Optimization - non-linear eqn. genetic algorithm

Hello,

I want to solve the system of non-linear equations:

0.8*x(1)+0.2*x(2)<0.2

0.45*x(3)+0.55*x(4)<0.2

0.45*x(3)+0.55*x(4)<0.8*x(1)+0.2*x(2)

x(2)<x(3)

x(4)<x(1)

I tried with genetic algorithm. However, a few times fourth condition (x(2)<x(3)) is getting violated. Can anyone help me please.

Thanks in advance

format short
fun=@(x)-(x(1)+x(2)+x(3)+x(4));
nonlcon=@nonlinearconstr;
lb=[0.01 0.01 0.01 0.01];
ub=[0.99 0.99 0.99 0.99];
Aeq = []; % No other constraints
beq = [];
A = [];
b = [];
x0=lb;
options = optimoptions('ga','ConstraintTolerance',1e-6,'PopulationSize',150,'PlotFcn', @gaplotbestf);
x = ga(fun,4,A,b,Aeq,beq,lb,ub,nonlcon,options);
disp(x);
function [c,ceq] = nonlinearconstr(x)
c(1)=0.8*x(1)+0.2*x(2)-0.2;
c(2)=0.45*x(3)+0.55*x(4)-0.2;
c(3)=-0.45*x(3)-0.55*x(4)+0.8*x(1)+0.2*x(2);
c(4)=x(2)-x(3);
c(5)=x(4)-x(1);
ceq = [];
end

Answer 1

[Torsten]

Your problem is linear - thus use linprog instead of ga:

f = -[ 1 1 1 1];
A = [0.8 0.2 0 0;0 0 0.45 0.55;-0.8 -0.2 -0.45 -0.55;0 1 -1 0;-1 0 0 1];
b = [0.2 0.2 0 0 0].';
lb=[0.01 0.01 0.01 0.01];
ub=[0.99 0.99 0.99 0.99];
sol = linprog(f,A,b,[],[],lb,ub)

Optimal solution found.

sol = 4×1

0.1419 0.4322 0.4322 0.0100

By the way:

Your constraint

c(3)=-0.45*x(3)-0.55*x(4)+0.8*x(1)+0.2*x(2);

is wrong. Must read

c(3)=-0.45*x(3)-0.55*x(4)-0.8*x(1)-0.2*x(2);

[sankalp yerra]

Hello Torsten,

Thanks for your comments. We have the same issue here, x(2)=x(3), However I x(2)<x(3).

[Torsten]

Strict inequality (<, >) cannot be imposed in optimization problems.

The reason is that in general, no solution would exist.

Consider e.g. the problem

min: x

under the constraint

x > 0

and try to find the solution.