1. N- Queens Solution with Genetic Algorithm By Mohammad A. Ismael

2. N-Queens problem Definition Place N queens on an N*N board so that no queen is attacking another queen. A queen can move horizontally, vertically, or diagonally. The problem can be solved with genetic algorithm for a n queens problem. (n is between 8 and 30) Here N=8

3. 8-Queens problem Simple solutions may lead to very high search costs  64 fields, 8 queens ==> 64^8 possible sequences Genetic algorithm solution trim the search space.

4. Problem formulation Initial State: n queens placed randomly on the board, one per column. Successor function: moving one queen to a new location. Cost: The number of queens that hit each others.

5. Genetic consists of Genes Chromosomes Populations

6. In n-queens… A gene is a number between 0 to n-1. Is a position of any queen in the board A chromosome is an array of these genes. It could be the solution. Population is a generated set of chromosomes.

7. Chromosomes and genes {3,6,8,5,1,4,0,7,9,2} {7,6,9,5,1,4,0,3,8,2} {9,6,1,5,8,4,0,7,3,2} {6,3,8,5,2,4,0,7,9,1} {3,6,8,5,1,4,0,7,9,2}. Gene Population A chromosome (array of genes. It could be an answer) Here N=10

8. Create a random initial population An initial population is created from a random selection of chromosomes. The number of generations needed depends on the random initial population.

9. Finding the cost To find the assigned cost for each chromosome a cost function is defined. The result of the cost function is called cost value. This value is used for chromosomes ranking The best (minimum value) is placed on top and the worst (maximum) is placed in the bottom.

10. Producing next generation Those chromosomes with a higher fitness (lesser cost) value are used to produce the next generation. The offspring (or Child) is a product of the two parents, whose composition consists of a combination of genes from them (this process is known as "crossing over"). If the new generation (Child) contains a chromosome that produces an output that is close enough or equal to the desired answer then the problem has been solved. If this is not the case, then the new generation will go through the same process as their parents did. This will continue until a solution is reached.

11. Steps to solving the problem with GA Clear the board. Generate the initial population. This generation is a purely random generation. Fill the chess board with a chromosome.  For example, Let Chromosome Matrix= {3,6,8,5,1,4,0, 7,9,2}, Here Chess Board Length =10 (n=10).

12. Steps to solving the problem with GA Determines the cost value for each chromosome matrix. For example,  For chromosome ={ 2,6,9,3,5, 0,4,1,7,8 }, the cost value will be 2  Because of there are two queens that hit each other

13. Steps to solving the problem with GA Sort the new generation according to their cost value. The best (minimum) is placed on top and the worst (maximum) is placed in the bottom. Generate the cross over matrix. This matrix contains 0s and 1s.

14. Steps to solving the problem with GA Generate children from parents using cross over matrix.  Genes are drawn from P 0 and P 1.  A gene is drawn from one parent and it is appended to the offspring (child) chromosome.  The corresponding gene is deleted in the other parent  This step is repeated until both parent chromosomes are empty and the offspring contains all genes involved.

15. Steps to solving the problem with GA Apply mutation to the current generation.  First of all, a random chromosome is selected but the first (best) one in the list.  Then, two random genes of this chromosome are selected and replaced with each other.  Increasing the number of mutations increases the algorithm’s freedom to search outside the current region of chromosome space.

16. Example of such software

17. Questions?