1. Optimization and Learning via Genetic Programming
AI Project #2
Biointelligence lab
Cho, Dong-Yeon

2. Optimization of Boolean Functions (1/2)
Parity Functions
Even-2 Parity
Function set F = {AND, OR, NAND, NOR}
Terminal set T = {D0, D1}
Fitness function
The number of fitness cases for which the individual is incorrect OR D0 D1
Out 1
NOR
AND D1 D0 D0 D1
© 2005 SNU CSE Biointelligence Lab

3. Optimization of Boolean Functions (2/2)IF
6-Multiplexer
2 address bits, 4 data bits
Function set F = {AND, OR, NOT, IF}
Terminal set T = {A0, A1, D0, D1, D2, D3}
Fitness function
The number of fitness cases for which the individual is incorrect IF
AND D3 D0 D1
Out IF A0 A1 A0 D1 D2 D3 A1 D2 D0 A0 A1
© 2005 SNU CSE Biointelligence Lab

4. © 2005 SNU CSE Biointelligence Lab
Learning a Classifier
Pima Indian Diabetes
Functions
Numerical and condition operators
{+, -, *, /, exp, log, sin, cos, sqrt, iflte ifltz, …}
Some operators should be protected from the illegal operation.
Terminals
Input features and constants
{x0, x1, … x7, R} where R  [a, b]
Additional parameters
Threshold value
For normalization
© 2005 SNU CSE Biointelligence Lab

5. © 2005 SNU CSE Biointelligence Lab
Cross Validation (1/3)
K-fold Cross Validation
The data set is randomly divided into k subsets.
One of the k subsets is used as the test set and the other k-1 subsets are put together to form a training set. D1 D2 D3 D4 D5 D6
128
128
128
128
128
128 D1 D2 D3 D4 D6 D5
128
128
128
128
128
128 D2 D3 D4 D5 D6 D1
128
128
128
128
128
128
© 2005 SNU CSE Biointelligence Lab

6. © 2005 SNU CSE Biointelligence Lab
Cross Validation (2/3)
Calculation of the error
Confusion Matrix
True
Predict
Positive
Negative
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7. © 2005 SNU CSE Biointelligence Lab
Cross Validation (3/3)
Cross validation and Confusion Matrix
At least 10 runs for your k value.
Show the confusion matrix for the best result of your experiments.
Run
Test Error 1 2
 10
Average
© 2005 SNU CSE Biointelligence Lab

8. © 2005 SNU CSE Biointelligence Lab
Initialization
Maximum initial depth of trees Dmax is set.
Full method (each branch has depth = Dmax):
nodes at depth d < Dmax randomly chosen from function set F
nodes at depth d = Dmax randomly chosen from terminal set T
Grow method (each branch has depth  Dmax):
nodes at depth d < Dmax randomly chosen from F  T
nodes at depth d = Dmax randomly chosen from T
Common GP initialisation: ramped half-and-half, where grow and full method each deliver half of initial population
© 2005 SNU CSE Biointelligence Lab

9. © 2005 SNU CSE Biointelligence Lab
Selection (1/2)
Fitness proportional (roulette wheel) selection
The roulette wheel can be constructed as follows.
Calculate the total fitness for the population.
Calculate selection probability pk for each chromosome vk.
Calculate cumulative probability qk for each chromosome vk.
© 2005 SNU CSE Biointelligence Lab

10. © 2005 SNU CSE Biointelligence Lab
Procedure: Proportional_Selection
Generate a random number r from the range [0,1].
If r  q1, then select the first chromosome v1; else, select the kth chromosome vk (2 k  pop_size) such that qk-1 < r  qk. pk qk 1 2 3 4 5 6 7 8 9 10
© 2005 SNU CSE Biointelligence Lab

11. © 2005 SNU CSE Biointelligence Lab
Selection (2/2)
Tournament selection
Tournament size q
Ranking-based selection
2    POP_SIZE
1  +  2 and - = 2 - +
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12. © 2005 SNU CSE Biointelligence Lab
GP Flowchart
GA loop
GP loop
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13. © 2005 SNU CSE Biointelligence Lab
Bloat
Bloat = “survival of the fattest”, i.e., the tree sizes in the population are increasing over time
Ongoing research and debate about the reasons
Needs countermeasures, e.g.
Prohibiting variation operators that would deliver “too big” children
Parsimony pressure: penalty for being oversized
© 2005 SNU CSE Biointelligence Lab

14. © 2005 SNU CSE Biointelligence Lab

15. © 2005 SNU CSE Biointelligence Lab
Experiments
Two optimization problems
Parity
Even(odd)-3, Even(odd)-4, Even(odd)-5, …
11-multiplexer
3 address bits, 8 data bits
One classification problems
Pima Indian diabetes
Cross validation
Various experimental setup
Termination condition: maximum_generation
Each setting  10 runs
Effects of the penalty term
Selection methods and their parameters
Different function and terminal sets
Crossover and mutation probabilities …
© 2005 SNU CSE Biointelligence Lab

16. Results For each problem Result table and your analysis
Present the optimal function.
Compare with the results of neural networks
Draw a learning curve for the run where the best solution was found.
Training (optimization)
Test (classification)
Average  SD
Best
Worst
Setting 1
Setting 2
Setting 3
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17. © 2005 SNU CSE Biointelligence Lab
Fitness (Error)
Generation
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18. © 2005 SNU CSE Biointelligence Lab
References
Source Codes
GP libraries (C, C++, JAVA, …)
MATLAB Tool box
Web sites …
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19. © 2005 SNU CSE Biointelligence Lab
Pay Attention!
Due: Nov. 1, 2005
Submission
Source code and executable file(s)
Proper comments in the source code
Via
Report: Hardcopy!!
Running environments
Results for many experiments with various parameter settings
Analysis and explanation about the results in your own way
© 2005 SNU CSE Biointelligence Lab