N-Queen Problem using Genetic Algorithms

• Download new.zip - 6.9 KB

Introduction

In this article, we describe a solution for solving the 8-queen problem. My solution is based on Genetic algorithms that is not a good method for solving this type of a problem.

In my code, first initiate the primary population (as chromosomes). For example: a={3 1 4 2} means queen is in row 1 and column 3, next queen is in row 2 and column 1, and etc.

Then select the best chromosomes from the population. In the next step generate some children from the population (crossover) and some of this children mutate. And between children and parents select the best chromosome.

This cycle repeats for n times (for example, n= 100).

Using the code

1. Before you run the program you should understand the variants that they use for population size, table size, and fitness (for genetic algorithms).

   fixedsize=100;
   tablesize=8;
   fitness=0; 

2. First, generate the primary population that shows as a decimal array: for example, (4-queens) : a={3 1 4 2} means queen is in row 1 and column 3, next queen is in row 2 and column 1, and etc.  

   for i=1:fixedsize
       cromo(i,1:tablesize)=randperm(tablesize);
       cromo(i,tablesize+1)=-1;
   end;
   for i=1:fixedsize
       for j=1:tablesize
           for k=j+1:tablesize
               if (cromo(i,j)==cromo(i,k)) || (abs(cromo(i,j)-abs(cromo(i,k))) == abs(j-k))
                   fitness=fitness+1;
               end;
           end;
       end;
       cromo(i,tablesize+1)=fitness;
       fitness=0;
   end;

3. Select the best parents to generate the children: 

   cromo=sortrows(cromo,9);

4. Generate the children and mutate them. Repeat this step for n times (example, n=1500). 

    for cnt=1:1500
       if(cromo(1:fixedsize,9)==0)
           level=cnt;
           checkboard(cromo(1,1:tablesize),tablesize,tablesize);
           break;
       end;
       %pm=(1/240)+(0.11375/2^cnt);
       pc=1/cnt ;
       slct=cromo(1:fixedsize,:);
       n=0;
       for i=1:2:fixedsize/2
           u=rand(1);
           if(u<=pc)
               n=n+2;
               child(n-1:n,1:tablesize)=crossover(slct(i:i+9,:),tablesize);
           end;
       end;
       %n=n+1;
       %if(n>0)
       child(:,tablesize+1)=-1;
       
       cromo((fixedsize+1)-length(child):end,:)=[];
       cromo=[cromo;child];
       for i=(fixedsize+1)-length(child):fixedsize
           cromo(i,1:tablesize)=mutation(cromo(i,1:tablesize),tablesize);
       end;
       %end;
       fitness=0;
       for i=1:fixedsize
           for j=1:tablesize
               for k=j+1:tablesize
                   if (cromo(i,j)==cromo(i,k)) || 
                              (abs(cromo(i,j)-abs(cromo(i,k))) == abs(j-k))
                       fitness=fitness+1;
                   end;
               end;
           end;
           cromo(i,tablesize+1)=fitness;
           fitness=0;
       end;
       cromo=sortrows(cromo,9);
   end;

History

• Version 1.0.