How to enter a matrix of variables within the linear equality function in genetic algorithm ?

My linear equality function is as shown below:

A*b*A' - c = 0

In my current problem:

A is a 1 by 4 matrix

b is a 4 by 4 matrix

c is just a constant

and A*b*A' would return a number that is equal to c

I want it to work in such a way that the genetic algorithm does not change any values in 'b' because b in my problem(resistance of lines) should remain a constant.

whereas i want the algorithm to make changes in A where A is subject to certain bounds.

I have been able to solve the question by expanding A*b*A', ie do the matrix multiplications on paper with A having variables x(4),x(5),x(6),x(7)

(x(4)*x(4)*(5.697)+x(4)*x(5)*(-1.91)+x(4)*x(6)*(-2.01)+x(4)*x(7)*(-1.77)+x(4)*x(5)*(-1.91)+x(5)*x(5)*(5.3801)+x(5)*x(6)*(-3.47)+x(4)*x(6)*(-2.01)+x(5)*x(6)*(-3.47)+x(6)*x(6)*(8.31)+x(6)*x(7)*(-2.8)+x(4)*x(7)*(-1.77)+x(6)*x(7)*(-2.8)+x(7)*x(7)*(4.6)) - c 

but then the expanded version looks like this

I would like to mention that i do have initial values for x(4),x(5),x(6),x(7)

I want to tweak the variables in A keeping b as a constant while fulfilling the equality function where the variables in A are subject to upper and lower bounds

Help is very much appreciated, Thanks!

Answer 1

[Alan Weiss]

You should not use a genetic algorithm to solve this equation. Instead, use lsqnonlin, which accepts bound constraints.

Alan Weiss

MATLAB mathematical toolbox documentation