Week 5 - Genetic Algorithm

x = ga(fun,nvars,A,b) finds a local minimum x to fun, subject to the linear inequalities A*x ≤ b. ga evaluates the matrix product A*x as if x is transposed (A*x').

x = ga(fun,nvars,A,b,Aeq,beq,lb,ub) defines a set of lower and upper bounds on the design variables, x, so that a solution is found in the range lb ≤ x ≤ ub. (Set Aeq=[] and beq=[] if no linear equalities exist.)

x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon) subjects the minimization to the constraints defined in nonlcon. The function nonlcon accepts x and returns vectors C and Ceq, representing the nonlinear inequalities and equalities respectively. ga minimizes the fun such that C(x) ≤ 0 and Ceq(x) = 0. (Set lb=[] and ub=[] if no bounds exist.)

x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,options) minimizes with the default optimization parameters replaced by values in options. (Set nonlcon=[] if no nonlinear constraints exist.) Create options using optimoptions.

x = ga(fun,nvars,A,b,[],[],lb,ub,nonlcon,IntCon) or x = ga(fun,nvars,A,b,[],[],lb,ub,nonlcon,IntCon,options) requires that the variables listed in IntCon take integer values.

MATHEMATICAL EQUATION

%A program on Genetic Algorithm unbounded condition
clear all
close all
clc

%defining our search space
x = linspace(0,0.6,150);
y = linspace(0,0.6,150);
num = 150;
%creating 2D mesh
[xx,yy] = meshgrid(x,y);

%Evaluating the stalagmite function
for i=1:length(xx) 
    for j = 1:length(yy)
        input_vector(1) = xx(i,j);
        input_vector(2) = yy(i,j);
        f(i,j) = stalagmite(input_vector);
    end
end

% statistical behaviour of unbound condition input
tic
for i=1:num
    [inputs,fopt(i)] = ga(@stalagmite,2);
    xopt(i) = inputs(1);
    yopt(i) = inputs(2);
end
study1_time = toc
figure(1)
subplot(2,1,1)
hold on
surfc(x,y,-f)
shading interp
title('Statistical behaviour of unbounded input')
plot3(xopt,yopt,-fopt,'marker','o','markersize',4,'markerfacecolor','r')
subplot(2,1,2)
plot(-fopt)
xlabel('number of iterations')
ylabel('maximum points of the function')

% statistical behaviour of bound condition input


for i=1:num
    [inputs,fopt(i)] = ga(@stalagmite,2,[],[],[],[],[0,0],[1,1]);
    xopt(i) = inputs(1);
    yopt(i) = inputs(2);
end
study1_time = toc
figure(2)
subplot(2,1,1)
hold on
surfc(x,y,-f)
shading interp
title('Statistical behaviour of unbounded input')
plot3(xopt,yopt,-fopt,'marker','o','markersize',4,'markerfacecolor','r')
subplot(2,1,2)
plot(-fopt)
xlabel('number of iterations')
ylabel('maximum points of the function') 

%%statical condition poulation minima and maxima


options= optimoptions('ga');
options=optimoptions(options,'PopulationSize',500);
for i=1:num
    [inputs,fopt(i)] = ga(@stalagmite,2,[],[],[],[],[0,0],[1,1],[],[],options);
    xopt(i) = inputs(1);
    yopt(i) = inputs(2);
end
study1_time = toc
figure(3)
subplot(2,1,1)
hold on
surfc(x,y,-f)
shading interp
title('Statistical behaviour of unbounded input')
plot3(xopt,yopt,-fopt,'marker','o','markersize',4,'markerfacecolor','r')
subplot(2,1,2)
plot(-fopt)
xlabel('number of iterations')
ylabel('maximum points of the function')