Optimization for multi variables and mulit functions

Hi, I've been working on an optimization for multi variables and mulit functions.

gamma1,gamma2,gamma3 are the functions that I want to optimize, and the variables will be a1,a2,a3. I want to use 'gamultiobj' as my optimization tool.

I've tried several ways but I keep getting error, I'm appreciate if someone is wiling to help!

Here's my code:

clear
Z01=50;
Z02=75;
v=3e+8;
section=10;
L=10;
a=L/section;
a0=50;
B1=0.4;
B2=1.6;
w1=2*pi*v*B1/L;
w2=2*pi*v*B2/L;

syms x w a1 a2 a3 

beta=w/v;

% ABCD elements

for m=1:1:section
    
    l=m*a;
    
    Z0=a0+(a1*l)+(a2*(l^2))+(a3*(l^3));
    
    A(m)=1;
    
    B(m)=1i*Z0*sin(beta*a);
    
    C(m)=1i*(1/Z0)*sin(beta*a);
    
    D(m)=1;
    
end

% Turn into a cell array

for n=1:1:section
    
    M{n}=[A(n) B(n) ; C(n) D(n)];
    
end

% Cascade each ABCD matrix

ABCD=M{1};

for m=2:1:section
    
    ABCD=(ABCD)*(M{m});
    
end

ABCDcas=ABCD;

% Convert into S11

S11=((ABCDcas(1,2)-ABCDcas(2,1)*Z01*Z02)+((ABCDcas(1,1)*Z02)-(ABCDcas(2,2)*Z01)))/((ABCDcas(1,2)+ABCDcas(2,1)*Z01*Z02)+((ABCDcas(1,1)*Z02)+(ABCDcas(2,2)*Z01)));

gamma=(abs(S11));

gamma_edge=(1/abs(S11));

% Optimize objective

gamma1=vpa(subs(gamma_edge,w,w1),3);

gamma2=vpa(subs(gamma,w,(w1+w2)/2),3);

gamma3=vpa(subs(gamma_edge,w,w2),3);

function F = optfun(z)

[Torsten]

Please state your problem in a mathematical notation. I don't understand your weird code.

[Pooja Kumari]

Variable "z" is not defined. Can you specify the error. Could you provide the complete code for the optimization function optfun?

function F = optfun(z)

Answer 1

[Yash]

Hi Guan,

I understand that you would like to use the 'gamultiobj' function for multi-variable and multi-function optimization. For this, you need to define an objective function that takes a vector of variables as input and returns a vector of objective function values.

Based on your code, it seems like you have already defined the objective functions 'gamma1', 'gamma2', and 'gamma3'. To use them in the 'gamultiobj' optimization, you can define an anonymous function as your objective function.

Here's an example of how you can modify your code:

gamma1 = @(a) vpa(subs(gamma_edge, [w a1 a2 a3], [w1 a(1) a(2) a(3)]), 3);
gamma2 = @(a) vpa(subs(gamma, [w a1 a2 a3], [(w1+w2)/2 a(1) a(2) a(3)]), 3);
gamma3 = @(a) vpa(subs(gamma_edge, [w a1 a2 a3], [w2 a(1) a(2) a(3)]), 3);

% Define the objective function to be optimized
objective = @(a) [gamma1(a), gamma2(a), gamma3(a)];

% Define the number of variables and their bounds
nvars = 3;

lb = [lower_bound1, lower_bound2, lower_bound3]; % Replace with appropriate lower bounds

ub = [upper_bound1, upper_bound2, upper_bound3]; % Replace with appropriate upper bounds

% Perform multi-objective optimization using gamultiobj

options = optimoptions('gamultiobj','Display','final');
[x,fval] = gamultiobj(objective, nvars, [], [], [], [], lb, ub, options);

In this example, the 'objective' function is defined as an anonymous function that takes a vector of variables 'a' as input and returns a vector of objective function values '[gamma1(a), gamma2(a), gamma3(a)]'. The 'nvars' variable represents the number of variables, and 'lb' and 'ub' represent the lower and upper bounds for each variable.

The 'gamultiobj' function performs the multi-objective optimization using the defined objective function and variable bounds. The resulting optimal variable values are stored in x, and the corresponding objective function values are stored in 'fval'.

Make sure to replace the placeholder values in the code with the appropriate values based on your specific problem and constraints.

I hope this helps you address the issue.