Adaptive Re-Start Hybrid Genetic Algorithm in Matlab

function YY=population(p,nv,lb,ub)
% p = population size
% nv = number of variables
% lb = Lower bound
% ub = Upper bound
for i = 1:p
    for j = 1:nv
        Y(i,j)=(ub(j)-lb(j))*rand+lb(j);
    end
end
YY = Y;

function Y=crossover(P,n)
% P = population
% n = the number of pairs of chromosomes to be ...
% crossed (equivalent to the trational crossover rate)
[x1 y1]=size(P);
Z=zeros(2*n,y1);
for i = 1:n
    r1=randi(x1,1,2); % select 2 random parent chromosomes
    while r1(1)==r1(2)
        r1=randi(x1,1,2); % make sure 2 selected chromosomes are not the same
    end
    A1=P(r1(1),:); % parent 1
    A2=P(r1(2),:); % parent 2
    r2=1+randi(y1-1); % random cutting point
    B1=A1(1,r2:y1); % exchange
    A1(1,r2:y1)=A2(1,r2:y1); % exchange
    A2(1,r2:y1)=B1; % exchange
    Z(2*i-1,:)=A1;
    Z(2*i,:)=A2;
end
Y=Z;

function Y=mutation(P,n)
% P = population
% n = the number of pairs of chromosomes to ...
% be mutated (equivalent to the trational mutation rate)
[x1 y1]=size(P);
Z=zeros(2*n,y1);
for i = 1:n
    r1=randi(x1,1,2);
    while r1(1)==r1(2)
        r1=randi(x1,1,2);% make sure 2 selected chromosomes are not the same
    end
    A1=P(r1(1),:); % parent 1
    A2=P(r1(2),:); % parent 2
    r2=randi(y1); % random gene
    A0 = A1(r2); % exchange the selected gene
    A1(r2)=A2(r2); % exchange the selected gene
    A2(r2)=A0; % exchange the selected gene
    Z(2*i-1,:)=A1;
    Z(2*i,:)=A2;
end
Y=Z;

function Y = objective_function(X)
% X = candidate solution
d = length(X);
sum = 0;
for z = 1:d
    xi = X(z);
    new = xi^4 -16*xi^2 + 5*xi;
    sum = sum + new;
end
Y = sum/2;

function YY=evaluation(P,ot,co)
% P = population
% ot = optimization type, max or min
% co = coefficient for converting min to max problem (to make sure ...
% that the objective function is always positive
[x1 y1]=size(P);
H=zeros(1,x1);
for i = 1:x1
   H(i)= objective_function(P(i,:)); 
end
% depending on type of optimization
if ot == 1 % for maximization problem
    Y = H + co; % add co to make sure all elements in Y are positive
else       % for minimization problem
    K=zeros(1,x1);
    for i = 1:x1
        K(i) = 1/(co + H(i)); % convert from min to max
    end
    Y = K;
end
YY = Y;

function Y=local_search(X,s,lb,ub)
% X = current best chromosome
% s = step size
% lb = Lower bound
% ub = Upper bound

[x y]=size(X);
A=ones(2*y,1)*X;
j=1;
for i=1:y
        L1=X(1,j)+s*rand;
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function [YY1 YY2] = selection(P,B,p,s)
% P - population
% B - fitness value 
% p - population size
% s = Keep top s chromsomes
%------------------------------
% Top selection operation
[x1 y1]=size(P);
Y1 = zeros(p,y1);
Fn = zeros(1,p);
for i =1:s
    [r1 c1]=find(B==max(B));
    Y1(i,:)=P(max(c1),:);
.
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clear all
clc
close all
tic
%--------------------------------------------------------------------------
nv = 2;       % number of variables
lb = [-5 -5]; % lower bound
ub = [5 5];   % upper bound
ot = -1;      % minimization ot = -1; maximization ot = 1
t = 5;        % computing time (s)
%--------------------------------------------------------------------------
% Parameters of GA
p=50;     % population size
c=10;     % the number of pairs of chromosomes to be crossed (equivalent to the trational crossover rate)
m=5;      % the number of pairs of chromosomes to be mutated (equivalent to the trational mutation rate)
rs=20;    % adaptive restart search process (generations)
g=2;      % keep top chromosomes
r=2;      % number of chromosomes in initial guess
ms = 0.2; % max step size for local search
co = 200;  % coefficient for converting min to max problem (to make sure 
% that the objective function is always positive
%-------------------------------------------------------------------
% Stoping criterion
tg=10000000; % number of generattion - set be be large to use computing time
%--------------------------------------------------------------------------
figure
xlabel('Generation')
ylabel('Objective function value')
if ot ==1
    title('Blue dots = Maximum value         Red dots = Average value');
else
    title('Blue dots = Minimum value         Red dots = Average value');
end
hold on

P1=population(r, nv, lb, ub); % Initial guess
w=1;
ww=1;
for j = 1:tg
    P=population(p-r, nv, lb, ub);
    P(p-r+1:p,:)=P1;
    for i=1:tg   
        % Extended population
        P(p+1:p+2*c,:)=crossover(P,c);
        P(p+2*c+1:p+2*c+2*m,:)=mutation(P,m);
        P(p+2*c+2*m+1:p+2*c+2*m+2*nv,:)=local_search(P(1,:),ms,lb,ub);
.
.
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Sorry! This is only a half of the code.