binary GA
Chromosome=[x,y]
x,y: encode by 10bits
Ngood=population*0.4
Crossover rate=0.6
Mutation rate=0.05
Iteration number=50
Elitism
Run number=30
population size
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39. Selection mechanism Paring from top to bottom Random Paring
Rank weighting (ˇ)
Cost weighting
Tournament selection (ˇ)
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40. Which crossover is better?
binary GA:
uniform crossover
Continuous parameter GA:
blending crossover
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41. The number of iteration
Best choice
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42. The selection of GA operators and parameters is depend on problem.
Conclusion
The selection of GA operators and parameters is depend on problem.
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43. Thank you for your attention
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