problem related to multi objective optimization using matlab tool box

sir,

I have a multi objective optimization problem, which is stated as below:

minimize y1(x)= x1*x2*x3
maximize y2(2)= (x1*x2)/0.36,

subject to LOWER BOUND[1.3 0.4 0.22] AND UPPER BOUND [8 1.0 0.27] Y1(X)<=500;Y2(X)>=0.13

I have typed this function and used optimization tool box.

function f= power1(x)
%it is a multi objective function
%f(1)....objective1...equation for pow minimise
%f(2)....objective2...equation for fc maximize
% 
% x(1)....specific energy
% x(2)....width of cut
% x(3)....forward velocity

f(1)= x1*x2*x3;

f(2)= (x2*x3)/0.36;

end

then used the solver multi objective optimization using genetic algorithim. But I am getting a error as under defined function or variable x1. Kindly suggest some way to optimize the problem with matlab.

Answer 1

[Walter Roberson]

After the line

function f= power1(x)

add

x1 = x(1); x2 = x(2); x3 = x(3);

[Arjya Sahoo]

thank you very much

[Arjya Sahoo]

I have got the result. But the result are coming as lower bound value.However I want to add the constrains: Y1(X)<=500; Y2(X)>=0.13; into the optimization problem. could you please suggest some way to use optimization tool box or any other methods to add this constrains into the optimization problem

[Walter Roberson]

nvars = 3;
A = []; b = [];
Aeq = []; beq = [];
lb = [-inf 0.13 -inf]; ub = [500 inf inf];
bestx = gamultiobj(@power1, nvars, A, b, Aeq, beq, lb, ub)

[Arjya Sahoo]

I have tried this but still not getting the result. I would like to explain it again. I want to maximize one objective and minimize the other objective. two of my objectives are

f(1)= x(1)*x(2)*x(3)......(minimize)

f(2)= (x(2)*x(3))/0.36.....(maximize)

where x(1),x(2),x(3) are the variables

the lower bound of the variables are [1.5 0.4 0.22] and the upper bound are[2.1 0.9 0.27]

and the objectives f(1)<=0.5 and f(2)>= 0.13. kindly suggest some way to solve the problem. Previously what I have done, I got all the lower bound values of variable, next as when I tried this: vars = 3; A = []; b = []; Aeq = []; beq = []; lb = [-inf 0.13 -inf]; ub = [500 inf inf]; bestx = gamultiobj(@power1, nvars, A, b, Aeq, beq, lb, ub)

I got the some higher value result. kindly suggest some ways to do this optimization problem

Answer 2

[Arjya Sahoo]

I have got the result. But the result are coming as lower bound value.However I want to add the constrains: Y1(X)<=500; Y2(X)>=0.13; into the optimization problem. could you please suggest some way to use optimization tool box or any other methods to add this constrains into the optimization problem.

function f= power1(x)
x1=x(1);x2=x(2);x3=x(3);
%it is a multi objective function
%f(1)....objective1...equation for pow minimise
%f(2)....objective2...equation for fc maximize
% 
% x(1)....specific energy
% x(2)....width of cut
% x(3)....forward velocity

f(1)= x1*x2*x3;

f(2)= (x2*x3)/0.36;

end