Optimization of multiple variables

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Guan Hao
Guan Hao 2023-8-23
评论： Florian Bidaud 2023-8-23
Hi,
I want to optimize three functions y1,y2,y3,all of them have three variables a1,a2,a3. However, I kept getting errors.Could someone help me?Thx!!!
I try to optimize using fminsearch.
x0=[0 0 0]
result = fminsearch(@optfun,x0);
This is the three functions I want to optimize,and I make them into a vector called optfun(z).
function [y1,y2,y3] = optfun(z)
a1 = z(1);
a2 = z(2);
a3 = z(3);
y1 = abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) + vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("102.0i"))/abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) - vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("102.0i"));
y2 = abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) - vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("147.0i"))/abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) + vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("147.0i"));
y3 = abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) + vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("186.0i"))/abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) - vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("186.0i"));
end
  7 个评论
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Stephen23
Stephen23 2023-8-23
编辑：Stephen23 2023-8-23
"I want to solve y1,y2,y3 as a set of simultaneous equations"
MATLAB already has very efficient tools for solving systems of linear equations:
https://www.mathworks.com/help/matlab/ref/mrdivide.html
https://www.mathworks.com/help/matlab/ref/mldivide.html
It is not clear why you need FMINSEARCH or symbolic variables, I don't think they help you.
Guan Hao
Guan Hao 2023-8-23
The reason I can't change it into equations is that I can't set the equation to a value.
That's ok, cuz I think the weighted output method is a possible way!
Thanks a lot for your help.

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回答（1 个）

Florian Bidaud
Florian Bidaud 2023-8-23
编辑：Florian Bidaud 2023-8-23
I assume you want to have three solutions optimizing respectively y1, y2 and y3 ?
In this case you need to split them into 3 functions:
x0=[0 0 0];
result1 = fminsearch(@optfun1,x0)
result2 = fminsearch(@optfun2,x0)
result3 = fminsearch(@optfun3,x0)
function y1 = optfun1(z)
a1 = z(1);
a2 = z(2);
a3 = z(3);
y1 = abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) + vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("102.0i"))/abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) - vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("102.0i"));
end
function y2 = optfun2(z)
a1 = z(1);
a2 = z(2);
a3 = z(3);
y2 = abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) - vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("147.0i"))/abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) + vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("147.0i"));
end
function y3 = optfun3(z)
a1 = z(1);
a2 = z(2);
a3 = z(3);
y3 = abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) + vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("186.0i"))/abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) - vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("186.0i"));
end
Or maybe you want to minimize the sum of these three functions ?
In this case :
x0=[0 0 0];
result = fminsearch(@optfun,x0)
function y = optfun(z)
a1 = z(1);
a2 = z(2);
a3 = z(3);
y1 = abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) + vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("102.0i"))/abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) - vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("102.0i"));
y2 = abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) - vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("147.0i"))/abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) + vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("147.0i"));
y3 = abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) + vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("186.0i"))/abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) - vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("186.0i"));
y = y1 + y2 + y3;
end
Maybe you want to do something else, in any case, fminsearch will only minimize the first output, therefore you need to come up with one variable to minimize, or to call it three times
  2 个评论
Guan Hao
Guan Hao 2023-8-23
I see...I want to solve y1,y2,y3 as a set of simultaneous equations. a1,a2,a3 should share the same values.
Thus it might be unable to use fminsearch to complete my objective,are there other ways to do that?(Maybe gamultiobj?)
Florian Bidaud
Florian Bidaud 2023-8-23
Well, technically, since y1, y2 and y3 are positive, if you minimize y1 + y2 + y3, and find a solution for which y1 + y2 + y3 = 0 then you will have y1 = 0, y2 = 0 and y3 = 0, and therefore you will have solve you system.
You can then use :
x0=[0 0 0];
result = fminsearch(@optfun,x0)
function y = optfun(z)
a1 = z(1);
a2 = z(2);
a3 = z(3);
y1 = abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) + vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("102.0i"))/abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) - vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("102.0i"));
y2 = abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) - vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("147.0i"))/abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) + vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("147.0i"));
y3 = abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) + vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("186.0i"))/abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) - vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) - vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("25.0") + vpa("186.0i"));
y = y1 + y2 + y3;
end
However, as Stephen23 said, this is not the best way to solve a system.

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