How to code the given below nonlinear constrained optimization problem using genetic algorithm in matlab?

I need to optimize (minimize) the function,

   f = (632.7*((x(1)*1000)^1.327)) + (506.16*((x(2)*1000)^1.327))...
       + (759.24*((x(3)*1000)^1.327)) + (253.08*((x(4)*1000)^1.327));

subjected to the following nonlinear constraints:

ceq(1) = (100*0.971014*(x(1)^2.63)/((abs(100 - x(5)))^0.46))...
   - (x(5)*((0.971014*(x(1)^2.63)/((abs(100 - x(5)))^0.46))...
  + (1.09536*(x(2)^2.63)/((abs(x(5) - x(6)))^0.46))))...
  + (x(6)*1.09536*(x(2)^2.63)/((abs(x(5) - x(6)))^0.46)) - (2/60);

ceq(2) = (x(5)*1.09536*(x(2)^2.63)/((abs(x(5) - x(6)))^0.46))...
     - (x(6)*((0.879969*(x(3)^2.63)/((abs(x(6) - x(7)))^0.46))...
     + (1.09536*(x(2)^2.63)/((abs(x(5) - x(6)))^0.46))))...
   + (x(7)*0.879969*(x(3)^2.63)/((abs(x(6) - x(7)))^0.46)) - (5/60);

ceq(3) = (100*1.592623*(x(4)^2.63)/((abs(100 - x(7)))^0.46))...
    - (x(7)*((0.879969*(x(3)^2.63)/((abs(x(6) - x(7)))^0.46))...
    + (1.592623*(x(4)^2.63)/((abs(100 - x(7)))^0.46))))...
    + (x(6)*0.879969*(x(3)^2.63)/((abs(x(6) - x(7)))^0.46))...
    - (3/60);

c = [];

number of variables = 7

LB = [0.15 0.15 0.15 0.15 90 90 90];
UB = [1 1 1 1 100 100 100];

There are no linear (equality and inequality) constraints. >>When I used the ga in solver, I got incorrect answers. Kindly help me by providing the coding for this problem.

[Torsten]

Use fmincon instead of ga.

Best wishes

Torsten.

[Alan Weiss]

In addition to what Torsten suggested, allow me to suggest that you mark your question with the {} Code button so that we might be able to read it more easily.

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 1

[Matt J]

If you know the solution that ga() gave you is incorrect, then you must know, approximately at least, what the solution must be. You can use gaoptimset to put that approximate point in the initial population and inform ga's search. You would be well-advised incorporate all prior knowledge that you have into the the initial population somehow, since the problem does look pretty horrible...

There are no linear (equality and inequality) constraints

You might want to add some. Denominator expressions like abs(x(6) - x(7) need to be kept away from zero.