Adaptive Restart Hybrid Genetic Algorithm for Constrained Optimization Problems (Case study 2 – Mishra’s Bird function)

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);
    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);
    A2(1,r2:y1)=B1;
    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);
    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);
    A2(r2)=A0;
    Z(2*i-1,:)=A1;
    Z(2*i,:)=A2;
end
Y=Z;

function YY = objective_function(X)
% X = solution
x = X(1);
y = X(2);
YY = sin(y)*exp((1-cos(x))^2) + cos(x)*exp((1-sin(y))^2) + (x-y)^2;