Matlab Code of Hybrid Genetic Algorithm for Non-linear Constrained Optimization Problems

function Y=population(p,nv,lb,ub)
% nv = number of variables
% p = population size
% 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
Y = Y;

function Y=crossover(P,n)
% P = population
% n = pair of chromosomes to be crossovered
[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),:);
    A2=P(r1(2),:);
    r2=1+randi(y1-1);
.
.
.

function Y=mutation(P,n)
% P = population
% n = pair of chromosomes to be mutated
[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),:);
    A2=P(r1(2),:);
    r2=1+randi(y1-1);
.
.
.

function Y=evaluation(P,ot)
[x1 y1]=size(P);
H=zeros(x1,1);
for i = 1:x1
   H(i,1)= ObjectiveFunction(P(i,:)); 
end
if ot == 1
    Y = H;
else
    Y=10^6-H;
end

function [YY1 YY2] = selection(P1,B,p,s)
% P1 - population
% B - fitness value 
% p - population size
% s = select top s chromsomes
%-------------------------------------------------------------------------
% Top selection operation
B=B';
for i =1:s
    [r1 c1]=find(B==max(B));
    Y1(i,:)=P1(max(c1),:);
    Fn(i)=B(max(c1));
.
.
.

function Y = constraints_and_repair(X,nv,lb,ub)
% Customize here to solve your problem. The rest will be handled automatically
if sum(X.^2)<=40-0.00001 |sum(X.^2)>=40+0.00001 % tolerance of equality constraint
    A1=X(1:nv-1);
    A2=40-sum(A1.^2);
    if A2 < 0
        for j = 1:nv
            X(j)=(ub(j)-lb(j))*rand+lb(j); % generate new one
        end
    else
        X(nv)=sqrt(A2);
    end
end

if X(1)*X(2)*X(3)*X(4)< 25     % inequality constraint
    X(4)=25/(X(1)*X(2)*X(3));
end
Y=X;

function Y=local_search(X,s,lb,ub)
% X = current best solution
% step size
[x y]=size(X);
A=ones(2*y,1)*X;
j=1;
for i=1:y
        L1=X(1,j)+s*rand;
        if L1 > ub(i)
            L1 = ub(i);
.
.
.

function [c ceq]=nonlinear_constraints(X)
% Customize here to solve your problem. The rest will be handled automatically
c = -X(1)*X(2)*X(3)*X(4)+25; % <= 0 constraint
ceq = sum(X.^2)-40;          %  = 0 constraint

function Y = ObjectiveFunction(X)
% Customize here to solve your problem. The rest will be handled automatically
lb = [1 1 1 1];              % lower bound
ub = [5 5 5 5];               % upper bound
O = X(1)*X(4)*[X(1)+X(2)+X(3)]+X(3); % objective function here
%.............................................
%.............................................
P = penalty_function(X,lb,ub);
Y = O+100*P;

function Y = penalty_function(X,lb,ub)
[c ceq]=nonlinear_constraints(X);
if c <= 0
    c = 0;
else
    c = c;
end
V = c + abs(ceq);
% check the bounds
[x1 y1]=size(X);
H=zeros(2,y1);
for i = 1:y1
    if X(i)< lb(i)
        H(1,i)=abs(X(i)-lb(i));
.
.
.

function [x,fval,exitflag,output,lambda,grad,hessian] = fmincon_solver(x0,lb,ub,MaxIterations_Data)
%% This is an auto generated MATLAB file from Optimization Tool.

%% Start with the default options
options = optimoptions('fmincon');
%% Modify options setting
options = optimoptions(options,'Display', 'off');
options = optimoptions(options,'MaxIterations', MaxIterations_Data);
[x,fval,exitflag,output,lambda,grad,hessian] = ...
fmincon(@ObjectiveFunction,x0,[],[],[],[],lb,ub,@nonlinear_constraints,options);

clear all
clc
close all
tic
%--------------------------------------------------------------------------
% Customize here to solve your problem. The rest will be handled automatically
nv =4;                 % number of variables
lb = [1 1 1 1];          % lower bound
ub = [5 5 5 5];            % upper bound
ot = -1;                   % minimization ot = -1; maximization ot = 1
t = 20;                    % computing time (s)
%--------------------------------------------------------------------------
% Maximize performance of the GA (optional)
p=20; % population size
c=10;  % crossover rate
m=5; % mutation rate
s=5;  % adaptive restart search process
g=3;  % keep top chromosomes
r=3; % number of chromosomes in initial guess
ms = 0.001; % max step size for local search
%-------------------------------------------------------------------
% Stoping criteria
tg=10000000; % number of generattion - set be be large to use computing time
%--------------------------------------------------------------------------
P1=population(r, nv, lb, ub); % Initial guess
w=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);
.
.
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Sorry! This is only a half of the code.