The document describes using a genetic algorithm to solve, rate, and generate Sudoku puzzles. It discusses representing Sudoku puzzles and their solutions as chromosomes. The genetic algorithm uses crossover and mutation operators to evolve puzzle solutions over generations. It also uses a fitness function based on puzzle difficulty metrics to evaluate and rank generated puzzles according to their difficulty level.

1. Sudoku

2. Sudoku
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Sudoku

3. Sudoku



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Sudoku
Sudoku

4. Sudoku
GAuGE
Sudoku GA
Sudoku Maker
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Sudoku

5. GA
Sudoku
Sudoku
Sudoku
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Sudoku

6. chromosome
uniform
swap
Pm=0.6
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Sudoku

7. for(i=POP-1; i>=ELIT; i--)
{
ii=ord[i];
p1 = ord[i*Math.random()];
p2 = ord[i*Math.random()];
crossover(indiv[ii], indiv[p1], indiv[p2]);
mutation(indiv[ii]);
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Sudoku

8. Sudoku
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Sudoku

9. /
Sudoku

10. /
Sudoku

11. /
Sudoku

12. /
Sudoku

13. restart
cataclysmic
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Sudoku

14. A = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A
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Sudoku

15. A = {1, 2, 3, 4, 5, 6, 7, 8, 9}
gi3(x) = |A - xi|
gj3 (x) = |A – xj|
-
-
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Sudoku

16. 1 star, Easy,
2 star, Challenging
3 star, , Difficult,
4 star, Super
5 star. Difficult
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Sudoku

17. 1 2 3 4 5
Challenging Difficu Super
star stars stars stars stars Easy
Difficult
lt
Super Difficult
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Sudoku

18. -
GA
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Sudoku

19. –
GA
Easy
Open
1 star
2 stars
3 stars
4 stars
Challenging
5 stars
Difficult
Super Difficult
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Sudoku

20. -
N -
SudokuExplainer
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Sudoku

21. Sudoku
Sudoku
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Sudoku

22. /
Sudoku

23. 
Sudoku
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

Sudoku
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Sudoku 
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Sudoku

24.  1. T. Mantere, J. Koljonen, “Solving, Rating and
Generating Sudoku Puzzles with GA,” in 2007 IEEE
Congress on Evolutionary computation – CEC2007,
Singapore, 2007
 2. T. Mantere, J. Koljonen, “Solving and rating Sudoku
puzzles with genetic algorithms,” in Finnish Artificial
Intelligence Conference (STeP 2006), October 26-27,
FAIS, Espoo, Finland, 2006
 3. T. Mantere, J. Koljonen, “Solving and Analyzing
Sudokus with Cultural Algorithms” in 2008 IEEE
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Sudoku