# Solving the problem of eight queens with genetic algorithm

Source: Internet
Author: User

The convergence speed of this algorithm can also be found within 10,000 generations.

Main program

`clear;clc;%%% Eight queen problem, 8x8 on the board, placing 8 queens, so that 22 can not attack the initial state, randomly placed on the board 8 Queens, each column put an n = 8;    %8 Queen percent percent% the genetic algorithm is used to calculate the number of individuals randomly, and to form a population of 10 individuals no_of_people = 10;        People = Randi (N,[no_of_people,n]);    % the H value of each initial population people_h = ones (no_of_people,1);    For i = 1:no_of_people People_h (i) = Fun_c (People (I,:));    End% evolved how many generations, by g to count g = 1;    G_max = 1e5;    PLT = zeros (1,g_max); While prod (people_h) ~=0 && g<=g_max% Elite retention policy, retain the initial population of 1/100 of elite individuals% retain how many elite No_elite = fix (no_        OF_PEOPLE/100);        If No_elite = = 0 No_elite = 1;        End% Select these elites by H value [~,ind] = sort (people_h);        index = IND (1:no_elite);                       People_elite = People (index,:);                % calculates the advantage of each individual in this population, expressed as a percentage, that the sum of all individual advantages is 1 ADV = people_h./sum (PEOPLE_H);        % randomly selected from the population of 10 pairs of individuals, according to individual advantages to choose, the greater the advantage, the greater the probability of being selected People_dad = people;        People_mom = people;        For i=1:no_of_people pick = ones (2,1);    While pick (1) ==pick (2) pick = RANDSRC (2,1,[1:no_of_people; Adv ']);            End People_dad (i,:) = people (pick (1),:);        People_mom (i,:) = people (pick (2),:); End% then cross-breed, chromosome crosses.            A couple gave birth to only one child for i=1:no_of_people% randomly generates an intersection point P = Randi (n-1);        People (i,:) = [People_dad (i,1:p), People_mom (i,p+1:n)];            End% then generates a random mutation for i=1:no_of_people% at a certain probability to randomly generate a mutation site P_change = rand (1);            P_dot = Randi (n);            The probability of setting a mutation is 10% if P_change <= 0.1 people (I,p_dot) = Randi (n);        End end% Update population h value for i = 1:no_of_people People_h (i) = Fun_c (People (I,:));        End% finds the worst individuals in the offspring of reproduction, number of individuals = number of elites [~,ind] = sort (people_h, ' descend ');        Index_bad = IND (1:no_elite);                        % delete the worst individual people (Index_bad,:) = []; % to join the elite in the population peoplE_tmp = [people; people_elite];               people = people_tmp;        % Update population h value for i = 1:no_of_people People_h (i) = Fun_c (People (I,:));        End PLT (G) = min (people_h);                            g = g + 1;    End Plot (PLT (1:g-1));        Axis Auto;        Percent if prod (people_h) ==0 disp (' Genetic algorithm convergence ');        index = FIND (People_h = = 0);        Disp (' Possible solution for ');    Disp (People (index,:));    Else disp (' Genetic algorithm does not converge '); End DISP ([' Experienced ', Num2str (G-1), ' Generation of heredity ']);`

`function [h] = fun_c (state)% evaluates its cost functions h = 0 according to a condition;    n = length (state);        Percent% of the state of each column, see how many can attack each other, count every 22 attacks for i=1:n count = Length (find (state = = i));            if Count > 1;        H = h + nchoosek (count,2);    End end percent% converts state to nxn matrix State_full = zeros (n,n);            For I=1:n for j=1:n if j = = State (i) state_full (i,j) = 1;    End end% percent per left diagonal state, see how many can attack each other, every 22 attacks counted once i=1;    J=1;    add = 0; While i<n+1 && j<n+1 && i>0 && j>0% calculate left diagonal diagonal How many queens per line are there? count = Fun_calc_le            FT (i,j,n,state_full);                if Count > 1;            H = h + nchoosek (count,2);                End If Add = = 0;            j = j + 1;                 ElseIf add = = 1;            i = i + 1;    End add = ~add;    End percent% each right diagonal state, see how many can attack each other, every 22 attacks counted once i=1;    J=n;    add = 0; While I<n+1 &&J<n+1 && i>0 && j>0% calculates the right diagonal diagonal how many queens count = Fun_calc_right (i,j,n,state_full);                if Count > 1;            H = h + nchoosek (count,2);                End If Add = = 0;            j = j-1;                 ElseIf add = = 1;            i = i + 1;    End add = ~add;     End End`

```function count = Fun_calc_left (i,j,n,state_full)   percent% statistic i,j point, lower left corner    count = 0;    i_l = i;    I_r = i;    j_l = j;    J_r = j;    While i_l>0 && j_l>0 && i_l<n+1 && j_l<n+1        count = Count + state_full (i_l,j_l);
i_l = i_l + 1;        j_l = j_l-1;    end%%   % of upper right corner while    i_r>0 && j_r>0 && i_r<n+1 && j_r<n+1        count = Count + state_full (i_r,j_r);        I_r = i_r-1;        J_r = J_r + 1;    End    percent% is repeated plus, minus    count = Count-state_full (i,j); end```

```function count = Fun_calc_right (i,j,n,state_full)   percent% statistic i,j point, upper left corner    count = 0;    i_l = i;    I_r = i;    j_l = j;    J_r = j;    While i_l>0 && j_l>0 && i_l<n+1 && j_l<n+1        count = Count + state_full (i_l,j_l);
i_l = i_l-1;        j_l = j_l-1;    end%%   % lower right corner number while    i_r>0 && j_r>0 && i_r<n+1 && j_r<n+1        count = Count + state_full (i_r,j_r);        I_r = I_r + 1;        J_r = J_r + 1;    End    percent% is repeated plus, minus    count = Count-state_full (i,j); end```

Solving the problem of eight queens with genetic algorithm

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