approaching goal attaining optimization problem

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Chandra Sekhar Kommineni 2022-1-13

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https://ww2.mathworks.cn/matlabcentral/answers/1628590-approaching-goal-attaining-optimization-problem

回答： Aman 2024-1-23

I have a equation, I'm trying to aim for certrain fixed output but I have single equation and two variables to change. i'm trying achieve fixed sigma value. L0, t01 are optimized output values for fixed sigma values. I have no clue, how to approach this problem, I tried few things but they did't work out. Could someone help me with my problem? Thank you in advance.

%Below Rt and N are user defined
%T is fixed as well
% L0 upperbound 200 
%t01 upperbound 28
j = sym('j');
Area= eval((L0*t01*symsum((4^(j+1))*((0.5)^j)*(Rt^j),j,0,N-1))-((t01^2)*symsum(2^(2*j+1)*(Rt^((2*j)-1)),j,1,N-1))-((t01^2)*symsum(2^(2*j+2)*Rt^(2*j),j,0,N-1)));
Sigma= (Area/T^2)*100;
x0=[200 20];
A  = []; Aeq = []; Beq = [];  B=[];
options = optimoptions(@fmincon,'Algorithm','trust-region-reflective','TolFun',1e-14,'TolX',1e-14,'MaxFunEvals',10000,'MaxIter',10000,'Display','iter');
lb=[180 20]
ub=[200 28]
sigma
fun = @(L0,t01)(Sigma-(Area/T^2)*100);
[fval1,fval2]=fmincon(@fun,x0,A,B,Aeq,Beq,lb,ub,@confunc)

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Chandra Sekhar Kommineni 2022-1-14

在 MATLAB Online 中打开

i tried using fmicon, but similar results(output as lower bound values, I'm getting fval negative). I don't know, I'm missing something.

x0=[1 1  0.1];
lb=[ 150 10 0.1];
ub=[210 30 0.5];
[x,fval] = fmincon(@ (x) myfun (x (1), x (2), x (3)),x0,[],[],[],[],lb,ub);

function Sigma= myfun(L0,t01,Rt)
T=320;
N=2;
 j = sym('j');
Area= ((L0*t01*symsum((4^(j+1))*((0.5)^j)*(Rt^j),j,0,N-1))-((t01^2)*symsum(2^(2*j+1)*(Rt^((2*j)-1)),j,1,N-1))-((t01^2)*symsum(2^(2*j+2)*Rt^(2*j),j,0,N-1)));
%Sigma=double((Area/T^2))*100
Sigma= double(Area/T^2 * 100) -33; 
end

Chandra Sekhar Kommineni 2022-1-14

在 MATLAB Online 中打开

I did tweaks to the above code, somewhat I achieved the goal. I added "options" to fgoalattain, its working sometimes, sometimes error is more. Can you please tell whats happening in optimset? is there anything else to improve the code

clc;clear all;
goal=29;
weight=0.0001;
x0=[1.0 1.0 0.1];
lb=[204 18 0.4];
ub=[230 26 0.48];
options = optimset( 'Display' , 'iter' , ...
    'GoalsExactAchieve' ,2);
%options = optimoptions(@lsqnonlin,'Algorithm','trust-region-reflective','TolFun',1e-14,'TolX',1e-14,'MaxFunEvals',10000,'MaxIter',10000,'Display','iter');
 [x, feval]= fgoalattain(@ (x) myfun (x(1), x(2), x(3)), x0, goal, weight, [], [], [], [],lb,ub,[],options);

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回答（1 个）

Aman 2024-1-23

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1628590-approaching-goal-attaining-optimization-problem#answer_1394861

Hi Chandra,

As per my understanding, you are trying to solve the multi-objective goal attainment problem and are facing issues with that.

For "fgoalattain", the recommended optimization option is "optimoptions", so instead of using "optimset", you can use "optimoptions" and try setting tolerance flag options such as "OptimalityTolerance", which sets termination tolerance for first-order optimality. Please refer to the below link to learn more about "optimoptions".